Constitutive model for shape memory polymer based on the viscoelasticity and phase transition theories

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1 Original Article Constitutive model or shape memory polymer based on the viscoelasticity and phase transition theories Journal o Intelligent Material Systems and Structures, Vol. 7() Ó The Author(s) 5 Reprints and permissions: sagepub.co.uk/journalspermissions.nav DOI:.77/59X557 jim.sagepub.com Xiaogang Guo,LiwuLiu,BoZhou, Yanju Liu and Jinsong Leng Abstract As a kind o smart materials, shape memory polymer has covered broad applications or its shape memory eect. Precise description o the mechanical behaviors o shape memory polymer has been an urgent problem. Since the phase transition was a continuous time-dependent process, shape memory polymer was composed o several individual transition phases. Owing to the orming and dissolving o individual phases with the change in temperature, shape memory eect emerged. In this research, shape memory polymer was divided into dierent kinds o phases including rozen and active phases or its thermodynamics properties. Based on the viscoelasticity theory and phase transition theories, a new constitutive model or shape memory polymer which can explain the above assumptions was studied. In addition, a normal distribution model, which possesses less but physical meaning parameters, was proposed to describe the variation in the volume raction in shape memory polymer during heating or cooling process. Keywords shape memory polymer, constitutive model, phase transition, viscoelasticity and phase transition theories Introduction Since the shape memory polymer (SMP) was discovered in 9s, it has drawn much attention and has been vastly developed during the past decades (Ratna and Karger-Kocsis, 7; Wei et al., 99). SMP possesses the ability o returning rom deormed shape to original shape under a reasonable stimulus such as temperature, light, electric ield, magnetic ield, ph, speciic ions, or enzyme (Behl and Lendlein, 7; Fei et al., ; Hu et al., ; Leng et al., ; Meng and Li, ; Xu et al., ). And the thermal-actuated SMP has been widely studied as a typical one. With the variation in temperature, the thermal mechanical cycle o shape memory eect (SME) is as shown in Figure. Depending on the phase transition temperature T g,the process can be classiied into the ollowing steps: () heat and deorm SMP at a high temperature above T g ; () cool and remove the external orce at a lower temperature; and () heat the pre-deormed SMP above T g and then the polymer will recover to its original shape. Compared with other smart materials such as shape memory alloy, SMP possesses the advantages o large deormation capacity, low density, and cost. However, the main drawbacks o SMP are their low actuation orces and long recovery time. For the sake o their low stiness and strength, SMP composites, which were illed with particles, carbon nanotubes, and short ibers (Basit et al., ; Tan et al., ; Yu et al.,, ; Zhang and Li, ), were investigated. Now, SMP composites and their products such as deployable and morphing structures have been researched and developed (Leng et al., ; Liu et al., ; Meng and Hu, 9). In order to investigate the mechanical behaviors o SMP, various constitutive models and a large tensile, compression, torsion, and lexure experiments (Chen et al., ; Diani et al., ; Guo et al., ; Liu College o Aerospace and Civil Engineering, Harbin Engineering University, Harbin, China Department o Astronautical Science and Mechanics, Harbin Institute o Technology, Harbin, China College o Pipeline and Civil Engineering, China University o Petroleum, Qingdao, China Center or Composite Materials and Structures, Harbin Institute o Technology, Harbin, China Corresponding authors: Yanju Liu, Department o Astronautical Science and Mechanics, Harbin Institute o Technology, Harbin 5, China. yj_liu@hit.edu.cn Jinsong Leng, Center or Composite Materials and Structures, Harbin Institute o Technology, Harbin 5, China. lengjs@hit.edu.cn

2 Guo et al. 5 Applied Force Applied Force Heating Cooling under the constraint strain Remove the orce and heating Original Shape Pre- deormed Shape Original Shape Figure. Schematic o phase transition in shape memory eect during typical thermal mechanical cycle. et al., ; Srivastava et al., ) were carried out. Tobushi et al. (997) established a simple thermal mechanical model describing the mechanical behaviors o the thermal-actuated polymer using a rheological model based on the viscoelasticity theory. Through taking nonlinear mechanical behaviors into account, a nonlinear one-dimensional (D) constitutive model or SMP was proposed in (Tobushi et al., ). Considering the strain rate during the loading and unloading processes, Shim and Mohr () built a new constitutive model which was composed o two Maxwell elements. Most o these modeling eorts have adopted rheological models consisting o spring, dashpot, and rictional elements in D constitutive models. Though these models are simple, they only agree qualitatively with the experimental results. In the constitutive model o SMP, the concept o phase transition was