Model For Shape Memory Polymers Research Articles

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

As a kind of smart materials, shape memory polymer has covered broad applications for its shape memory effect. Precise description of the mechanical behaviors of shape memory polymer has been an urgent problem. Since the phase transition was a continuous time-dependent process, shape memory polymer was composed of several individual transition phases. Owing to the forming and dissolving of individual phases with the change in temperature, shape memory effect emerged. In this research, shape memory polymer was divided into different kinds of phases including frozen and active phases for its thermodynamics properties. Based on the viscoelasticity theory and phase transition theories, a new constitutive model for 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 fraction in shape memory polymer during heating or cooling process.

A simplified constitutive model for predicting shape memory polymers deformation behavior

Shape memory polymers (SMPs) can keep a temporary shape after pre-deformation at a higher temperature and subsequent cooling. When they are reheated, their original shapes can be recovered. Such special characteristics of SMPs make them widely used in aerospace structures, biomedical devices, functional textiles and other devices. Increasing usefulness of SMPs motivates us to further understand their thermomechanical properties and deformation behavior, of which the development of appropriate constitutive models for SMPs is imperative. There is much work in literatures that address constitutive models of the thermo-mechanical coupling in SMPs. However, due to their complex forms, it is difficult to apply these constitutive models in the real world. In this paper, a three-element model with simple form is proposed to investigate the thermo-mechanical small strain (within 10%) behavior of polyurethane under uniaxial tension. Two different cases of heated recovery are considered: (1) unconstrained free strain recovery and (2) stress recovery under full constraint at a strain level fixed during low temperature unloading. To validate the model, simulated and predicted results are compared with Tobushi's experimental results and good agreement can be observed.

Vibration behaviors of hybrid smart composites with SMA strips reinforced SMP lamina under blast loading

The dynamic responses of a hybrid smart composite incorporating shape memory alloys (SMAs) and shape memory polymers (SMPs) being exposed to blast loading are investigated. In order to use new and higher functions by combining the excellent qualities of both SMAs and SMPs, SMA strips reinforced with SMP lamina are sandwiched and adhered between two identical carbon fibers reinforced plastic. The recovery force of the SMA strips and the viscoelasticity of SMPs are applied to mitigate structural vibration induced by blast loading. Constitutive models for SMA strips and SMPs are established to observe their thermomechanical behaviors. Experimental tests of the SMAs and the SMPs are analyzed to acquire the parameters needed for the models. The responses of the hybrid smart composite panel are compared with those of the conventional composite panel taking into consideration the weight of the panels as the crucial design parameter for a fair comparison.

Development of a finite strain two-network model for shape memory polymers using QR decomposition

The aim of this paper is to develop a thermodynamically consistent finite deformation continuum model to simulate the thermomechanical response of shape memory polymers (SMPs). The SMP is modeled as a thermoviscoelastic material whose response in a thermomechanical cycle is modeled as a combination of a rubbery (viscoelastic) and a glassy (elastic) network in series. The activation criterion for the breakage of temporary network junctions is governed by a temperature dependent rate equation (akin to a thermal Bauschinger effect). We further show how the decomposition of the deformation gradient into an upper triangular matrix and a rotation (the QR) decomposition can be used instead of the more traditional polar (RU) decomposition in the development of models for such materials with persistent configurational changes. Such a decomposition has both physical meaning as well as computational advantages due to their convenient structure. Using these assumptions, we propose a specific form for the Helmholtz potential and the rate of dissipation. The model is simple (deliberately ignoring some aspects such as anisotropy that affect the quantitative but not the qualitative response features) and is able to capture the major phenomena of interest in SMPs. The efficacy of the resulting model, which is in a state evolution form, is demonstrated by comparing with published experimental data for simple shear. We study the response of the SMP model for monotonic shear deformation, different deformation rates as well as cyclic shear deformation at different temperatures. Comparisons with experiments show good agreement. Finally, we implement the thermomechanical cycle under shear deformations and study the behavior of the model.

A finite deformation constitutive model for shape memory polymers based on Hencky strain

In many engineering applications, shape memory polymers (SMPs) usually undergo arbitrary thermomechanical loadings at finite deformation. Thus, development of 3D constitutive models for SMPs within the finite deformation regime has attracted a great deal of interest. In this paper, based on the classical framework of thermodynamics of irreversible processes, employing the logarithmic (or Hencky) strain as a more physical measure of strain, a 3D large-strain macromechanical model is presented. In the constitutive model development, we adopt a multiplicative decomposition of the deformation gradient into elastic and stored parts. In addition, employing the averaging scheme, the logarithmic elastic strain tensor is decomposed into the rubbery and glassy parts. The evolution equations for internal variables are introduced for both cooling and heating processes. The time-discrete form of the proposed model in the implicit form is also presented. Comparing the predicted results with experimental data reported in the literature, the model is validated. Finally, using the finite element method, two boundary value problems e.g., a 3D beam and a medical stent made of SMPs are numerically simulated.

