Model For Shape Memory Polymers Research Articles

Constitutive model for shape memory polymer and its thermodynamic responses in finite element analysis.

As a new intelligent polymer material, shape memory polymer (SMP) was a potential orthodontic appliance material. This study aimed to investigate the thermodynamic responses of SMP under different loads via finite element analysis (FEA). FEA specimens with a specification of 0.1 × 0.1 × 1 mm were designed. One end of the specimen was fixed, and the other was subjected to displacement load. Different loading, cooling, and heating rates were separately exerted on the specimen in its shape recovery process and used to observe the responses of the SMP constitutive model. Furthermore, specimens with various tensile elongation and sectional areas were simulated and used to elucidate their effect on shape recovering force. The specimens obtained a similar stress of 0.5, 0.44, and 1.07 Mpa for different loading, cooling, and heating rates after a long time. The shape recovering force of specimen increased from 0.0102 to 0.0315 N when the elongation improved from 10% to 40% and to 0.0408 N when the sectional areas were expanded to 0.2 × 0.2 mm. The stiffness of SMP was small at a high temperature but large at a low temperature. The effects of the loading, cooling, and heating rates on SMP can be eliminated after a long time. Furthermore, it was possible to increase the recovering force by increasing the elongation or expanding the sectional area of the specimen. The force was quadratically dependent on the elongation ratio.

Thermodynamically-consistent constitutive modeling of moisture- and thermo-responsive shape memory polymers

Abstract Taking into account that shape memory polymer (SMP)-based devices are often subject to multiple environmental conditions during application, it is difficult to accurately predict their shape memory effect (SME). Thus, constitutive modeling for SMPs in multi-field environments is of great importance. However, most of the models available are limited to describing the temperature-driven SME and do not refer to multi-field conditions. In this paper, a constitutive model for SMPs in hygrothermal environments is developed under a consistent thermodynamic framework. The derivation is based on an additive decomposition of the Helmholtz free energy density and satisfying the first law and second law of thermodynamics. In this paper, the absorbed moisture is categorized into free and bound phases and it is considered that they have different effects on the material properties. Accordingly, it is the first time to study the variation of configurational entropy with different phases in the polymer–moisture system during the moisture diffusion process. For the first time, the validity of the constitutive model proposed in this paper can be confirmed by systematically comparing the modeling results and experimental data of various types of hygrothermal-induced shape memory cycles.

A 3D finite strain constitutive model for shape memory polymers combined viscoelasticity and storage strain

A 3D finite strain constitutive model combined viscoelasticity and storage strain for shape memory polymers (SMPs) is proposed. SMPs are phenomenally regarded as a homogeneous material of the viscoelastic glassy phase and hyperelastic rubbery phase in this model. Based on energy decomposition, the constitutive equation is derived using Clausius inequality and unified Helmholtz free energy. Then, an analytical expression for storage strain is presented, significantly simplifying the prediction of shape memory recovery process. The model is implemented in MATLAB and the commercial finite element software package ABAQUS using the UMAT subroutine. Our additional DMA tests and experimental data from the literature for various SMPs with different shape structures are used to verify the proposed model. All simulation results demonstrate the effectiveness of the proposed model in predicting the shape memory effect and complex thermomechanical behaviors of various SMPs.

A constitutive model of dual-component shape memory hybrids considering isothermal crystallization and debonding damage

The concept of shape memory hybrids (SMHs) has been proposed in recent years as a new kind of shape memory materials. By carefully selecting the actual composition of SMHs, some special features could be realized to meet the requirements of particular engineering applications. However, in terms of simulation, conventional constitutive models for shape memory polymers (SMPs) struggle to precisely characterize certain unique properties of these SMHs. In this study, a constitutive model integrating both rheology and phase transition conceptions is proposed to simulate the mechanical behaviors including shape memory effect of dual-component SMHs. The specific yielding phenomenon at room temperature of SMHs, induced by debonding between two components, is explained by incorporating particle-damage theory. Compared with the experimental and simulated results from a kind of SMH which can be programmed isothermally, it is indicated that the proposed constitutive model effectively captures the mechanical characteristics as well as the shape memory behaviors and the phenomenon of particle debonding damage of these SMHs. Furthermore, the influences of different parameters, such as component proportion, temperature, and isothermal shape fixing time, on these SMHs are discussed as well. This versatile model offers valuable insights for the development of constitutive models in this field as it is not limited to this case only, but could also be promoted to various different kinds of dual-component SMH systems.