also used. Although there is a slight dierence between physical nature o melting and glass transition, they both can explain SME or certain macroscopic characteristics. And the concept o phase transition is convenient or analyzing the mechanical behaviors o SMP (Long et al., ). Based on modeling the crystallization and taking the phase transition into account, several constitutive models or SMP were also developed. In, a new thermal mechanical model that divided the polymer into rozen and active phases was investigated, and a three-dimensional (D) micromechanical constitutive model was built by Liu et al. (). In Liu et al. s () article, the strain o the materials was decomposed into mechanical strain, thermal strain, and storage strain which was the critical actor or the SME. And the active and rozen phases were all treated as elastic materials and could not describe the viscoelasticity o SMP at a constant loading condition and temperature. However, the SMP in this article was treated as the elastic materials, not time dependency materials (Baghani et al., ). Based on Liu et al. s () work and the experience o investigating the phase transition o shape memory alloys, Chen and Lagoudas (a, b) studied the micromechanism o SME and created a D constitutive model or SMP under large deormation. Meanwhile, a constitutive model or crystallization o SMP was proposed and the interaction between original amorphous and semicrystalline phase was also investigated (Barot et al., ). In order to explain the molecular mechanisms o the SME in amorphous SMPs, Nguyen et al. () established a thermal-viscoelastic constitutive model and assumed that structural relaxation and stress relaxation were the key actors or SME. Taking the non-equilibrium relaxation processes into account, Westbrook et al. () established a D inite deormation constitutive model or amorphous SMP. Based on micromechanics ramework, Shojaei and Li () developed a multi-scale theory, which links micro-scale and macro-scale constitutive behaviors o the polymers. For the sake o the inluence o material parameters on the response characteristics o the constitutive model, Ghosh and Srinivasa () proposed a D continuum two-network or a thermal elastic response model o SMP. And during the last ew years, a new phenomenon or SMP multi-smes was discovered by which SMP can memorize more than one temporary shape (Xie, ). And the research on the mechanisms o multi-smes was investigated (Yu et al., ). The purpose o this article is to establish a constitutive model that can uniy the linear elasticity and viscoelasticity into one equation. The concepts o phase transition and the theory o multi-smes were also considered and described. Using the our-element model, the mechanical behaviors o the individual transition phases were analyzed. The volume ractions o transition phases which can join them together were discussed, and a normal distributed equation that can simulate the change in these ractions in SMP during heating or cooling process was built. Finally, in order to conirm the parameters in this new constitutive model, the dynamic mechanical analysis (DMA) tests and creep experiments were also accomplished. The phase transition in SMP The phase transition process in SMP during heating or cooling is complex. Obviously, SMP consists o a lot o molecule chains with dierent lengths and angles.

3 Journal o Intelligent Material Systems and Structures 7() Taking the pre-stress and storage energy into account, the entropy o each chain also diers rom the others, as well as their phase transition temperatures. During cooling process rom a high temperature, the phase transition will come out irst in the molecule chain with higher entropy. That is, when cooled to a speciic temperature, phase transition in the molecule chain will happen and the relevant parts will change rom active phase to rozen phase. Thus, the speciic temperature is the phase transition temperature o those molecule chains. With the decrease in temperature, the molecule chain will shrink while the stiness o SMP will increase. The shrinkage o the chain was due to the removal o residual stress ormed in the polymer process step (shown in Figure ). Based on the statistics, the molecule chains in SMP can be divided into several classes by their phase transition temperatures. The volume raction o each active class can be expressed by i while the one o rozen phase is. In this model, the variation in volume raction controls the strain release and storage in thermomechanical cycle. And they can be deined as = V V i = V i V + X i = ðþ in which and i are the volume raction o rozen phase and ith relevant active phase, respectively. V is the total volume o the SMP. When the SMP is loaded during heating or cooling process, the strain energy will almost be absorbed by active phase or conormation rotation o the polymer. When cooled down to phase transition temperature, the phase transition will happen and the strain in ith active phase will also be stored as storage strain. Finally, the strain energy and deormation are almost stored in SMP even ater unloading at a low temperature. During the recovery process, the strain