Micromechanical model of shape memory polymer including temperature-strain history dependence

Shape memory polymers (SMPs) have thermomechanical property drastically altering around the glass-transition temperature (Tg), temporary shape fixity and shape recovery property, and so on. To understand the mechanisms of such unique properties and design products including SMPs optimally, a mathematical model which is simple yet can represent these properties reasonably and accurately is necessary. Especially, it is important for the model to be able to consider the effect of temperature and strain history on the properties because the properties are considered to depend on not only the temperature and the strain themselves but also their history. Therefore, in this paper first the effect of the temperature and strain history on the shape fixity and shape recovery properties was examined. Then, a micromechanical model of SMP was developed to describe this effect. This model consisted of a lot of unit elements having four springs, two dash pots, one latch, and one thermal expansion element. Different Tg was assigned to each element because Tg depends on local condition inside of SMP and distributed in general. It was found from the experiment that the temperature and strain history applied to SMP when the shape is gradually frozen has an influence on the shape recovery process. With respect to the model, it was shown that the proposed micromechanical model can capture the thermomechanical behaviors of SMP and, especially, the temperature and strain histories dependence on the shape recovery process quite well.

Analytical study on torsion of shape-memory-polymer prismatic bars with rectangular cross-sections

In this paper, the response of shape memory polymer (SMP) bars with rectangular cross-sections under torsional loadings is analytically studied. To this end, we first reduce the recently proposed small-strain 3D phenomenological constitutive model for SMPs to the shear case. Then, an analytical solution for torsional response of SMP rectangular bars in a full cycle of stress-free strain recovery is derived. We also implement the 3D constitutive equations in a finite element program and simulate a full cycle of stress-free strain recovery of a rectangular SMP bar. Analytical and numerical results are then compared showing that the analytical solution gives, besides the global load–deflection response, accurate stress distributions in the cross-section of the rectangular SMP bar. Some case studies are also presented to show the validity of the presented analytical method. Results are compared with the experimental data recently reported in the literature which showing an agreement between the predicted results and experiments. The analytical solution can also be used for analysis of helical springs in which both the curvature and pitch effects are negligible. This is the case for helical springs with large ratios of mean coil radius to the cross-sectional equivalent radius (spring index) and also small pitch angles. Using this solution simplifies the analysis of the helical springs to that of the torsion of a straight bar with rectangular cross-section.

Thermomechanical behavior of a two-way shape memory composite actuator

Shape memory polymers (SMPs) are a class of smart materials that can fix a temporary shape and recover to their permanent (original) shape in response to an environmental stimulus such as heat, electricity, or irradiation, among others. Most SMPs developed in the past can only demonstrate the so-called one-way shape memory effect; i.e., one programming step can only yield one shape memory cycle. Recently, one of the authors (Mather) developed a SMP that exhibits both one-way shape memory (1W-SM) and two-way shape memory (2W-SM) effects (with the assistance of an external load). This SMP was further used to develop a free-standing composite actuator with a nonlinear reversible actuation under thermal cycling. In this paper, a theoretical model for the PCO SMP based composite actuator was developed to investigate its thermomechanical behavior and the mechanisms for the observed phenomena during the actuation cycles, and to provide insight into how to improve the design.

On response functions in linear thermoelastic models of shape memory polymers

AbstractThis paper is concerned with the broad class of Liner Thermoelastic (LTE) models for Shape Memory Polymers (SMPs) which unifies numerous constitutive theories proposed in the literature for this kind of smart material. It is shown that the response functions for the general model of this class may be determined directly from experimental data measured in standard thermomechanical cyclic tests. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Multi‐phase modeling of shape memory polymers

AbstractIn the present work, we propose a model for shape memory polymers based on the idea of the multiplicative decomposition of the deformation gradient. Evolution equations for the several deformation components are presented that provide for the storage of the entropy‐elastic strain and its recovery during the transition between the frozen phase and the active phase. First characteristic shape memory cycles for small and large deformations will be shown as a last point. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Development and implementation of a beam theory model for shape memory polymers

