Discrete Element Modeling of Graphene Using PFC 2D


 Alexis Ward
 10 months ago
 Views:
Transcription
1 Discrete Element Modeling of Graphene Using PFC 2D Mohammad Jamal Khattak 1 and Ahmed Khattab 2 1 Infrastructure and Transportation Materials Laboratory, Department of Civil Engineering, University of Louisiana at Lafayette, USA. 2 Laboratory of Composite Materials, Department of Industrial Technology, University of Louisiana at Lafayette, USA. Abstract Discrete element modeling (DEM) technique is currently used for largescale simulations of soil and rock mechanics. However, in this study, the DEM has been successfully applied to graphene sheet. Carbon atoms were clustered to form a single discrete element, which was then allowed to interact with other similar discrete elements through contact bonds. The parameters for discrete elements and associated contact bonds were derived from previously established atomiclevel fundamental models for stiffness, covalent bond forces and van der Waals bond forces. Even though the developed DEM model is greatly simplified, the elastic behavior of the graphene sheet was well captured through the use of DEM. The predicted tensile and compressive strength values were comparable with other reported studies. It is believe that such developed model showed the high potential of DEM to be utilized for the simulations of nanomaterials such as carbon nanotubes and fibers. Keywords: discrete element modeling; grapheme; carbon nanotubes; elastic modulus; PFC 2D Introduction The discrete element modeling (DEM) is a numerical technique which has been successfully applied for the analysis of rocks and soil mechanics, and other solid materials with bonded contact models [14]. In this technique, a finitedifference scheme and Newton s second 1
2 law of motion are employed to study the interaction among discrete particles in contact [3]. Newton s second law is used to determine the translational and rotational motion of each particle arising from the contact forces, applied forces and body forces acting upon it, while the force displacement law is used to update the contact forces arising from the relative motion at each contact. The dynamic behavior is represented numerically by a timestepping algorithm in which the velocities and accelerations are assumed to be constant within each time step [3, 4]. Amongst various discrete elements codes [511] the particle flow code (PFC) 2D/3D has higher computation efficiency and the ability to model fracture behavior and element interaction, as well as the interface conditions (adhesion) between the various phases of composite materials [3]. PFC2D has also been used to developed discrete element models to predict the stiffness, strength and stressstrain response of the asphalt concrete, Portland cement concrete and fiberreinforced polymer composite materials [1215]. Even though DEM is commonly used for largescale simulations of soil and rock mechanics, in this study, it is shown that the DEM can be successfully applied to graphene sheet. In this study, carbon atoms are clustered to form a single discrete element, which is then allowed to 45 interact with other similar discrete elements through contact bonds using PFC 2D code. The parameters for discrete elements and associated contact bonds were derived from previously established atomiclevel fundamental models for stiffness, covalent bond forces and van der Waals bond forces. Although the presented DEM model is greatly simplified, not including the acoustic vibrations and other atomic scale effects, the elastic behavior of the graphene sheet is well captured through the use of DEM. It is believed that the developed DEM model can be enhanced and utilized for the simulations of carbon nanotubes (CNT) and carbon nanofibers (CNF) using PFC3D code. 2
3 Discrete Element Model for Graphene Sheet In PFC 2D DEM, each individual element is a rigid body characterized by a mass (m) uniformly distributed in a diskshaped element of radius (R) and moment of inertia (I). Although the elements are rigid, they can interpenetrate, indicating interaction between the elements. The contact surface of two elements defines the contact plane, which is perpendicular to the axis connecting the two centers of the elements. The mechanical behavior of each rigid element is described by the laws of classical mechanics, including the total force (F) and moments (M) acting on the element that arise due to the interactions with the elements in contact, as well as artificially introduced dissipative forces [3, 16]. 2.1 Contact Stiffness Model Simple contact constitutive models with complex geometrical features are combined in the DEM approach to simulate the complex behavior of a material. Three of the simple contact models, which are Shear and normal stiffness, static and sliding friction, and interparticle cohesion/adhesion, can be utilized. The elastic relationship between the contact force and relative displacement between particles can be provided by the stiffness model [3, 12, 13]. Two particles A and B in contact, are shown in Figure 1, where k A n and k B n are the normal stiffnesses and k A s and k B s are the shear stiffnesses. The contact stiffness, for a linear contact model, is determined based on the assumption that the stiffness of the two contacting entities acts in series. In a contactstiffness model, the composite stiffness and forcedisplacement law of the two particles in contact can be expressed as follows [3]: 74 3
4 75 K n A kn A n B n B kn k = (1) k + 76 K s A ks A s B s B ks k = (2) k + 77 F = nk U (3) n n n 78 Δ F = K ΔU (4) s s s Figure 1. Schematics of Contact Model [3, 12, 13] The relationship between the total normal force (Fn) to the normal displacement (Un) is shown in Equation 3. Equation 4 relates the incremental shear force (DFs) to the incremental shear displacement (Ds). The normal and shear cohesive strength between two contacting balls can be simulated using simple contact bond models, which are applied at the contact point (Figures 1). When the tensile and/or shear stress at a contact exceeds the tensile and shear strengths of the 4
5 bond, the bond breaks and separation and/or frictional sliding can occur. The friction force Fr is given by Fr=mFn, where m is coefficient of friction between the contacting bodies. The elastic constants (k A,B n, k A,B s ) can be related to Young s modulus (E) and Poison s ratio (n) of each constituent of a material. In the normal direction and for columnrow array, the following equations can be used [3]. 93 k A B n n 2 = k = Et (5) 94 k s A = k s B = 2Gt (6) 95 E= 2 G(1 + v) (7) 96 Where t is the thickness of a discrete element (disk) and G is the shear modulus of a material Contact Model for Covalent Bonding The individual CNF structure consists of strong covalent carboncarbon (cc) bonds. These bonds are formed by sharing of the valence electrons according to the laws of quantum mechanics. However, it is proposed to retain from fundamental atomic scale and lowfrequency acoustic vibrations [16]. It has been reported by various studies [1721] that the nanomechanics of carbon nanotubes (CNT) can be well represented by linear elastic behavior. Under large stresses these nanomaterials fail through plasticity or brittle fracture [18]. Since the elastic and continuum behavior of materials can be well captured by DEM, it is believed that the existing marcoscale scheme of DEM is well suited to study the nanomechanical behavior of graphene, CNT, and CNF using the current discrete element (DE) contact models [16]