A three-dimensional constitutive equation for shape memory polymer composites considering energy dissipation under single loading–unloading condition

Shape memory polymer composites (SMPCs), composed of shape memory polymers (SMPs) and fabrics, can recover their deformed shapes to initial configurations by changing temperature. The shape recovery energy of the SMPs and the elastic energy of the fabrics are regarded as key points to predict the restored configuration of the SMPCs. In this research, a three-dimensional constitutive equation for SMPCs is newly developed, considering the energy dissipation of fabrics under a single loading–unloading condition. The constitutive equation is derived from Mooney–Rivlin, viscoelastic, and stored strain energy models for SMPs, as well as polynomial functions for fabrics. The Mooney–Rivlin and viscoelastic models describe the time- and temperature-dependent hyperelastic properties, and the stored strain energy model can explain the shape recovery. The polynomial functions are newly proposed to take into account the dissipated energy of fabrics, such as residual deformation and hysteresis effect. Because the elastic energy of fabrics considerably influences the shape recovery of SMPCs, the proposed constitutive equation can accurately predict the recovered configuration. Analyses of SMPCs are conducted using the finite element method and validated by comparing them with the results obtained from experiments. The constitutive equation is used to analyze the shape recovery behaviors of an SMPC skin. The skin can be largely stretched, and the deformed shape can be restored to its initial shape by applying electricity. The SMPC skin is applied to a morphing flap, and its shape-changing behaviors are demonstrated experimentally.

A numerical approach for modeling response of shape memory polymer composite corrugated structure

This study presents a numerical framework for a unidirectional shape memory polymer-based composite (SMPC) corrugated structure. The framework combines an empirically modified constitutive model of shape memory polymer (SMP) with modified temperature-dependent laminate theory. Model parameters in the SMP constitutive relation are determined and calibrated from the dynamic mechanical analysis tests. Subsequently, the numerical implementation of the SMP model is validated with experimental results from the three-point bending test. This was followed by simulations to investigate the thermo-mechanical response of SMPC lamina. The findings from the simulations revealed the influence of SMPC fiber orientation and volume fraction on stored strain through the spring back effect. Finally, the framework is applied to investigate the shape memory response of a unidirectional SMPC trapezoidal corrugated structure. The simulations highlight the potential of the SMPC corrugated structure as a load bearing adaptive structure for wing morphing applications.

New perspective on the creep characteristic of fiber–dependent shape memory polymers: variable–order fractional constitutive model

With the aim of describing and explaining the creep tensile property of shape memory polymers (SMPs) better, a variable--order fractional creep constitutive model with fewer parameters and good simulation performance was constructed on the basis of existing constitutive models. The consists of a Hookean spring connected in series with a Newtonian dashpot was employed to propose a new variable--order fractional Maxwell model for SMPs. Drawing support from the Laplace transform, we derive the analytical solution of this novel model. The verification of the obtained theoretical results with the creep test data for different fiber weight fractions and stress levels available from the literature reveals their satisfactory agreement. It can be concluded that the developed variable--order fractional constitutive model can better describe the complex viscoelastic relationship of shape memory polymers which is difficult to be described by the classical integer order derivative, and obtain a more accurate constitutive model of shape memory polymers with fewer parameters.