energy and deormation stored in the ith active phase during loading and cooling process will release at its phase transormation temperature. Then, the deormed SMP will recover to its original shape. And the SME will emerge. In addition, when a multi-load is applied on SMP at dierent temperatures, the mechanical strain caused by multi-stress will be stored in dierent active phases such as ith, jth, or kth. Thus, during the heating or recovery process, the storage strain in certain active phase will be released when these phases experience the relevant temperature again, which is the reason or multi-smes. In addition, not only the storage strain but also the viscoelasticity behaviors o SMP such as stress relaxation play an important role on SME. Based on the above discussions, the volume raction o rozen phase and active phase is a very important parameter or SMP during phase transition process. The researches about this issue have been carried out, and kinds o models such as trigonometric unction model and quadratic polynomial model have been built in order to indicate the relationship between the raction and the temperature. But the cosine model consisted o two equations, so the slope o two equations at demarcation point T g was not equal. The quadratic polynomial model built in was an empirical equation, whose two parameters were conirmed by itting the experiment results. In this article, a new volume raction model that can indicate the phase transition accurately in a simple ormation was brought up and the volume raction o the SMP during phase transition can be given by = ð T Ts p S iiiiii e p (T Tg ) S dt ðþ in which S is the variance o the normal distribution unction and can be expressed as S = T T g n ðþ where n is a constant. T g is the average value o the normal distribution and it is also the temperature at which the volume raction is.5. As indicated in Figure, with the increase in temperature, the volume raction o rozen phase decreases nonlinearly, the rate o which grows rapidly until to the phase transition temperature T g. The phase transition temperature is about K, while the starting temperature is 7 K. When T=T g reaches., at which the environment temperature is 5 K, the phase transition ends and the volume raction o rozen phase will decrease to. Based on the comparison results, the normal distribution unction can describe the variation in the volume raction accurately. volume raction o rozen phase..5. experiment result simulation result T/Tg Figure. Comparisons with simulation results using experiment results (Liu et al., ) o volume raction.

4 Guo et al. 7 A new constitutive model or SME In the ith active phase, the strain is decomposed into two parts: thermal expansion strain e T i and mechanical strain e m i. Thus, the total strain o active phase can be expressed as So, the strain in SMP which is the unction o time and temperature can be deined as e = (e S + e m )+ Xn i e m i + e T = s( (T)J (T, t) e i = e m i + e T i ðþ + Xn i (T)J i (T, t)+ e S + e T ðþ While the strain in rozen phase is constituted by storage strain e S, mechanical strain e m and thermal expansion strain e T For multi-load conditions, the strain in the SMP can be given as e = e S + e m + e T ð5þ e = Xm (T)J (T, t t j )s j So, the strain o SMP during heating or cooling process can be inally shown as e = e + S i e i ðþ And the total thermal expansion strain e T, which is divided into several parts, is given as e T = e T + i e T i =( a + i a i )DT ð7þ where DT is the change in temperature and a i and a are the thermal expansion coeicients o ith active and rozen phases, respectively. In order to describe the mechanical behavior o SMP, the D rheological model or the new constitutive model is shown in Figure. G and G represent the elastic modulus o rozen phase model and G i and Gi are o the ith phase model. h and h are the viscosity coeicients o rozen phase model, while the coeicient o ith phase model can be expressed by h i and h i. Due to the viscoelasticity behaviors o active and rozen phases, the mechanical strains e m i and e m are indicated as e m i = sj i (T, t)=s + t ( e t=t G i G i )+ i h i! e m = sj (T, t)=s + t ( e t=t G G )+ h In equation (), the parameter t is the retardation time and can be expressed by G and h. That is t = h G ð9þ + Xm X n i (T)J i T, t t j ) + e S + e T ðþ Here, t j is the time when s j applied during the loading or recovery process. The phase transition process in SMP is continuous deinitely during cooling or heating process. In order to simpliy calculations, we assume that J i (T, t)=j a (T, t), a i = a a ðþ The thermal expansion strain e T expressed as e T = e T + S i e T i = ð T T ( a + a a a )dt can be inally And the mechanical strain in active phase e m a simply expressed as ðþ can be e m a = em i = sj a (T, t) ðþ in which J a (T, t) is the creep compliance o active phase J a (T, t)= + t G a Ga ( e t=t a )+ h a ð5þ Incorporating equations () and () into equation (), we have e = (e S + e m )+ Xn i e m a + et = s (T)J (T, t)+ a (T)J a (T, t) + e S + e T ðþ G η G η G η η G G i ηi G i η η G n T i n η n ε G n σ Figure. D rheological representations or the developed model.