6 Constitutive behavior of interaction between two discrete elements (DE) can be modeled using the parallelbond. These bonds can be envisioned as a finitesized disk of elastic massless material with a thickness of xr at the contact and centered on the axis connecting the centers of two DE as shown in Figure 2. In PFC 2D, the parallel bond is also characterized by a radius multiplier (x), a maximum value of 1 indicates that the parallel bond (cementatious effect) extends to the mean diameter of the two contact elements. A set of ideal springs are associated with this DE with normal (k pn ) and shear (k ps ) stiffness uniformly distributed over its cross sectional area. Such bonds establish an elastic interaction between elements that acts in parallel with the slip or contactbond models described earlier [3]. 118 Figure 2. Parallel bond illustration 119 The parallel bonds k pn and k ps can be found using the following equations [3]: 120 k pn E a k n = = and T 2T k ps Ga ks = = (8) T 2T Where, T is the bond width, E a and G a are atomistically determined Young s and shear modulus, and k n and k s are atomistically computed normal and shear force elastic constants, respectively
7 The total force and moment act on the two bonded particles can be related to maximum normal (s m ) and shear (t m ) stresses acting within the bonded material at the bond periphery. The maximum tensile and shear stresses acting on the parallel bond periphery are calculated using the beam theory as follows: 128 σ m = F n A + M s I R m < σ c σ!"# = !! +!!!! R! < σ! (9) 129 F = τ!"# =!! < τ!! (10) A s τ m < τ c Where, R m is the mean radius of contacting particles, A and I are the area and moment of inertia of the parallel bond cross section, respectively. M s denote the sheardirected moment, and s c and t c are normal and shear contact forces, respectively. If either of these maximum stresses exceeds its corresponding bond strength (s c and t c ), the parallel bond breaks and it is removed from the model along with the corresponding force, moment and stifnesses. The constitutive behavior relating the bond force and displacement for two particles in contact is shown in Figure 3. At any given time, either the bond model or the slip model is active. When the corresponding component of the force exceeds either of these values, the bond breaks. Additionally, moment may also be acting, as well as the force shown in Figure 3. In PFC 2D code, the normal (f n ) and shear (f s ) bond forces for a unit DE thickness (t) are calculated as : φ n = σ c (2R)t (11) 142 φ s = τ c (2R)t (12) The normal and shear force elastic constants and bond forces for covalent bond interactions can be determined from Morse potential and AMBER force field models [24, 25, 26, 27]. 7
8 145 Tension F n F s Bond breaks Contact bond φ n φ n F r Bond breaks Contact bond Slip model Slip model U n K n 1 a) Normal component of contact force. b) Shear component of contact force. Figure 3. Constitutive behavior for contact bonds 1 K s U s Figure 4 shows DE for a single sheet graphene molecule and its interaction with other similar molecule constructed for conducting DEM simulation for the study. Here six carbon atoms (Figure 4b) are lumped in one DE for a graphene sheet. Higher number of atoms can also be lumped to make a DE, which can save computational time. It should be noted that DE radius (R) is selected as such that the van der Waals forces can also be captured while interacting with other elements. It can be seen from Figure 4 that R of DE is 1.5 times the covalent bond radius (r c ) and the parallel bond width for covalent bonding (T c ) becomes 3r c
9 R r c (b) (a) T c R R: Descrete element radius r c : Covalent bond radius d c : Covalent bond distance T c : Parallel bond width d c Figure 4. a) Single sheet graphene, b) Graphene molecule comprised of six atoms clustered to form DE, c) DE interaction using parallelbonds formed due to Covalent bonding. 2.3 Contact Model for van der Waals Bonds The interaction of DE due to van der Waals forces can also be simulated using the parallel bonds by utilizing the contact force associated with van der Waals interaction, as shown in Figure T v = d v R (a) d v (b) R Figure 5. a) Graphene atoms clustered in DE showing van der Waals bond distance (d v ), b) Two DE showing parallel bond width representing van der Waals bonding (T v ). 9
10 The figure shows two DE from two adjacent graphene sheets interacting with each other through van der waals force, having a distance of d v. Unlike parallel bond representing covalent bonding, the parallel bond for van der Waals bonding will have the width (T v ) equal to the van der Waals bond distance (d v ). Such interaction can be determined by simple analytical form of LennardJones (LJ) 612 potential, which can facilitate determination of normal and shear force elastic constants and bond forces needed for DEM simulations [22]: Since minimum of two graphene sheets are required to model the van der Waals interaction, it becomes impossible to incorporate both the covalent and van der Waals interactions in 2D DEM modeling of graphene sheets. Hence, in this study, the 2D DEM simulation for covalent bond is presented for a signgle graphene sheet. It should be noted that the above approach could be utilized to conduct DEM simulations in 3D code. For PFC 3D DEM code, the DE (discrete element) becomes like a sphere interacting with other DE spheres within a single graphene sheet through covalent bond, as well as with the adjacent graphene sheet through van der Waals bond Model Parameters and Simulation The model parameters for parallel bonds are k pn, k ps (normal and shear stiffnesses), and s c, t c (normal and sheer strengths). In this study, the DEM model parameters are based on the Morse force model for covalent bond [24, 25, 26]. The k n and k s used are 32.6 nn/ o A and 6.5 nn/ o A [24]. Based on DE schematic shown in Figure 4 and covalent bond length of 1.42 o A [28], the DE radius (R) and T c of parallel bond were calculated as 2.13 o A and 4.26 o A, respectively. Graphene sheet consists of carbon atoms bonded with both single and double cc covalent bonds having bond energies of 473kJ/mole and 618kJ/mole, respectively [28, 29, 30]. The PFC 2D code does not allow associating different parallel bond values for a DE, therefore average bond 10
11 value of 545kJ/mole was used in this study. Using the average bond energy the force required to disassociate a single carbon atom of bond length 1.42 o A was calculated as 45 N. Hence, the parallel bond normal strength for a unit DE thickness (1m) was determined as 105 GPa using equation (8). The parallel bond shear strength was taken as half of the normal strength. Since six parallel bonds originated from each DE (Figure 4), it was logical to use hexagonal packing of DE to develop synthetic specimen for tensile or compression test simulation in PFC 2D code (Figure 6a). The current DEM virtual test was limited to 2D analysis techniques and involved the simulation of uniaxial rectangular specimens. The simulated specimens contained up to 6,000 diskshaped DE. In a 2D plane, the model is composed of about of 36,000 atoms as shown in Figure 6b. Higher number of atoms clumped in a DE element can also be generated to increase the speed of simulation. Tensile loading was applied to the top and bottom loading plate of the synthetic specimen in PFC 2D. After a certain continuous incremental tensile loading, the response of each DE was monitored (Figure 6b). The results of simulation generated stress and strain data which was plotted as shown in Figure 5c. The stress strain curve shown in Figure 6c exhibits an elastic response and brittle mode of failure for a graphene sheet due to tensile loading. The initial slope of the stress strain curve was used to determine the Young s modulus (E) of the graphene sheet. The stress at failure was obtained as the strength (S) of the graphene sheet. The 215 Poisson s ratio (n) was calculated as the ratio of horizontal to vertical strain and G was determined using the equation 7. It was found that a reasonable values of E, G and S of 1.5 TPa, TPa and 95 GPa, respectively were obtained using the develop DEM model (Figure 6c). These values were in agreement with elastic properties reported in literature for Graphene, see Table 1 [2324, 3033]