In this paper we focus on the development of a beam theory for a small strain continuum model of thermoviscoelastic shape memory polymers (SMP). Rather than a history integral model that is common for viscoelastic materials, a thermodynamically based state evolution model developed by Ghosh and Srinivasa (2011a) is used as the basis for the beam model based on the Euler–Bernoulli beam theory. An example of a three-point bend test is simulated using the beam theory model. The numerical solution is implemented by using an operator split technique that utilizes an elastic predictor and dissipative corrector. The key idea is that the elastic predictor is based on the solution to a beam theory boundary value problem while the dissipative corrector is entirely local (and hence can be parallelized) and is applied by considering the beam as a two or three dimensional body. This enables a very rapid solution of the problem yet maintaining fidelity of the distribution of inelastic strains across the cross-section. A displacement based convergence criterion is used in each time step. This algorithm is validated by using a three-point bending experiment for three different material cases: elastic, plastic and thermoplastic response. Time step convergence and mesh density convergence studies are carried out for the thermoviscoelastic FEM model. Finally, we implement and study this model for a SMP beam undergoing three-point bending strain recovery and stress recovery thermomechanical loading.

A thermodynamically-consistent 3 D constitutive model for shape memory polymers

The ever increasing applications of shape memory polymers have motivated the development of appropriate constitutive models for these materials. In this work, we present a 3D constitutive model for shape memory polymers under time-dependent multiaxial thermomechanical loadings in the small strain regime. The derivation is based on an additive decomposition of the strain into six parts and satisfying the second law of thermodynamics in Clausius–Duhem inequality form. In the constitutive model, the evolution laws for internal variables are derived during both cooling and heating thermomechanical loadings. The viscous effects are also fully accounted for in the proposed model. Further, we present the time-discrete form of the evolution equations in the implicit form. The model is validated by comparing the predicted results with different experimental data reported in the literature. Finally, using the finite element method, we solve two boundary value problems e.g., a 3D beam and a medical stent made of shape memory polymers.

A constitutive model for shape memory polymers with application to torsion of prismatic bars

In this article, satisfying the second law of thermodynamics, we present a 3D constitutive model for shape memory polymers. The model is based on an additive decomposition of the strain into four parts. Also, evolution laws for internal variables during both cooling and heating processes are proposed. Since temperature has considerable effect on the shape memory polymer behavior, for simulation of a shape memory polymer–based structure, it is required to perform a heat-transfer analysis. Commonly, an experimentally observed temperature rate–dependent behavior of shape memory polymers is justified by a rate-dependent glassy temperature, but using the heat-transfer analysis, it is shown that the glassy temperature could be considered as a constant material parameter. To this end, implementing the constitutive model within a nonlinear finite element code, we simulate torsion of a shape memory polymer rectangular bar and a circular tube. Moreover, we compare the predicted results with experimental data recently reported in the literature, which shows a good agreement.

A torsion test for the study of the large deformation recovery of shape memory polymers

A torsion device was designed and built for testing the shape fixity and shape recovery of shape memory polymers at large deformations. A simple thermal chamber was used to regulate the thermal environment during testing and a CCD camera was used for recording the deformation. Such a torsion testing system provided a quantitative estimate of the kinematics and kinetics of shape recovery for samples submitted to large deformations at moderate strains that are more likely to be expected in actual shape memory applications. In addition, such measurements are complementary to those obtained from large strain uniaxial tension tests usually used during traditional shape memory effect characterization. As a result, the torsional shape memory testing device and testing method described is expected to contribute to building complementary data for the thermomechanical modeling of shape memory polymers.

A macro-mechanical constitutive model for shape memory polymer

It is of theoretical and engineering interest to establish a macro-mechanical constitutive model of the shape memory polymer (SMP), which includes the mechanical constitutive equation and the material parameter function, from the viewpoint of practical application. In this paper, a new three-dimensional macro-mechanical constitutive equation, which describes the mechanical behaviors associated with the shape memory effect of SMP, is developed based on solid mechanics and the viscoelasticity theorem. According to the results of the DMA test, a new material parameter function is established to express the relationship of the material parameters and temperature during the glass transition of SMP. The new macro-mechanical constitutive equation and material parameter function are used to numerically simulate the process producing the shape memory effect of SMP, which includes deforming at high temperature, stress freezing, unloading at low temperature and shape recovery. They are also used to investigate and analyze the influences of loading rate and temperature change rate on the thermo-mechanical behaviors of SMP. The numerical results and the comparisons with Zhou’s material parameter function and Tobushi’s mechanical constitutive equation illustrate that the proposed three-dimensional macro-mechanical constitutive model can effectively predict the thermo-mechanical behaviors of SMP under the state of complex stress.