5 Journal o Intelligent Material Systems and Structures 7() G η G η ε S Ga η a G a ηa ε T σ where G(T) is the elastic modulus o SMP during cooling process. In this model, the elastic modulus o SMP G(T) can be represented by the elastic modulus o rozen phase G and active phase G a Figure. A simpliied D rheological representation or the developed model. G(T) = a G a + G ð9þ As Liu indicated, G is a constant and G a possesses a linear relationship with temperature G ε η G ε η ε S Ga ε ε a η a G a ε a ηa ε a ε T σ G = Constant, G a = NKT ðþ In order to explore the mechanical behaviors during recovery process, the total strain o SMP was decomposed into several parts (as shown in Figure 5) Figure 5. A simpliied D rheological representation or the developed model with several decomposed strains. Here, a, G a, t a, and h a are the volume raction, elastic modulus, retardation time, and viscosity coeicient o active phase, while, G, t, and h are the correspondent parameters o rozen phase, respectively. During cooling process with a constant stress or strain, the phase transition comes out and the mechanical strain in ith active phase will be stored in rozen phase. So, the storage strain e S is given as e S = V ð V e m a dv = V V ð V e m a d v V = ð e m a d ð7þ Equation (), which combines viscoelasticity theory and phase transition model, is the constitutive model or SMP during cooling or heating. In this theory, the above viscoelasticity model shown in Figure was replaced by a simpliied developed model which consisted o only two phases rozen phase and active phase (Figure ). Moreover, the two distinct phases possess the equal stress but dierent strains. Generally, stress relaxation will happen during cooling process at a constant strain e. And with the decrease in temperature, the increase in elastic modulus will play an important role compared with stress relaxation. Meanwhile, the active and rozen phases during cooling process were also treated as elastomeric. And during cooling process, the mechanical strain will be stored due to phase transition and becomes an irrecoverable deormation which cannot undertake stress. Thus, the stress s m used or maintaining the deormation which is the unction o temperature can be inally expressed as s m = G(T)(e e S e T ) ðþ e = e + e a + e S + e T = e + e + e + e a + e a + e a + es + e T ðþ Thus, the storage strain e S will not undertake the load so is the thermal expansion strain e T. Thereore, when the load is constant, these strains can be expressed as ollows s = G e >< >< s = G a e s = G e + h de a dt s = Ga >: e a + h de a a dt ðþ de >: s = h de s = h a dt a dt During the recovery process, the stress in the SMP is obviously and the boundary conditions would be predicted that ds=dt = and s =. So, the strain in SMP can be rewritten as = G e >< >< = G a e = G e + h de a = G dt a >: e a + h de a a dt ðþ de >: = h de = h a dt a dt And the total strain during recover process can be inally indicated as e rec = e + e a + a(t)e S + et = e ( e t=t + a e t=t a )+ a (T)e S + et ðþ Here, e is the strain that ormed during cooling process due to the molecule relaxation. s and G are the original applied stress and elastic modulus, respectively. The parameter a (T)e S represents the released storage strain at temperature T, while e S is the original storage strain beore recovery process. When the deormed specimen was heated at a low temperature, the stored strain was only released partly and the specimen could not recover to its original shape completely. And the residual strain will depend on the value o active and rozen phases at that temperature.