12 Table 1 Comparison of elastic properties from other studies Model Type E(Tpa) ν G(Tpa) S(Gpa) Brasedtruss (Theoretical) [24] Brasedtruss Finite Element (FE) [24] Stretchinghinging [24] Stretchinghinging (Shear Beam) [24] All Deformation mechanism [24] Potential Energy Minimization FE [24] FE [31] Atomistic simulation [33] Experimental Nanoindentationatomic force microscope [32] DDEM [This study] It was also observed that by creating a random flaw in terms of weak parallel bond or no bond in few DE generated reasonable picture of moments, tensile and shear stresses developed at the vicinity of flaw as shown in Figure 5a. Similarly the test simulation for compressive loading predicted a Young s modulus and compressive strength of 1.45 TPa and 98 GPa, respectively. Figure 7 shows a clear failure in shear due to excessive compressive loading. The aforementioned DEM approach provided a reasonable physical portrayal of the force chains developed in the graphene sheet, which is known to be a critical aspect of mechanical modeling. Such simulations can predict the stressstrain response, modulus/stiffness and potential crack initiation zones. The test simulation for van der Waals bonds could not be performed in PFC 2D as it involves the overlap of at least two graphene sheets, which make the model threedimensional (3D). Hence, it is recommended to utilize the approach outlined in this study to 12
13 develop a 3D model of graphene sheets for van der Waals bonds. Such a model will further the understanding to develop 3D DEM models of CNT and CNF using PFC 3D codes (6a) (6b) 13
14 Tensile Stress, Gpa Strain, mm/mm (6c) Figure 6. a) DEM tensile test simulation of graphene sheet, (b) effect of random flaw in terms of weak bond showing high tensile and shear stresses in the flawed region Figure 7. DEM compressive test simulation of graphene sheet 14
15 Conclusions and Recommendations Discrete element model was presented for armed chair graphene sheet. The DEM parameters were characterized based on atomicscale fundamental stiffness and bond models such as covalent and van der Waals bonds. A synthetic homogenous model of graphene in PFC 2D was constructed based on elastic constitution models. Uniaxial virtual tensile and compressive test simulations were conducted. Based on the simulation results the following conclusions and recommendation were drawn. 1. The elastic constitutive behavior of graphene sheet was well captured by the developed model using PFC 2D. The contact force chains between particles exhibited a reasonable distribution of moments, shear and normal contact forces. 2. The elastic modulus and tensile strength of graphene obtained from the simulation were comparable to other reported studies. 3. It is recommended to utilize the approach outlined in this study to develop a 3D model of graphene sheets for van der Waals bonds. It is believed such a model will further the understanding of developing 3D DEM models for CNT and CNF using PFC 3D code Acknowledgments The authors wish to express their sincere thanks to the University of Louisiana at Lafayette for using their facility and financial support
16 References [1] Cundall P. A, (1971) A Computer Model for Simulating Progressive Large Scale Movements in Blocky Rock Systems. Symposium of the International Society for Rock Mechanics, Nancy, Vol. 1, Nancy, France, Paper No. II8. [2] Cundall P.A. and Strack O.D.L. (1979) A discrete Numerical Model for Granular Assemblies, Geotechnique, Vol. 29, No. 1, pp [3] Itasca Consulting Group (2004a) A manual of PFC 2D Ver. 3.1, Minneapolis. [4] Potyondya, D.O. and Cundall, P.A. (2004) A BondedParticle Model for Rocks. International Journal of Rock Mechanics & Mining Sciences, Vol 41, pp [5] Y.C. Chen and H.Y. Hung (1991) Soils Foundation, Vol. 31, No. 4. [6] D.W. Washington and J.N. Meegoda (2003) MicroMechanical Simulation of Geotechnical Problems Using Massively Parallel Computers. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 27, No. 14, pp [7] Dickens J.G. and Walkerr P.J. (1996) Use of distinct element model to simulate behavior of drystone walls. Structural engineering review, Vol. 8, pp [8] Idris J, Verdel T, and AlHeib M (2008) Numerical modelling and mechanical behaviour analysis of ancient tunnel masonry structures. J. Tunnelling and Underground Space Technology, Vol. 23, No. 3, pp [9] Vardakos S.S, Gutierrez M.S, and Barton, N.R, (2007) Backanalysis of Shimizu Tunnel No. 3 by distinct element modeling. Tunnelling and Underground Space Technology, Vol. 22, No. 4, pp [10] Zhao X.B, Zhao J., Cai J. G., and Hefny AM (2008) UDEC Modeling On Wave Propagation Across Fractured Rock Masses. Computers and Geotechnics, Vol. 35, No. 1, pp
17 [11] Abbas A., Masad E., Papagiannakis T., and Harman T, (2007) Micromechanical Modeling of the Vis coelastic Behavior of Asphalt Mixtures Using the DiscreteElement Method. International Journal of Geomechanics, Vol. 7, No. 2, pp [12] Buttlar W.G., and You Z (2001) Discrete Element Modeling of Asphalt Concrete: A Micro Fabric Approach. Journal of the Transportation Board, no. 1757, National Research Council, pp [13] Khattak M. J., and Roussel C. (2009) Micromechanical Modeling of HotMix Asphalt Mixtures by Imaging and Discrete Element Methods. Journal of the Transportation Research Board, Transportation Research Board of the National Academies, Vol [14] Khattab A, Khattak M. J, and Fadhil I. (2011) MicroMechanical Discrete Element Modeling of Fiber Reinforced Polymer Composites. Journal of Polymer Composites. Vol. 32, No. 10, pp [15] Khattak M. J. (2012) MicroMechanical Modeling of Portland Cement Concrete Mixture. Proceedings of ICCOEE2012, Kuala Lumpur, Malaysia, June [16] Tyler Anderson, et al. (2010) Toward Distinct Element Method Simulations of Carbon Nanotube Systems. Polymer Composite, Vol. 1/ , Nov., 2010 [17] Trends in Computational Nanomechanics: Transcending Length and Time Scales, T. Dumitric, ed., Springer, New York, [18] Dumitric, T., Hua, M., and Yakobson, B., (2006) Symmetry, Time, and Temperature Dependent Strength of Carbon Nanotubes. Proc. Natl. Acad. Sci. U.S.A., 103_16_, pp [19] Yakobson, B., Brabec, C., and Bernholc, J., (1996) Nanomechanics of Carbon Tubes: Instabilities Beyond Linear Response. Phys. Rev. Lett., 76_14, pp