A Modified Constitutive Model for Shape Memory Polymers Based on Nonlinear Thermo-Visco-Hyperelasticity with Application to Multi-Physics Problems

Shape memory polymers (SMPs) as a class of smart material have provided diverse attributes recently used in different applications. Raising the usage of SMPs, especially in more sensitive environments, such as the human body or similar high-risk circumstances, highlights the necessity of more accurate simulations. Suitable constitutive modeling is the foundation of an accurate simulation. Not only should such modeling consider precise details to diminish errors, but also it must provide a robust and powerful procedure to calibrate the material parameters. To achieve these goals, in this paper a modified constitutive model for SMPs based on the concept of internal state variables and rational thermodynamics is proposed in large deformation. Taking its basis from the nonlinear hyperelasticity and viscoelasticity, the model can provide a more accurate prediction of SMPs response. In comparison to other available constitutive models based on viscoelastic approach, the number of material parameters is smaller. Furthermore, performing a new approach for material parameters extraction, two different SMP materials were calibrated. The proposed model’s capability was assessed by comparing the model outputs with experimental results in diverse conditions such as different temperature rates and applied stretch ratios. The user-friendly implementation process of this model in multi-physics software based on the finite element method can be counted as another advantage of the proposed model. Hence, to simulate smart systems containing SMP elements, three multi-physics analyses in various fields and conditions were performed, and the importance of conducting such multi-physics phenomena has been discussed.

Photo-induced spatiotemporal bending of shape memory polymer beams

In response to external stimuli, such as heat, light, or magnetic fields, stimuli-responsive soft materials can change their current configuration to a new equilibrium state through non-equilibrium kinetic processes, including reaction, diffusion, and viscoelastic relaxation, which generates novel spatiotemporal shape-morphing behavior. Using a photothermal shape memory polymer (SMP) cantilever beam as a model system, this work analytically, numerically, and experimentally studies its non-equilibrium kinetic processes and spatiotemporal bending under light illumination. We establish a thermomechanical model for SMPs capturing the concurrent non-equilibrium processes of heat transfer and viscoelastic relaxation, which induces inhomogeneous temperature and strain distributions through the thickness of the beam, resulting in its bending and unbending. By varying the key dimensionless parameters, we theoretically and experimentally observe different types of bending dynamics. Moreover, our theory takes into consideration changes in the angles of incidence caused by extensive beam bending, and demonstrates that this effect can dramatically delay the bending due to reduction of the effective light intensity, which is further validated experimentally. This work demonstrates programmable and predictable spatiotemporal morphing of SMPs, and provides design guidelines for SMP morphing structures and robots.

Deep learning for predicting the thermomechanical behavior of shape memory polymers

Thermomechanical constitutive modeling is essential for shape memory polymers (SMPs) to be used in engineering structures and devices. However, the classical method of deriving constitutive models is difficult, time consuming, and relies heavily on trial and error. In this work, we aim to decrease the time and resources needed to develop new thermomechanical models for SMPs. The method proposed in this work uses deep learning (DL) to predict the thermomechanical behavior of SMPs under thermomechanical cycles. Particularly, a semicrystalline two-way shape memory polymer (2W-SMP) is selected as an example. Predicting such behavior will give insight on the SMP properties and help validate its characteristics. In this paper, we have compared several DL models to find which one can predict the experimental thermomechanical behavior with the highest accuracy within a reasonable time frame. The results reveal that the fully connected neural network (FCNN) and the convolutional neural network (CNN) were the most accurate DL models. Overall, using one of the selected DL models, we can predict the results of new iterations of the experiment without spending as much time and resources.

Insight in thermomechanical constitutive modeling of shape memory polymers

Shape memory polymers (SMPs) are a new member of the smart materials family. SMPs have found wide applications or potential applications in almost all manmade structures and devices. In order to better design smart structures and devices using SMPs, thermomechanical constitutive modeling is essential. In this insight paper, we will focus on presenting several multi-length-scale and multi-physics modeling frameworks, including the thermodynamics consistent model, elasto-viscoplastic model, statistical mechanics model, and phase evaluation law model. The SMPs modeled will include amorphous one-way shape memory polymers, semicrystalline one-way shape memory polymers, semicrystalline two-way shape memory polymers, and functional and mechanical damage effects on SMPs. Finally, we will give some in-depth perspectives on future development in this area of study.

Tutorial: Thermomechanical constitutive modeling of shape memory polymers

Shape memory polymers (SMPs) are one of the intriguing functional materials and have been widely and intensively studied. In order to apply these new polymers to load bearing engineering structures and devices, developing physics-based thermomechanical constitutive models is mandatory. The aim of this Tutorial is to demonstrate how to establish a thermomechanical constitutive model for SMPs. It begins with classifications of SMPs, followed by a discussion on the underlying physics for different SMPs. After that, three classical SMP thermomechanical modeling frameworks are introduced, which include the visco-elasto-plastic based rheological framework, the storage strain-based phase transition framework, and the representative unit cell based multi-branch framework. Next, three commonly adopted new model establishment methods are presented within these frameworks with detailed examples. Finally, future perspectives on this research direction are discussed. We hope that this Tutorial will help readers understand the roadmap from physics to mathematical modeling of SMPs.

A thermodynamic constitutive model for shape memory polymers based on phase transition

Shape memory polymers (SMPs) are a type of soft smart materials that can recover from the pre-deformed shape to the original shape under different external stimuli. Existing constitutive models fail to describe SME of SMPs under large and complex deformation. Based on thermodynamics and phase transition, we develop a constitutive model related to the deformation gradient and temperature for thermal-induced SMPs. A phenomenological expression of the stored deformation is introduced into the free-energy function to describe SME of SMPs. To verify the proposed model, we first compare our model with the literature experiments. Good consistency between our model and experimental results can be found out. We further carry out the experiments for a 3D printing SMP to investigate the availability of the model. The results demonstrate that the proposed model is effective to describe SME of SMPs under finite deformation. The proposed model can provide insights on describing SME of SMPs.

Electro-thermo-mechanical modeling of shape memory polymers filled with nano-carbon powder

Generally, adding the electroconductive fillers into the polymer matrix is a popular approach to endow the shape memory polymers (SMPs) with electroconductivity. Therefore, the shape memory effects (SMEs) of thermally induced SMPs can also be triggered by the electrical current. In essence, both the thermally activated and electrically activated SMEs share the same driving mechanism without considering the effect of heat conduction. In the paper, the constitutive model for the thermally induced SMPs filled with nano-carbon powder is briefly introduced. Then, a modified model is developed to characterize the effects of filler, deformation, and moisture on the electrical conductivity for the first time. After developing the correlation of electric field with Joule heat, the simulation is executed to display the free recovery of the shape memory polymer composites (SMPCs) with different filler content. It is found that the recovery ratio decreases with the increase of carbon powders for the SMPCs with filler content above the percolation threshold. Besides, a good recovery ratio can also be achieved through the application of a lower voltage.

Study on carbon nanotube/shape memory polymer composites and their applications in wireless worm actuator

Abstract In this study, the surface of the carbon nanotubes was modified by chemical functionalization. The carbon nanotubes were placed in a mixed acid solution with a nitric acid-to-sulfuric acid volume ratio of 1:3. The results of the functionalization of the carbon nanotubes were investigated by controlling the reaction time. From the experimental results, the functionalized carbon nanotubes with a reaction time of 12 hours show good dispersibility. In the study of the essential characteristics of composite materials, it was observed that the tensile strength decreased with increase of carbon nanotube content. Compared with the result of the tensile strength test, it can be found that with increasing carbon nanotube content, the microwave heating and shape recovery speed are greatly improved. The experimental results show that the shape memory polymer composite with 4 wt% carbon nanotubes has the fastest microwave heating rate, so it takes only 2 minutes to achieve complete shape recovery. Finally, this study used shape memory polymer composites doped with 4 wt% carbon nanotubes as the driving end, combined with an elastic structure made of polyimide (PI) film using origami techniques to form a worm actuator. In the test, the system could move a distance of 6 mm forward during a microwave time of 1 minute. In addition, this research also constructed a physical model of shape memory polymer and explored the simple movement mechanism of the system.