6 Guo et al. 9 In the creep experiments at a constant temperature, the viscous low rarely happens and the storage strain is also. So, the strain in rozen phase e c and active phase e c a can be, respectively, expressed as e c = s + s G G ( e (t=t ) ) e c a = s + s G a Ga ( e (t=ta) ) Storage modulus(mpa) storage modulus(mpa) K Tan Delta Tan Delta At the beginning o the creep, the power exponent on the right side o equation (5) is nearly. So, the strains in rozen phase e c and active phase e c a are all linear as time goes on e c = e c + ae c a = s G + a s G a ðþ When the time t is ininitely great, the power exponent is approximately or the measurements o the parameters t and t a! e c = e c + ae c a = s + s s G G + a + s G a Ga Experimental and simulated results ð7þ In order to investigate the mechanical behaviors o SMP and the correctness o the new constitutive model built in this article, several experiments such as the creep experiments and DMA test were completed. In the section o DMA tests, the phase transition temperature o SMP was obtained. And the experimental results are also shown in Figure. And the accuracy o the phase transition model (equation ()) was veriied in the section o comparison between the simulated and experimental results rom Liu et al. s () research work. Finally, the creep experiments under a constant stress and temperature ( and K) were conducted to veriy the precision o constitutive model built in this article. In this article, all the specimens used or mechanical experiments were made o styrene, one typical kind o SMP. DMA test Figure is the DMA test results o SMP. The experiment sample was cut into pieces o 9 mm mm mm using laser cutting machine at the environment temperature o K. The experimental requency and temperature range were Hz and rom 9 to K, respectively. As indicated in Figure, the relationship between temperature and elastic modulus was obtained. The glass transition temperature T g is about K. Temperature (K) Figure. Dynamic mechanical analysis test results o shape memory polymer. Table. Parameters o styrene obtained through creep experiments at dierent temperatures. T (K) E (MPa) J (MPa ) t (s) Creep experiment at a constant temperature For the sake o determining the parameters in equations () and (5), the creep experiments at several high temperatures T g were inished. The creep experiments were conducted using ZWICK/Z at several constant temperatures. The SMP was irst preheated or about min at the target temperature beore loading. The stress at and K was.5 MPa, while the stress at K was. MPa. The experiment results are shown in Figures 7 to 9. According to the DMA test and creep experiments, several parameters o SMP at dierent temperatures can be obtained and are listed in Table. Though it is diicult to measure the retardation and relaxation time at a low temperature, these two parameters can be indirectly achieved ollowing the Arrhenius-type behavior (O Connell and McKenna, 999) ln a T (T)= AF c k B T T g ðþ in which k B is the Boltzmann constant, A is a constant, and F c is the conigurationally ree energy which is the reciprocal o the conigurationally entropy S c. Signiicantly, F c is a constant below the glass transition temperature. a T is the time temperature superposition shit actor.

7 Journal o Intelligent Material Systems and Structures 7() K,.5MPa a T = t t ð9þ Figure 7. Creep behavior o shape memory polymer at K and.5 MPa. K,.5MPa Figure. Creep behavior o shape memory polymer at K and.5 MPa. K,.MPa Figure 9. Creep behavior o shape memory polymer at K and. MPa. So, the retardation time in active phase at a room temperature can be indirectly obtained. In this model, there were several parameters to be determined through the experiments at high or low temperature to describe the mechanical behaviors o SMP. G a and G are the elastic moduli o active and rozen phases, which can be obtained rom the tensile experiments at high and low temperatures with a constant strain rate. t a and h a are the retardation time and viscosity coeicient o active phase, while t and h are the correspondent parameters o rozen phase, respectively. Ga, t a, and h a canbemeasuredthroughthe creep experiments at a high temperature, while t and h were measured at a low temperature which will cost a lot o time. So, in this model, the Arrheniustype equation was proposed to estimate the values o t and h. Besides, the phase transition temperature T g would be obtained by DMA tests. And these parameters o SMP used in this constitutive model are listed in Table. As shown in Table, the retardation time and viscosity coeicient o rozen phase are nearly 7 times than those o active phase. And the elasticity characters play a more important role than viscoelasticity characters in rozen phase. For simpliication, rozen phase is analyzed as elastomeric materials with an elastic modulus G (as shown in Figure ). So rozen phase also can be interpreted as the phase used to ix geometry o the materials. Based on the theories established in this article, the simulated results o creep and recovery processes were obtained. In addition, the comparison results between simulation and experiments at dierent temperatures (,, and K) are indicated in Figures to. As the creep results show, the mechanical property o SMP was elastic at the beginning o loading process. As time goes on, the viscoelasticity o SMP gradually emerges and the relationship between strain and time is nonlinear. The creep compliance can be obtained i plenty o time condition is allowed. As the comparison results show, the constitutive model built in this article can describe the creep behaviors o styrene precisely, especially at and K. Cooling experiment under a constant strain In order to investigate the mechanical behavior o SMP during cooling process, the cooling experiments at a constant strain were carried out. The samples were irst stretched to an elongation o % using a 5%/s strain rate at the temperature o K (T g + K). The respective temperature was kept constant or about s beore cooling down to the room temperature (with a cooling rate o : K= min).