18 [20] Zhang, D.B., James, R., and Dumitric, T., (2009) Electromechanical Characterization of Carbon Nanotubes in Torsion via Symmetry Adapted Tight Binding Objective Molecular Dynamics, Phys. Rev.B, 80_11_, p [21] Nikiforov, I., Zhang, D.B., James, R., and Dumitric, T., (2010) avelike Rippling in Multiwalled Carbon Nanotubes Under Pure Bending. Appl. Phys.Lett., 96, p [22] Potyondy, D. (2010) Molecular Dynamics with PFC, PFC Example on Itasca website, Itasca Consulting Group, Inc., Minneapolis, MN, Technical Memorandum ICG6522L, January 6. [23] Zhao, H. Min, K., and Aluru, N. R., (2009) Size and Chirality Dependent Elastic Properties of Graphene Nanoribbons under Uniaxial Tension. ACS, Nano Lett., Vol. 9, No. 8, p [24] F Scarpa, S Adhikari and A Srikantha Phani (2009). Effective elastic mechanical properties of single layer graphene sheets. Nanotechnology vol. 20, (11pp) doi: / /20/6/ [25] T. Belytschko, S. P. Xiao, G. C. Schatz, and R. S. Ruoff (2002) Atomistic simulations of nanotube fracture, Phys. Rev. B 65, [26] Wendy D. Cornell, Piotr Cieplak, Christopher I. Bayly,s Ian R. Gould, Kenneth M. Merz, Jr., David M. Ferguson,& David C. Spellmeyer: Thomas Fox, James W. Caldwell, and Peter A. Kollman. (1995). A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules. J. Am. Chem. SOC. Vol. 117, [27] Jorgensen, W. L. and Severance, D. L. (1990). Aromaticaromatic interactions: free energy profiles for the benzene dimer in water, chloroform, and liquid benzene. J. Chem. Am. Soc. Vol. 112,
19 [28] Erickson, K., Erni, R., Lee, Z., Alem, N., Gannett, W., and Zettl, A (2010). Determination of the Local Chemical Structure of Graphene Oxide and Reduced Graphene Oxide. Adv. Mater. 2010, 22, [29] Brenner,D.W., Shenderova, O. A., Harrison,J. A., Stuart,S. J., Ni, B., and Sinnott, S.D. (2002). A secondgeneration reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter 14 (2002) [30] Stephen J. Blanksby, Andg. Barney Barney Ellison (2003). Bond Dissociation Energies of Organic Molecules. Acc. Chem. Res. 2003, 36, [31] Michele Meo, Marco Rossi (2006) Prediction of Young s modulus of single wall carbon nanotubes by molecularmechanics based finite element modeling. Composites Science and Technology 66 (2006) [32] Lee, C.; Wei, X.; Kysar, J. W.; and Hone, J. (2008) Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene. Science, 321, [33] Rassin Grantab1, Vivek B. Shenoy1, Rodney S. Ruoff, (2010). Anomalous Strength Characteristics of Tilt Grain Boundaries in Graphene. Science, Vol. 330 no pp
CHARACTERIZING MECHANICAL PROPERTIES OF GRAPHITE USING MOLECULAR DYNAMICS SIMULATION
CHARACTERIZING MECHANICAL PROPERTIES OF GRAPHITE USING MOLECULAR DYNAMICS SIMULATION JiaLin Tsai and JieFeng Tu Department of Mechanical Engineering, National Chiao Tung University 1001 University Road,
More informationNonlocal material properties of single walled carbon nanotubes
Nonlocal material properties of single walled carbon nanotubes J. V. Araújo dos Santos * and C. M. Mota Soares IDMEC, Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal Av. Rovisco Pais,
More informationNonlinear Mechanics of Monolayer Graphene Rui Huang
Nonlinear Mechanics of Monolayer Graphene Rui Huang Center for Mechanics of Solids, Structures and Materials Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin
More informationCHEMC2410: Materials Science from Microstructures to Properties Composites: basic principles
CHEMC2410: Materials Science from Microstructures to Properties Composites: basic principles Mark Hughes 14 th March 2017 Today s learning outcomes To understand the role of reinforcement, matrix and
More informationIntroduction to Engineering Materials ENGR2000. Dr. Coates
Introduction to Engineering Materials ENGR2 Chapter 6: Mechanical Properties of Metals Dr. Coates 6.2 Concepts of Stress and Strain tension compression shear torsion Tension Tests The specimen is deformed
More informationChapter 7. Highlights:
Chapter 7 Highlights: 1. Understand the basic concepts of engineering stress and strain, yield strength, tensile strength, Young's(elastic) modulus, ductility, toughness, resilience, true stress and true
More informationMaterials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon.
Modes of Loading (1) tension (a) (2) compression (b) (3) bending (c) (4) torsion (d) and combinations of them (e) Figure 4.2 1 Standard Solution to Elastic Problems Three common modes of loading: (a) tie
More informationDynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models
Dynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models I. Rhee, K.J. Willam, B.P. Shing, University of Colorado at Boulder ABSTRACT: This paper examines the global
More informationMechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering
Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected
More informationMechanics of Irregular Honeycomb Structures
Mechanics of Irregular Honeycomb Structures S. Adhikari 1, T. Mukhopadhyay 1 Chair of Aerospace Engineering, College of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, UK Sixth International
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain  Axial Loading
MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain  Axial Loading MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain  Axial Loading Statics
More information3.032 Problem Set 2 Solutions Fall 2007 Due: Start of Lecture,
3.032 Problem Set 2 Solutions Fall 2007 Due: Start of Lecture, 09.21.07 1. In the beam considered in PS1, steel beams carried the distributed weight of the rooms above. To reduce stress on the beam, it
More informationMECHANICS OF MATERIALS. Prepared by Engr. John Paul Timola
MECHANICS OF MATERIALS Prepared by Engr. John Paul Timola Mechanics of materials branch of mechanics that studies the internal effects of stress and strain in a solid body. stress is associated with the
More informationFCP Short Course. Ductile and Brittle Fracture. Stephen D. Downing. Mechanical Science and Engineering
FCP Short Course Ductile and Brittle Fracture Stephen D. Downing Mechanical Science and Engineering 001015 University of Illinois Board of Trustees, All Rights Reserved Agenda Limit theorems Plane Stress
More informationNumerical study of AE and DRA methods in sandstone and granite in orthogonal loading directions
Water Science and Engineering, 2012, 5(1): 93104 doi:10.3882/j.issn.16742370.2012.01.009 http://www.waterjournal.cn email: wse2008@vip.163.com Numerical study of AE and DRA methods in sandstone and
More informationMining. Slope stability analysis at highway BR153 using numerical models. Mineração. Abstract. 1. Introduction
Mining Mineração http://dx.doi.org/10.1590/037044672015690040 Ricardo Hundelshaussen Rubio Engenheiro Industrial / Doutorando Universidade Federal do Rio Grande do Sul  UFRS Departamento de Engenharia
More informationIntensity (a.u.) Intensity (a.u.) Raman Shift (cm 1 ) Oxygen plasma. 6 cm. 9 cm. 1mm. Singlelayer graphene sheet. 10mm. 14 cm
Intensity (a.u.) Intensity (a.u.) a Oxygen plasma b 6 cm 1mm 10mm Singlelayer graphene sheet 14 cm 9 cm Flipped Si/SiO 2 Patterned chip Plasmacleaned glass slides c d After 1 sec normal Oxygen plasma
More information6. NONLINEAR PSEUDOSTATIC ANALYSIS OF ADOBE WALLS
6. NONLINEAR PSEUDOSTATIC ANALYSIS OF ADOBE WALLS Blondet et al. [25] carried out a cyclic test on an adobe wall to reproduce its seismic response and damage pattern under inplane loads. The displacement
More informationFIXED BEAMS IN BENDING
FIXED BEAMS IN BENDING INTRODUCTION Fixed or builtin beams are commonly used in building construction because they possess high rigidity in comparison to simply supported beams. When a simply supported
More informationMechanical properties 1 Elastic behaviour of materials
MME131: Lecture 13 Mechanical properties 1 Elastic behaviour of materials A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Deformation of material under the action of a mechanical
More informationTerraMechanical Simulation Using Distinct Element Method
Shinya Kanou Masaharu Amano Yuji Terasaka Norihisa Matsumoto Tatsuo Wada To our company that designs and manufactures equipment for handling soil and rock, analyzing the interaction or contact between
More informationMATERIALS. Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle?