Constitutive modeling of shape memory polymer based self-healing syntactic foam

In a previous study, it was found that the shape memory functionality of a shape memory polymer based syntactic foam can be utilized to self-seal impact damage repeatedly, efficiently, and almost autonomously [Li G., John M., 2008. A self-healing smart syntactic foam under multiple impacts. Comp. Sci. Technol. 68(15–16), 3337–3343]. The purpose of this study is to develop a thermodynamics based constitutive model to predict the thermomechanical behavior of the smart foam. First, based on DMA tests and FTIR tests, the foam is perceived as a three-phase composite with interfacial transition zone (interphase) coated microballoons dispersed in the shape memory polymer (SMP) matrix; for simplicity, it is assumed to be an equivalent two-phase composite by dispersing elastic microballoons into an equivalent SMP matrix. Second, the equivalent SMP matrix is phenomenologically assumed to consist of an active (rubbery) phase and a frozen (glassy) phase following Liu et al. [Liu, Y., Gall, K., Dunn, M.L., Greenberg, A.R., Diani J., 2006. Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modeling. Int. J. Plasticity 22, 279–313]. The phase transition between these two phases is through the change of the volume fraction of each phase and it captures the thermomechanical behavior of the foam. The time rate effect is also considered by using rheological models. With some parameters determined by additional experimental testing, the prediction by this model is in good agreement with the 1D test result found in the literature. Parametric studies are also conducted using the constitutive model, which provide guidance for future design of this novel self-healing syntactic foam and a class of light-weight composite sandwich structures.

A Thermoviscoelastic Approach for Modeling Shape Memory Polymers

AbstractThis paper presents a thermoviscoelastic model for shape memory polymers (SMPs). The model has been developed base on the hypothesis that structural and stress relaxation are the primary shape memory mechanisms of crosslinked, glassy SMP, and that consideration of these mechanisms is essential for predicting the time-dependence of the shape memory response. Comparisons with experiments show that the model can reproduce the rate-dependent strain-temperature and stress-strain response of a crossslinked, glassy SMP. The model also captures many important features of the temperature and time dependence of the free strain recovery and constrained stress recovery response.

Finite strain 3D thermoviscoelastic constitutive model for shape memory polymers

AbstractA 3D thermoviscoelastic model is proposed to represent the thermomechanical behavior of shape memory polymers. The model is based on a physical understanding of the material behavior and a mechanical interpretation of the stress–strain–temperature changes observed during thermomechanical loading. The model is thermodynamically motivated and is formulated in a finite strain framework in order to account for large strain deformations. Model predictions capture critical features of shape memory polymer deformation and, in some cases, provide very favorable comparisons with experimental results. POLYM. ENG. SCI. 46:486–492, 2006. © 2006 Society of Plastics Engineers.

Thermomechanical constitutive model of shape memory polymer

A nonlinear thermomechanical constitutive model of shape memory polymer (SMP) is developed by modifying a linear model. The coefficients in the model are expressed by the single exponential functions of temperature in order to describe the variation in mechanical properties of the material due to the glass transition. The proposed theory expresses well the thermomechanical properties of polyurethane-shape memory polymer, such as shape fixity, shape recovery and recovery stress. The proposed model is useful for design of shape-memory polymer elements.

Analysis of the isothermal mechanical response of a shape memory polymer rheological model

AbstractIn this paper, we derive the isothermal mechanical response of a 4‐element rheological model for shape memory polymers (SMP) in the context of (i) constant stress, (ii) constant strain, (iii) constant stress rate, (iv) constant strain rate, (v) periodic strain. The effect of shape memory strain (modeled by a friction element) and the temperature dependence of the material properties on the SMP response are examined for a polyurethane shape memory polymer of the polyester polypole series. In particular, it is possible to identify a threshold frequency during periodic loading, near which the damping capacity of the SMP is strongly affected by an increasing shape memory strain. On the other hand, when the applied frequency is much greater than the threshold value, an increasing shape memory strain ceases to have any effect on the damping. It is also shown that at a given frequency (significantly greater than the threshold value), the damping capacity as a function of temperature attains a maximum. While this maximum value is frequency‐dependent (being inversely proportional), the temperature at which the maximum is attained is frequency‐independent, and is analytically shown to be the glass transition temperature.