8 Guo et al. Table. Summary o shape memory polymer and simulation parameters. G a (MPa) G a (MPa) G (MPa) h a (MPa s) h (MPa s) t a (s) t (s) T g (K) AF c k B a ( =K) a a ( =K).75,.7. G Ga ηa G a ηa ε S εt σ Experimental Results Simulation Results Figure. A simpliied D rheological representation considering rozen phase as elastomer. Experiment Result Simulation Result Figure. Comparisons with simulation results used creep experiment results at K and. MPa Figure. Comparisons with simulation results using creep experiment results at K and.5 MPa. The comparisons between the simulation and experiment results during cooling under a constant strain (%) process are shown in Figure. At the beginning o cooling process, the stress used or maintaining pre-strain increased slowly and the stress was about. MPa at K. When the temperature reached K, the stress grew rapidly and nonlinear. The ultimate value o stress was. MPa at K. Simulation Results Experiment Results Figure. Comparisons with simulation results using creep experiment results at K and.5 MPa. Recovery experiment under a constant temperature In Figure 5, the recovery process at K o SMP was tested. When the pre-stress was removed at 5 s, the pre-strain deduced sharply and the strain energy was released. But due to low temperature, one part o pre-strain and energy in the material were stored. So, the deormed SMP could not recover to its original shape except at a higher temperature or with a plenty o time. Using equations () and (), the simulated results during the loading and recovery processes were obtained. In addition, the recovery process at K was also conducted and the experimental results are also shown in Figure. As Figure indicates, the deormed specimen can recover to its original shape completely at a high temperature ( K) in a shorter period o time. Besides, the simulated results were also obtained based

9 Journal o Intelligent Material Systems and Structures 7() 7 5 Simulation Results Experiment Results on equation (). Through the comparison between the simulated and experimental results, the constitutive model built in this article can describe the recovery process o SMP precisely. Stress(MPa) Cooling Process Temperature(K) Figure. Comparisons with simulation results using the experiment results o cooling under a constant strain (%). 7 5 Experimental Results Simulated Results 5 7 Time(s) Figure 5. Comparisons with simulation results using recovery experiment results at K. Strain (%) Experimental Results Simulated Results Time (s) Figure. Comparisons with simulation results using recovery experiment results at K. Conclusion The key o this article is to capture the SME o SMP. Equation () explains the mechanism o phase transition and multi-smes. For simplicity, SMP was divided into two parts: rozen phase and active phase while the strain was composed o several parts: the mechanical strain in rozen and active phases, storage strain, and thermal expansion strain. Here, the storage strain is the crucial element o SME. In addition, a normal distributed model was used to characterize the volume raction which is a key actor o equations () and (). Through creep and retardation experiments, the retardation and relaxation time o rozen and active phases were obtained directly or indirectly. Through comparison with the experimental results, the constitutive model established in this article can describe the SME and mechanical behaviors o SMP accurately. Acknowledgement This work was supported by the National Natural Science Foundation o China (Grant No 5). Declaration o Conlicting Interests The author(s) declared no potential conlicts o interest with respect to the research, authorship, and/or publication o this article. Funding The author(s) received no inancial support or the research, authorship, and/or publication o this article. Reerences Baghani M, Naghdabadi R, Arghavani J, et al. () A thermodynamically-consistent D constitutive model or shape memory polymers. International Journal o Plasticity 5:. Barot G, Rao IJ and Rajagopal KR () A thermodynamic ramework or the modeling o crystallizable shape memory polymers. International Journal o Engineering Science : 5 5. Basit A, L Hostis G and Durand B () Multi-shape memory eect in shape memory polymer composites. Materials Letters 7:. Behl M and Lendlein A (7) Actively moving polymers. Sot Matter : 5 7. Chen J, Liu L, Liu Y, et al. () Thermoviscoelastic shape memory behavior or epoxy-shape memory polymer. Smart Materials and Structures : 555.