MATERIALS Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: A. Composition
More informationLaboratory 4 Bending Test of Materials
Department of Materials and Metallurgical Engineering Bangladesh University of Engineering Technology, Dhaka MME 222 Materials Testing Sessional.50 Credits Laboratory 4 Bending Test of Materials. Objective
More informationThe Local Web Buckling Strength of Coped Steel IBeam. ABSTRACT : When a beam flange is coped to allow clearance at the
The Local Web Buckling Strength of Coped Steel IBeam Michael C. H. Yam 1 Member, ASCE Angus C. C. Lam Associate Member, ASCE, V. P. IU and J. J. R. Cheng 3 Members, ASCE ABSTRACT : When a beam flange
More informationMECHANICS OF MATERIALS
Third E CHAPTER 2 Stress MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University and Strain Axial Loading Contents Stress & Strain:
More information**********************************************************************
Department of Civil and Environmental Engineering School of Mining and Petroleum Engineering 333 Markin/CNRL Natural Resources Engineering Facility www.engineering.ualberta.ca/civil Tel: 780.492.4235
More information3D Finite Element analysis of stud anchors with large head and embedment depth
3D Finite Element analysis of stud anchors with large head and embedment depth G. Periškić, J. Ožbolt & R. Eligehausen Institute for Construction Materials, University of Stuttgart, Stuttgart, Germany
More informationSTRESS DROP AS A RESULT OF SPLITTING, BRITTLE AND TRANSITIONAL FAULTING OF ROCK SAMPLES IN UNIAXIAL AND TRIAXIAL COMPRESSION TESTS
Studia Geotechnica et Mechanica, Vol. 37, No. 1, 2015 DOI: 10.1515/sgem20150003 STRESS DROP AS A RESULT OF SPLITTING, BRITTLE AND TRANSITIONAL FAULTING OF ROCK SAMPLES IN UNIAXIAL AND TRIAXIAL COMPRESSION
More informationNumerical Modeling of Direct Shear Tests on Sandy Clay
Numerical Modeling of Direct Shear Tests on Sandy Clay R. Ziaie Moayed, S. Tamassoki, and E. Izadi Abstract Investigation of sandy clay behavior is important since urban development demands mean that sandy
More informationReview of Strain Energy Methods and Introduction to Stiffness Matrix Methods of Structural Analysis
uke University epartment of Civil and Environmental Engineering CEE 42L. Matrix Structural Analysis Henri P. Gavin Fall, 22 Review of Strain Energy Methods and Introduction to Stiffness Matrix Methods
More informationLecture #10: Anisotropic plasticity Crashworthiness Basics of shell elements
Lecture #10: 1510735: Dynamic behavior of materials and structures Anisotropic plasticity Crashworthiness Basics of shell elements by Dirk Mohr ETH Zurich, Department of Mechanical and Process Engineering,
More informationMicromeso draping modelling of noncrimp fabrics
Micromeso draping modelling of noncrimp fabrics Oleksandr Vorobiov 1, Dr. Th. Bischoff 1, Dr. A. Tulke 1 1 FTA Forschungsgesellschaft für Textiltechnik mbh 1 Introduction Noncrimp fabrics (NCFs) are
More informationDefense Technical Information Center Compilation Part Notice
UNCLASSIFIED Defense Technical Information Center Compilation Part Notice ADP012151 TITLE: Chemical Bonding of Polymer on Carbon Nanotube DISTRIBUTION: Approved for public release, distribution unlimited
More informationAN IMPORTANT PITFALL OF PSEUDOSTATIC FINITE ELEMENT ANALYSIS
AN IMPORTANT PITFALL OF PSEUDOSTATIC FINITE ELEMENT ANALYSIS S. Kontoe, L. Pelecanos & D.M. Potts ABSTRACT: Finite Element (FE) pseudostatic analysis can provide a good compromise between simplified
More informationPeriod #1 : CIVIL MATERIALS COURSE OVERVIEW
Period #1 : CIVIL MATERIALS COURSE OVERVIEW A. Materials Systems to be Addressed Metals and Alloys (steel and aluminum) Portland Cement Concrete Asphalt Cement Concrete Fiber Reinforced Composites Masonry
More informationU.S. South America Workshop. Mechanics and Advanced Materials Research and Education. Rio de Janeiro, Brazil. August 2 6, Steven L.
Computational Modeling of Composite and Functionally Graded Materials U.S. South America Workshop Mechanics and Advanced Materials Research and Education Rio de Janeiro, Brazil August 2 6, 2002 Steven
More informationFinite element modelling of infinitely wide Angleply FRP. laminates
www.ijaser.com 2012 by the authors Licensee IJASER Under Creative Commons License 3.0 editorial@ijaser.com Research article ISSN 2277 9442 Finite element modelling of infinitely wide Angleply FRP laminates
More informationInternational Journal of Advanced Engineering Technology EISSN
Research Article INTEGRATED FORCE METHOD FOR FIBER REINFORCED COMPOSITE PLATE BENDING PROBLEMS Doiphode G. S., Patodi S. C.* Address for Correspondence Assistant Professor, Applied Mechanics Department,
More informationUNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation.
UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The magnitude
More informationAnthony R. Ingraffea Symposium September 27, State Based Peridynamic Lattice Modeling of Reinforced Concrete Structures ! 1
Anthony R. Ingraffea Symposium September 27, 2014 State Based Peridynamic Lattice Modeling of Reinforced Concrete Structures Walter Gerstle Department of Civil Engineering University of New Mexico, U.S.A.
More informationELASTIC CALCULATIONS OF LIMITING MUD PRESSURES TO CONTROL HYDRO FRACTURING DURING HDD
North American Society for Trenchless Technology (NASTT) NODIG 24 New Orleans, Louisiana March 2224, 24 ELASTIC CALCULATIONS OF LIMITING MUD PRESSURES TO CONTROL HYDRO FRACTURING DURING HDD Matthew
More informationA discrete element analysis of elastic properties of granular materials
Granular Matter (213) 15:139 147 DOI 1.17/s13513393 ORIGINAL PAPER A discrete element analysis of elastic properties of granular materials X. Q. Gu J. Yang Received: 13 October 212 / Accepted: 1 January
More informationDETERMINING THE STRESS PATTERN IN THE HH RAILROAD TIES DUE TO DYNAMIC LOADS 1
PERIODICA POLYTECHNICA SER. CIV. ENG. VOL. 46, NO. 1, PP. 125 148 (2002) DETERMINING THE STRESS PATTERN IN THE HH RAILROAD TIES DUE TO DYNAMIC LOADS 1 Nándor LIEGNER Department of Highway and Railway Engineering
More informationNumerical Modeling of Delamination Resistance Improvement Through The Use of CNTReinforced Bonding Layers
21 st International Conference on Composite Materials Xi an, 2025 th August 2017 Numerical Modeling of Delamination Resistance Improvement Through The Use of CNTReinforced Bonding Layers Yassine ElAssami
More informationProceedings oh the 18th IAHR International Symposium on Ice (2006) DISCRETE ELEMENT SIMULATION OF ICE PILEUP AGAINST AN INCLINED STRUCTURE
DISCRETE ELEMENT SIMULATION OF ICE PILEUP AGAINST AN INCLINED STRUCTURE Jani Paavilainen, Jukka Tuhkuri and Arttu Polojärvi Helsinki University of Technology, Laboratory for Mechanics of Materials, Finland
More informationThe effect of discontinuities on stability of rock blocks in tunnel
International Journal of the Physical Sciences Vol. 6(31), pp. 71327138, 30 November, 2011 Available online at http://www.academicjournals.org/ijps DOI: 10.5897/IJPS11.777 ISSN 19921950 2011 Academic
More informationEVALUATION OF DEBONDING ENERGY RELEASE RATE OF EXTERNALLY BONDED FRP SHEETS FOR REHABILITATION OF INFRASTRUCTURES
EVALUATION OF DEBONDING ENERGY RELEASE RATE OF EXTERNALLY BONDED FRP SHEETS FOR REHABILITATION OF INFRASTRUCTURES Koji YAMAGUCHI 1, Isao KIMPARA 1, and Kazuro KAGEYAMA 1 1 Department of Environmental &
More informationOutline. TensileTest Specimen and Machine. StressStrain Curve. Review of Mechanical Properties. Mechanical Behaviour
TensileTest Specimen and Machine Review of Mechanical Properties Outline Tensile test True stress  true strain (flow curve) mechanical properties:  Resilience  Ductility  Toughness  Hardness A standard
More informationShear Behaviour of Fin Plates to Tubular Columns at Ambient and Elevated Temperatures
Shear Behaviour of Fin Plates to Tubular Columns at Ambient and Elevated Temperatures Mark Jones Research Student, University of Manchester, UK Dr. Yong Wang Reader, University of Manchester, UK Presentation
More information3. BEAMS: STRAIN, STRESS, DEFLECTIONS
3. BEAMS: STRAIN, STRESS, DEFLECTIONS The beam, or flexural member, is frequently encountered in structures and machines, and its elementary stress analysis constitutes one of the more interesting facets
More informationMECHANICS OF STRUCTURES SCI 1105 COURSE MATERIAL UNIT  I
MECHANICS OF STRUCTURES SCI 1105 COURSE MATERIAL UNIT  I Engineering Mechanics Branch of science which deals with the behavior of a body with the state of rest or motion, subjected to the action of forces.
More informationA NEW SIMPLIFIED AND EFFICIENT TECHNIQUE FOR FRACTURE BEHAVIOR ANALYSIS OF CONCRETE STRUCTURES
Fracture Mechanics of Concrete Structures Proceedings FRAMCOS3 AEDFCATO Publishers, D79104 Freiburg, Germany A NEW SMPLFED AND EFFCENT TECHNQUE FOR FRACTURE BEHAVOR ANALYSS OF CONCRETE STRUCTURES K.
