Polymers of two-way shape memory effects (SMEs) are of great application potential ranging from intelligent actuators to artificial muscles due to their reversible shape response on the basis of an on-off stimulus such as a cooling-heating cycle, which motivates the development of theoretical tools to support their design. In the paper, a three-dimensional phase transition finite deformation constitutive model is proposed to phenomenologically describe the underlying mechanisms of the one-way and two-way SMEs in thermal-responsive semi-crystalline polymers. A unified transition equation is proposed to depict the volume changes of crystalline phase during both crystallization and melting transitions. The crystallization-induced elongation and melting-induced contraction behaviours in two-way SMEs are assumed to be realized by an elongation-contraction element and its temperature-dependent strain evolution rules. The overall constitutive model is then implemented into Mathematica, and the model predictions are compared to and agree well with the experimental results. The paper provides an efficient method on modeling the thermal-induced two-way SMEs under stress conditions in semi-crystalline polymers and detailed discussion about the influence of several parameters such as the crosslinking density, the applied external load and the cooling/heating rate.

This paper presents intensive studies on the strain rate-, hold time-, and temperature-dependent cyclic behaviors of amorphous shape memory polymers (SMPs). The cyclic characteristics play a vital role in the application of SMPs since the materials suffer cyclic loadings commonly in engineering. A multi-branch fractional derivative model is employed in the paper to investigate the complicated mechanisms underlying the cyclic behaviors. And a modified Eying model is incorporated with the fractional derivative model to describe the temperature-dependent yielding and post-yielding behaviors. A rate-dependent yielding factor is proposed in the study to depict the influence of strain rates. The validity and adaptability of the model are verified through comparisons between the simulations and experimental results of two different materials subjected to different loading conditions. In addition, detailed parameter studies provide effective suggestions on improving the performance of SMPs under various conditions.

Nanocomposites based on a shape memory polymer matrix are emerging smart materials of great application potential due to their high deformability and good shape memory performance as well as decent mechanical properties. In the paper, a detailed theoretical study on the thermoviscoelastic behaviors and shape memory effects of multiwall carbon nanotubes (MWCNT) reinforced epoxy nanocomposites is presented. Different from the traditional shape memory cycle procedure, both the loading and memory processes in the study are programmed below the glass transition temperature, which is so-called cold deformation. A novel network transition constitutive model incorporated with a micro-mechanics model to determine the effective properties of the nanocomposites is proposed to study the underlying stress relaxation and shape memory mechanisms. The involved parameters are determined from standard thermomechanical experiments. Then we implement the model into Mathematica to predict the thermomechanical behaviors of both the neat and filled shape memory polymers subjected to different programming conditions, and the simulation results show good agreement with the experimental results. Moreover, the shape memory properties of the material as well as the influence of MWCNT on the material behavior are discussed in detail.

Four-dimensional (4D) printing has emerged as a branch of additive manufacturing that utilizes stimuli-responsive materials to generate three-dimensional structures with functional features. In this context, constitutive models play a paramount role in designing engineering structures and devices using 4D printing, as they help understand mechanical behavior and material responses to external stimuli, providing a theoretical framework for predicting and analyzing their deformation and shape-shifting capabilities. This article thoroughly discusses available constitutive models for single-printed and multi-printed materials. Later, we explore the role of machine learning (ML) algorithms in inferring constitutive relations, particularly in viscoelastic problems and, more recently, in shape memory polymers. Moreover, challenges and opportunities presented by both approaches for predicting the mechanical behavior of 4D printed polymer materials are examined. Finally, we concluded our discussion with a summary and some future perspectives expected in this field. This review aims to open a dialogue among the mechanics community to assess the limitations of analytical models and encourage the responsible use of emerging techniques, such as ML. By clarifying these aspects, we intend to advance the understanding and application of constitutive models in the rapidly growing field of 4D printing.

A new thermomechanical network transition constitutive model is proposed in the study to describe the viscoelastic behavior of shape memory polymers (SMPs). Based on the microstructure of semi-crystalline SMPs, a new simplified transformation equation is proposed to describe the transform of transient networks. And the generalized fractional Maxwell model is introduced in the paper to estimate the temperature-dependent storage modulus. In addition, a neo-KAHR theory with multiple discrete relaxation processes is put forward to study the structural relaxation of the nonlinear thermal strain in cooling/heating processes. The evolution equations of the time- and temperature-dependent stress and strain response are developed. In the model, the thermodynamical and mechanical characteristics of SMPs in the typical thermomechanical cycle are described clearly and the irreversible deformation is studied in detail. Finally, the typical thermomechanical cycles are simulated using the present constitutive model, and the simulation results agree well with the experimental results.