A hygro-thermo-mechanical constitutive model for shape memory polymers filled with nano-carbon powder

ABSTRACT The nano-carbon powders are often used as fillers to endow the shape memory polymers (SMPs) with electroconductivity. It has been found that the shape memory effects (SMEs) of SMPs filled with nano-carbon powder can be triggered both by temperature and by water. To reveal the driving mechanism of SMEs, a constitutive model for describing the thermally activated and moisture activated SMEs of these shape memory polymer composite (SMPCs) is developed here. Because both of the SMEs share the same driving mechanism, the variable moisture is incorporated into the framework of a thermo-mechanical modeling approach to disclose the effect of moisture on the thermoviscoelastic properties. The SMPCs are regarded as isotropic materials and the effect of carbon powder on the mechanical properties of the matrix is also considered in the paper. Because the complete recovery may not be reached even they are exposed to the stimulus environment long enough, the blocking mechanism is also considered here. This is the mainly new contribution compared to the early work. Using the method of parameter determination presented here, the effectiveness of the proposed hygro-thermo-mechanical constitutive model is confirmed by comparing the model results with the test data of uniaxial deformation from the literature.

Three-dimensional constitutive model for shape-memory polymers considering temperature-rate dependent behavior

The temperature-rate dependent thermomechanical behavior of shape-memory polymers (SMPs) is challenging to study, because the microstructure of SMPs cannot rearrange instantaneously to an equilibrium configuration in response to temperature changes. Herein, we report a temperature-rate dependent three-dimensional constitutive model for SMPs based on a two-phase model consisting of rubbery and glassy phases. To describe the effect of temperature rate on SMPs, the variation of the volume fraction of each phase affected by temperature was considered under different temperature-rate conditions. Additionally, the temperature-rate dependent thermal strain was incorporated into the two-phase model. The developed constitutive model was validated by simulating the shape-memory behavior of SMPs, and by comparing the simulation and experimental results under different temperature-rate conditions.

Computational Design of Self-Actuated Deformable Solids via Shape Memory Material

The emerging 4D printing techniques open new horizons for fabricating self-actuated deformable objects by combing strength of 3D printing and stimuli-responsive shape memory materials. This article focuses on designing self-actuated deformable solids for 4D printing such that a solid can be programmed into a temporary shape and later recovers to its original shape after heating. To avoid a high material cost, we choose a dual-material strategy that mixes an expensive thermo-responsive shape memory polymer (SMP) material with a common elastic material, which however leads to undesired deformation at the shape programming stage. We model this shape programming process as two elastic models with different parameters linked by a median shape based on customizing a constitutive model of thermo-responsive SMPs. Taking this material modeling as a foundation, we formulate our design problem as a nonconvex optimization to find the distribution of SMP materials over the whole object as well as the median shape, and develop an efficient and parallelizable method to solve it. We show that our proposed approach is able to design self-actuated deformable objects that cannot be achieved by state of the art approaches, and demonstrate their usefulness with three example applications.

A hygro-thermo-mechanical constitutive model for hygrothermally activated shape memory polymers under finite deformations

With regard to the application of shape memory polymers (SMPs) in smart structures, it is difficult to accurately predict their shape memory effects (SMEs) triggered by various external environments. Therefore, developing constitutive models for SMPs in multi-field environments is crucial. In this paper, a hygro-thermo-mechanical finite deformation constitutive model incorporated with structural relaxation and moisture diffusion is proposed for hygrothermally activated amorphous SMPs. One of the main novelties is that for the first time an internal state variable modeling approach is used in the model to describe the structural relaxation of hygrothermally activated SMPs in the vicinity of the glass transition. The other novelty is that the theory of moisture diffusion is applied to split the absorbed moisture into the mobile (free) and bound phases, and their respective effects on the hygro-thermo-mechanical behavior are also considered in the model. Comparisons between the model results and the test data for both, thermally activated and moisture-activated SMEs, present a good agreement.

3D phase-evolution-based thermomechanical constitutive model of shape memory polymer with finite element implementation

3D phase-evolution-based thermomechanical constitutive model of shape memory polymer with finite element implementation