More informationDelamination in fractured laminated glass
Delamination in fractured laminated glass Caroline BUTCHART*, Mauro OVEREND a * Department of Engineering, University of Cambridge Trumpington Street, Cambridge, CB2 1PZ, UK cvb25@cam.ac.uk a Department
More informationALASKA ENERGY AUTHORITY AEA ENGINEERING FEASIBILITY REPORT. Appendix B8. Finite Element Analysis
ALASKA ENERGY AUTHORITY AEA11022 ENGINEERING FEASIBILITY REPORT Appendix B8 Finite Element Analysis SusitnaWatana Hydroelectric Project Alaska Energy Authority FERC Project No. 14241 December 2014 Seismic
More informationVerification Examples. FEMDesign. version
FEMDesign 6.0 FEMDesign version. 06 FEMDesign 6.0 StruSoft AB Visit the StruSoft website for company and FEMDesign information at www.strusoft.com Copyright 06 by StruSoft, all rights reserved. Trademarks
More informationNonlinear Analysis Of An EPDM Hydraulic Accumulator Bladder. Richard Kennison, RaceTec
Nonlinear Analysis Of An EPDM Hydraulic Accumulator Bladder Richard Kennison, RaceTec Agenda RaceTec Overview Accumulator Experimental Testing Material Testing Numerical Analysis: 1. Linear Buckling
More informationBrittle Deformation. Earth Structure (2 nd Edition), 2004 W.W. Norton & Co, New York Slide show by Ben van der Pluijm
Lecture 6 Brittle Deformation Earth Structure (2 nd Edition), 2004 W.W. Norton & Co, New York Slide show by Ben van der Pluijm WW Norton, unless noted otherwise Brittle deformation EarthStructure (2 nd
More informationThe Frictional Regime
The Frictional Regime Processes in Structural Geology & Tectonics Ben van der Pluijm WW Norton+Authors, unless noted otherwise 1/25/2016 10:08 AM We Discuss The Frictional Regime Processes of Brittle Deformation
More informationMaterials and Structures. Indian Institute of Technology Kanpur
Introduction to Composite Materials and Structures Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 16 Behavior of Unidirectional Composites Lecture Overview Mt Material ilaxes in unidirectional
More informationSIMPLIFIED MODELING OF THINWALLED TUBES WITH OCTAGONAL CROSS SECTION AXIAL CRUSHING. Authors and Correspondance: Abstract:
SIMPLIFIED MODELING OF THINWALLED TUBES WITH OCTAGONAL CROSS SECTION AXIAL CRUSHING Authors and Correspondance: Yucheng Liu, Michael L. Day Department of Mechanical Engineering University of Louisville
More informationStress and fabric in granular material
THEORETICAL & APPLIED MECHANICS LETTERS 3, 22 (23) Stress and fabric in granular material Ching S. Chang,, a) and Yang Liu 2 ) Department of Civil Engineering, University of Massachusetts Amherst, Massachusetts
More informationThe Young s Modulus of SingleWalled Carbon Nanotubes
The Young s Modulus of SingleWalled Carbon Nanotubes Douglas Vodnik Faculty Advisor: Dr. Kevin Crosby Department of Physics, Carthage College, Kenosha, WI Abstract A new numerical method for calculating
More informationSeismic design of bridges
NATIONAL TECHNICAL UNIVERSITY OF ATHENS LABORATORY FOR EARTHQUAKE ENGINEERING Seismic design of bridges Lecture 3 Ioannis N. Psycharis Capacity design Purpose To design structures of ductile behaviour
More informationModelling Progressive Failure with MPM
Modelling Progressive Failure with MPM A. Yerro, E. Alonso & N. Pinyol Department of Geotechnical Engineering and Geosciences, UPC, Barcelona, Spain ABSTRACT: In this work, the progressive failure phenomenon
More informationChapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING )
Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING ) 5.1 DEFINITION A construction member is subjected to centric (axial) tension or compression if in any cross section the single distinct stress
More informationTensile behaviour of antisymmetric CFRP composite
Available online at www.sciencedirect.com Procedia Engineering 1 (211) 1865 187 ICM11 Tensile behaviour of antisymmetric CFRP composite K. J. Wong a,b, *, X. J. Gong a, S. Aivazzadeh a, M. N. Tamin b
More informationQUESTION BANK Composite Materials
QUESTION BANK Composite Materials 1. Define composite material. 2. What is the need for composite material? 3. Mention important characterits of composite material 4. Give examples for fiber material 5.
More informationEquilibrium & Elasticity
PHYS 101 Previous Exam Problems CHAPTER 12 Equilibrium & Elasticity Static equilibrium Elasticity 1. A uniform steel bar of length 3.0 m and weight 20 N rests on two supports (A and B) at its ends. A block
More informationMESH MODELING OF ANGLEPLY LAMINATED COMPOSITE PLATES FOR DNS AND IPSAP
16 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS MESH MODELING OF ANGLEPLY LAMINATED COMPOSITE PLATES FOR DNS AND IPSAP Wanil Byun*, Seung Jo Kim*, Joris Wismans** *Seoul National University, Republic
More informationApplication to modeling brittle materials
1.01, 3.01, 10.333,.00 Introduction to Modeling and Simulation Spring 011 Part I Continuum and particle methods Application to modeling brittle materials Lecture 7 Markus J. Buehler Laboratory for Atomistic
More informationUNIT I SIMPLE STRESSES AND STRAINS
Subject with Code : SM1(15A01303) Year & Sem: IIB.Tech & ISem SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) UNIT I SIMPLE STRESSES
More informationCHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS
CHAPTER THE EFFECTS OF FORCES ON MATERIALS EXERCISE 1, Page 50 1. A rectangular bar having a crosssectional area of 80 mm has a tensile force of 0 kn applied to it. Determine the stress in the bar. Stress
More informationSERVICEABILITY OF BEAMS AND ONEWAY SLABS
CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach  Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONEWAY SLABS A. J. Clark School of Engineering Department of Civil
More informationNumerical and Theoretical Study of Plate Load Test to Define Coefficient of Subgrade Reaction
Journal of Geotechnical and Transportation Engineering Volume 1 Issue 2 Numerical and Theoretical Study of Plate Load Test to Define Coefficient of Subgrade Reaction Naeini and Taherabadi Received 9/28/2015
More informationCRACK FORMATION AND CRACK PROPAGATION INTO THE COMPRESSION ZONE ON REINFORCED CONCRETE BEAM STRUCTURES
S. Kakay et al. Int. J. Comp. Meth. and Exp. Meas. Vol. 5 No. (017) 116 14 CRACK FORMATION AND CRACK PROPAGATION INTO THE COMPRESSION ZONE ON REINFORCED CONCRETE BEAM STRUCTURES SAMDAR KAKAY DANIEL BÅRDSEN
More informationTuesday, February 11, Chapter 3. Load and Stress Analysis. Dr. Mohammad Suliman Abuhaiba, PE
1 Chapter 3 Load and Stress Analysis 2 Chapter Outline Equilibrium & FreeBody Diagrams Shear Force and Bending Moments in Beams Singularity Functions Stress Cartesian Stress Components Mohr s Circle for
More informationChapter 6: Mechanical Properties of Metals. Dr. Feras Fraige
Chapter 6: Mechanical Properties of Metals Dr. Feras Fraige Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility Toughness
More informationFinite element analysis of diagonal tension failure in RC beams
Finite element analysis of diagonal tension failure in RC beams T. Hasegawa Institute of Technology, Shimizu Corporation, Tokyo, Japan ABSTRACT: Finite element analysis of diagonal tension failure in a
More informationISSN: ISO 9001:2008 Certified International Journal of Engineering Science and Innovative Technology (IJESIT) Volume 2, Issue 4, July 2013
Delamination Studies in FibreReinforced Polymer Composites K.Kantha Rao, Dr P. Shailesh, K. Vijay Kumar 1 Associate Professor, Narasimha Reddy Engineering College Hyderabad. 2 Professor, St. Peter s Engineering
More informationBending Analysis of a Cantilever Nanobeam With End Forces by Laplace Transform
International Journal of Engineering & Applied Sciences (IJEAS) Vol.9, Issue (Special Issue: Composite Structures) (07) 03 http://.doi.org/0.407/ijeas.34635 Int J Eng Appl Sci 9() (07) 03 Bending Analysis
More informationInstabilities and Dynamic Rupture in a Frictional Interface
Instabilities and Dynamic Rupture in a Frictional Interface Laurent BAILLET LGIT (Laboratoire de Géophysique Interne et Tectonophysique) Grenoble France laurent.baillet@ujfgrenoble.fr http://wwwlgit.obs.ujfgrenoble.fr/users/lbaillet/
More informationSize Effects In the Crushing of Honeycomb Structures
45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference 1922 April 2004, Palm Springs, California AIAA 20041640 Size Effects In the Crushing of Honeycomb Structures Erik C.