10 Guo et al. Chen Y-C and Lagoudas DC (a) A constitutive theory or shape memory polymers. Part I. Journal o the Mechanics and Physics o Solids 5: Chen Y-C and Lagoudas DC (b) A constitutive theory or shape memory polymers. Part II. Journal o the Mechanics and Physics o Solids 5: Diani J, Gilormini P, Frédy C, et al. () Predicting thermal shape memory o crosslinked polymer networks rom linear viscoelasticity. International Journal o Solids and Structures 9: Fei G, Li G, Wu L, et al. () A spatially and temporally controlled shape memory process or electrically conductive polymer carbon nanotube composites. Sot Matter : 5 5. Ghosh P and Srinivasa AR () A two-network thermomechanical model and parametric study o the response o shape memory polymers. Mechanics o Materials : 7. Guo X, Liu L, Liu Y, et al. () Constitutive model or a stress- and thermal-induced phase transition in a shape memory polymer. Smart Materials and Structures : 59. Hu J, Zhu Y, Huang H, et al. () Recent advances in shape-memory polymers: structure, mechanism, unctionality, modeling and applications. Progress in Polymer Science 7: 7 7. Leng J, Lan X, Liu Y, et al. () Shape-memory polymers and their composites: stimulus methods and applications. Progress in Materials Science 5: Liu Y, Du H, Liu L, et al. () Shape memory polymers and their composites in aerospace applications: a review. Smart Materials and Structures :. Liu Y, Gall K, Dunn ML, et al. () Thermomechanics o shape memory polymers: uniaxial experiments and constitutive modeling. International Journal o Plasticity : 79. Long KN, Dunn ML and Jerry Qi H () Mechanics o sot active materials with phase evolution. International Journal o Plasticity :. Meng H and Li G () A review o stimuli-responsive shape memory polymer composites. Polymer 5: 99. Meng Q and Hu J (9) A review o shape memory polymer composites and blends. Composites Part A: Applied Science and Manuacturing : 7. Nguyen T, Jerryqi H, Castro F, et al. () A thermoviscoelastic model or amorphous shape memory polymers: incorporating structural and stress relaxation. Journal o the Mechanics and Physics o Solids 5: 79. O Connell PA and McKenna GB (999) Arrhenius-type temperature dependence o the segmental relaxation below T g. The Journal o Chemical Physics : 5. Ratna D and Karger-Kocsis J (7) Recent advances in shape memory polymers and composites: a review. Journal o Materials Science : 5 9. Shim J and Mohr D () Rate dependent inite strain constitutive model o polyurea. International Journal o Plasticity 7:. Shojaei A and Li G () Viscoplasticity analysis o semicrystalline polymers: a multiscale approach within micromechanics ramework. International Journal o Plasticity : 9. Srivastava V, Chester SA and Anand L () Thermally actuated shape-memory polymers: experiments, theory, and numerical simulations. Journal o the Mechanics and Physics o Solids 5:. Tan Q, Liu L, Liu Y, et al. () Thermal mechanical constitutive model o iber reinorced shape memory polymer composite: based on bridging model. Composites Part A: Applied Science and Manuacturing :. Tobushi H, Hashimoto T, Hayashi S, et al. (997) Thermomechanical constitutive modeling in shape memory polymer o polyurethane series. Journal o Intelligent Material Systems and Structures : 7 7. Tobushi H, Okumura K, Endo M, et al. () Thermomechanical properties o polyurethane-shape memory polymer oam. Journal o Intelligent Material Systems and Structures : 7. Wei ZG, Sandstroröm R and Miyazaki M (99) Shape-memory materials and hybrid composites or smart systems. Part I: shape-memory materials. Journal o Materials Science : 7 7. Westbrook KK, Kao PH, Castro F, et al. () A D inite deormation constitutive model or amorphous shape memory polymers: a multi-branch modeling approach or nonequilibrium relaxation processes. Mechanics o Materials : 5 9. Xie T () Tunable polymer multi-shape memory eect. Nature : 7 7. Xu B, Fu YQ, Ahmad M, et al. () Thermo-mechanical properties o polystyrene-based shape memory nanocomposites. Journal o Materials Chemistry :. Yu K, Liu Y and Leng J () Shape memory polymer/cnt composites and their microwave induced shape memory behaviors. RSC Advances : 9 9. Yu K, Westbrook KK, Kao PH, et al. () Design considerations or shape memory polymer composites with magnetic particles. Journal o Composite Materials 7: 5. Yu K, Xie T, Leng J, et al. () Mechanisms o multi-shape memory eects and associated energy release in shape memory polymers. Sot Matter : Zhang P and Li G () Structural relaxation behavior o strain hardened shape memory polymer ibers or selhealing applications. Journal o Polymer Science Part B: Polymer Physics 5: