Mechanics of Soft Materials. Tuesday and Thursday L13, 2:00-3:30 PM

Transcription

1 Mecanics of Soft Materials Tuesday and Tursday L1, :00-:0 PM

2 Wat Are Soft Materials? Rubber Skin Tissue Paper Gel Modulus < 10 MPa Deformation wen subjected to load Tissue scafold Type of load Geometry: micro-nano structures Reological properties Interfacial properties

3 Soft Materials ave modulus of te order of few Pa to few MPa Elastic Viscoelastic Poroelastic Ductile Viscoplastic Gaskets Sealants Adesives Skin Soft Patterning Solid lubricants Prostetic devices Drug delivery devices Packaging Materials Components of automobile Soft robotic components Artificial Tissue Functional surfaces Etracellular Matri Sear Modulus Material (10 9 N/m, GPa ) Acrylic. Aluminum 69 Bone 9 Brasses Brones Reinforced Plastic 150 Concrete 0 Diamond 1,050-1,00 Glass Magnesium 45 grain) 11 Polycarbonate.6 Polyetylene HDPE 0.8 Tereptalate PET -.7 Polyimide.5 Polypropylene Polystyrene -.5 Silicon Carbide 450 Titanium Alloy Tungsten Tungsten Carbide Wrougt Iron Nylon - 4 Rubber Gels

4 Bio-inspired Patterned Adesives: Gorb et al, J. Micromec. Microeng. 000, 10, Hierarcical structure Strong and reusable adesion Aderes to almost all surfaces Self-cleaning Does not leave any residue Easy release during locomotion Patterned adesive Crack arrest, crack initiation Enancement of adesion by ~10 times Smoot adesive Gatak et al, Proc. Roy. Soc. London, A, 460, 75 (004)

5 Adesive suitable for dry and wet adesion and delivery of drugs and nutrients Tissue Scar Transdermal Patces Cosmetic patces Tissue adesive Reversible adesion: Clean adesion Good mecanical strengt: ability to sustain large deformation Multi-functionality: adesion and drug delivery Biocompatibility and biodegradability Resistance against particulate contamination Amenable for easy was or cleaning

6 Inspiration from naturally occurring Adesives Under water adesion of mussel Release of water repellent protein molecules at interface Crosslinking of tese molecules leading to a sticky glue Gecko inspired Adesive Adesion on dry and wet substrate van der Waals interaction in dry state Swelling of keratin protein of setae in moist environment r 4 r 4 r 4 r c A novel adesive patc satisfies tese requirements Rate of Vitamin C release (μg/cm /day) r 4 r 4 r 4 days 70 gm 0 1:5 :5 :5 Vitamin C solution-gelatin volume ratio

7 Blood Vessels in Climbing Organ of Insects: Climbing organ Rodnius Prolius (kissing bug) Adult Rodnius could climb te glass walls of te jars ability to climb smoot surfaces was due to te eistence in te adult insects of a flasy pad situated at te lower end of tibia of te first two pair of legs. Blood filled vessels Wiggleswort, et al, Proc. R. Soc. Lond. B 111, (19).

8 J. Comp. Pysiology A, 006, 186, Air Pockets at te Adesive Pads of Insects Attacment pad of Tettigonia viridissima AS: Air sack CL: Epidermal cell layer EXO: Rod containing eo- cuticle of te pad HM: Haemolymp TD: Tendon of te claw fleor mussle TK: Tanned cuticle

9 Majumder et al, Science, 18, 58-61, 007 Peeling off a Microfluidic Adesive a

10 M, Nm/m Peeling Torque: (X 10- ) G F. d, mm A peeled a G, J/m times enanceme nt in adesion , m d, m 1: smoot adesive 5: : : 10 cp 7 : : 1000 cp 8 : : 5000 cp 9 : : 80 cp 10 : m d 50 m

11 Asymmetry Induced by Pair of Embedded Cannels: Differently filled wit wetting liquid Fleible contacting plate Adesive film F Substrate t d 1 s 1 d s d 1 1 d t 50 μm, s 1 15 μm, d 550 μm s Majumder et al Soft Mat., 01 air air oil oil oil air 00 μm

12 δ ( μm) Dynamic Cange in Surface Profile During Separation of Aderent: μm ( )

13 4. peel direction.6.0 G ( J/m ) Case 1 1. Case 0.6 Case 0.0 s 1 ( μm) s 1 Case 4

14 Adesion Between a Fleible Plate on a Layer of Adesive Bonded to a Rigid Substrate: Elastic film Fleible plate Contact line Spacer Rigid substrate a Adesive: Elastic, Incompressible, Tin Aderent: Tin, Fleible & Rigid Plate

15 Stress Equilibrium Relations: ( u u u yy p + + p + + y ( v v v yy p + + ) ) ( w w w yy u, v, w are displacements in te, y and direction respectively ) Incompressibility relation: u + v + w y 0

16 + w 0 u Plane Strain Approimation: Stress equilibrium relation Incompressibility relation 0 y y yy e e e + + w w p u u p

17 ( ) ( ) Z W X W L Z P L Z U L X U L X P L L Z W X W Z P Z U Z U X U X P ε ε ε.,.,.,. ε ε p L W w U L u Z L X Dimensionless Quantities: Dimensionless Stress-Equilibrium relation: Lubrication Approimation: <<1 ε

18 Boundary Conditions for Film: u( u( 0) ) w( 0) 0, w( 0 ) ψ at 0 < < a σ σ 0 at <0 p( ) D 4 d ψ 4 d 0 w (, ) Elastic film ( ) u,

19 0 p u p p A B B A p u + + 0, 1 ( ) p u 1 ( ) p u w 1 C p w D ψ ψ Integration Boundary Condition Incompressibility relation Integration Boundary Condition

20 Equation for Plate: ψ 6 D ψ 6 1 < ψ 0 < < a 4

21 Boundary Conditions for Plate: (i) (iii) (v) ψ ψ p ψ 0 ψ 0 0+ (ii) (iv) (vi) ψ ψ ψ ψ a ψ 0 0+ (vii) D d d ψ a F or ψ a (viii-) ψ ψ ψ 0

22 ( ) ( ) ( ) ( ) ( ) ( ) F w k F u 1 ', ' 6, φ φ ( ) ( ) ( ) cos sin cos sin 4 1 k ak k ak e ak e k ak k ak e ak e k k k k φ φ Displacement Field in Adesive Film: 1 k ' F and ave dimension of lengt and are constants

23 Displacement of Plate and Normal Stress at Interface: ψ ' F ( ) ψ F' e k k ak + k k ak e + sin + ( + ) ak cos F 6 + 1ak + 9 ' ( ) ( ), ak + ak k 1 D 1 1 6

24 Adesive wit Spatially Varying Tickness and Modulus ( ) w, 0 ( ) u, adesive film contact line ( 0) y fleible aderent F In-pase variation of tickness and modulus ( ) φ ( ) ( 1+ ( k ) ) 0 0 δ sin ( ) f ( ) ( 1 ( k ) sin δ Out-of-pase variation of tickness and modulus rigid substrate O O (mm) a Gatak, Pys. Rev. E, (mm)

25 Adesive wit Pase Lag Between Tickness and Modulus Variation: φ l M ma M 0.5 (Nm/m) 0.0 δ 0.005, δ 0. 9 k k 1.5q, 0.50 (a) φ l (mm) 15 0 π π π M ma (Nm/m) (b) 0.5 π π 0 π Non-monotonic variation in torque wit pase lag φ l M ma π

26 Typical Content of Course: 1.Brief Introduction: Total Definition of strain, strain tensor, stress, stress tensor, Saint Venant s principle 1 Hooke s law, stress equilibrium relations 1 One dimensional stretcing of a rod 1.Solid bodies in contact wit and witout interactions: Total 9 Line loading of an elastic alf space, distributed loading 1 Aisymmetric loading of an elastic alf space 1 Normal contact of elastic solids: Hertian teory: 1 Contact wit adesion, JKR teory Compression of an elastic layer between two parallel plates 1.Equilibrium of rods and plates: Total 1 Equations of equilibrium of rods Euler s buckling instability 1 Twisting instability of rods 1 Equation of equilibrium for a tin bent plate 1 longitudinal deformation of plates 1 large deflection of plates 1 Contact of two rigid or fleible Aderents Analysis of wrinkling instability 1 Elasticity of an interfacial particle raft 1

27 4.Nonlinear elasticity: Total 8 Molecular approac to rubber elasticity 1 Neo-Hookean elasticity 1 Analysis of large deformation of an incompressible elastic material 4 Inflation of a balloon 1 Cavitation in crosslinked networks 1 5.Mecanics of cell wall: Total 8 Entropic elasticity-stretcing, bending and twisting, persistence lengt Mecanics of cellular filaments; D and D networks in cell Polymeriation and te generated force biomembranes, membrane undulations. Tet book: Teory of Elasticity, rd edition, by Landau and Lifsit. Course of teoretical pysics, vol-7. A treatise on te matematical teory of elasticity by A. E. H. Love. Contact Mecanics by K. L. Jonson. Stability problems in applied mecanics by A. K. Mallik and J. K. Battacarjee. Mecanics of te cell by David Boal. Researc Papers publised in variety of journals.

28 Tank You