More informationRESILIENT INFRASTRUCTURE June 1 4, 2016
RESILIENT INFRASTRUCTURE June 1 4, 2016 DAMAGE DETECTION OF UHPFRC PLATES USING RANDOM DECREMENT TECHNIQUE Azita Pourrastegar MASc Student, Ryerson University, azita2.pourrastegar@ryerson.ca, Canada Hesham
More informationfriction friction ab slow fast increases during sliding
µ increases during sliding faster sliding > stronger fault > slows sliding leads to stable slip: no earthquakes can start velocitystrengthening friction slow fast µ velocitystrengthening friction
More informationContinuum modeling of van der Waals interactions between. carbon nanotube walls
Contuum modelg of van der Waals teractions between carbon nanotube walls W.B. Lu 1, B. Liu 1a), J. Wu 1, J. Xiao, K.C. Hwang 1, S. Y. Fu 3,4 a), Y. Huang 1 FML, Department of Engeerg Mechanics, Tsghua
More informationA PROTOCOL FOR DETERMINATION OF THE ADHESIVE FRACTURE TOUGHNESS OF FLEXIBLE LAMINATES BY PEEL TESTING: FIXED ARM AND TPEEL METHODS
1 A PROTOCOL FOR DETERMINATION OF THE ADHESIVE FRACTURE TOUGHNESS OF FLEXIBLE LAMINATES BY PEEL TESTING: FIXED ARM AND TPEEL METHODS An ESIS Protocol Revised June 2007, Nov 2010 D R Moore, J G Williams
More informationTEMPERATURE DEPENDENCE OF THE TENSILE PROPERTIES OF SINGLE WALLED CARBON NANOTUBES: O(N) TIGHT BINDING MD SIMULATION GÜLAY DERELİ *, BANU SÜNGÜ
TEMPERATURE DEPENDENCE OF THE TENSILE PROPERTIES OF SINGLE WALLED CARBON NANOTUBES: O(N) TIGHT BINDING MD SIMULATION GÜLAY DERELİ *, BANU SÜNGÜ Department of Physics, Yildiz Technical University, 34210
More informationANALYSIS AND NUMERICAL MODELLING OF CERAMIC PIEZOELECTRIC BEAM BEHAVIOR UNDER THE EFFECT OF EXTERNAL SOLICITATIONS
Third International Conference on Energy, Materials, Applied Energetics and Pollution. ICEMAEP016, October 3031, 016, Constantine,Algeria. ANALYSIS AND NUMERICAL MODELLING OF CERAMIC PIEZOELECTRIC BEAM
More information3D ANALYSIS OF STRESSES AROUND AN UNLINED TUNNEL IN ROCK SUBJECTED TO HIGH HORIZONTAL STRESSES
3D ANALYSIS OF STRESSES AROUND AN UNLINED TUNNEL IN ROCK SUBJECTED TO HIGH HORIZONTAL STRESSES Abdel Meguid, M. Graduate Student, Department of Civil Engineering, University of Western Ontario, London,
More informationNUMERICAL SIMULATIONS OF CORNERS IN RC FRAMES USING STRUTANDTIE METHOD AND CDP MODEL
Numerical simulations of corners in RC frames using StrutandTie Method and CDP model XIII International Conference on Computational Plasticity. Fundamentals and Applications COMPLAS XIII E. Oñate, D.R.J.
More informationChapter 3 LAMINATED MODEL DERIVATION
17 Chapter 3 LAMINATED MODEL DERIVATION 3.1 Fundamental Poisson Equation The simplest version of the frictionless laminated model was originally introduced in 1961 by Salamon, and more recently explored
More informationEnhancing Prediction Accuracy In Sift Theory
18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS Enhancing Prediction Accuracy In Sift Theory J. Wang 1 *, W. K. Chiu 1 Defence Science and Technology Organisation, Fishermans Bend, Australia, Department
More informationStudies of Bimaterial Interface Fracture with Peridynamics Fang Wang 1, Lisheng Liu 2, *, Qiwen Liu 1, Zhenyu Zhang 1, Lin Su 1 & Dan Xue 1
International Power, Electronics and Materials Engineering Conference (IPEMEC 2015) Studies of Bimaterial Interface Fracture with Peridynamics Fang Wang 1, Lisheng Liu 2, *, Qiwen Liu 1, Zhenyu Zhang 1,
More informationEAS 664/4 Principle Structural Design
UNIVERSITI SAINS MALAYSIA 1 st. Semester Examination 2004/2005 Academic Session October 2004 EAS 664/4 Principle Structural Design Time : 3 hours Instruction to candidates: 1. Ensure that this paper contains
More informationThis thesis is approved, and it is acceptable in quality and form for publication:
Bhanu Kiran Tuniki Candidate Civil Engineering Department This thesis is approved, and it is acceptable in quality and form for publication: Approved by the Thesis Committee: Dr. Walter H. Gerstle, Chairperson
More informationCE 530 Molecular Simulation
1 CE 530 Molecular Simulation Lecture 1 David A. Kofke Department of Chemical Engineering SUNY Buffalo kofke@eng.buffalo.edu 2 Time/s MultiScale Modeling Based on SDSC Blue Horizon (SP3) 1.728 Tflops
More informationS Wang Beca Consultants, Wellington, NZ (formerly University of Auckland, NZ)
Wang, S. & Orense, R.P. (2013) Proc. 19 th NZGS Geotechnical Symposium. Ed. CY Chin, Queenstown S Wang Beca Consultants, Wellington, NZ (formerly University of Auckland, NZ) Jackson.wang@beca.com R P Orense
More informationLecture 8 Viscoelasticity and Deformation
HW#5 Due 2/13 (Friday) Lab #1 Due 2/18 (Next Wednesday) For Friday Read: pg 130 168 (rest of Chpt. 4) 1 Poisson s Ratio, μ (pg. 115) Ratio of the strain in the direction perpendicular to the applied force
More informationWellbore stability analysis in porous carbonate rocks using cap models
Wellbore stability analysis in porous carbonate rocks using cap models L. C. Coelho 1, A. C. Soares 2, N. F. F. Ebecken 1, J. L. D. Alves 1 & L. Landau 1 1 COPPE/Federal University of Rio de Janeiro, Brazil
More informationTHEME IS FIRST OCCURANCE OF YIELDING THE LIMIT?
CIE309 : PLASTICITY THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT? M M  N N + + σ = σ = + f f BENDING EXTENSION Ir J.W. Welleman page nr 0 kn Normal conditions during the life time WHAT HAPPENS DUE TO
More information