Thermoelasticity with phase transitions for 4D printing: diffuse interface models and mathematical analysis

Four dimensional (4D) printing refers to the newly developed field derived from 3D printing that fabricates objects using stimulus-responsive smart materials. These objects are capable of morphing into different configurations in response to various environmental stimuli, leading to structures with potential for self-assembly and multifunctionality. The shape-shifting behavior comes from the smart materials, such as shape memory alloys and shape memory polymers, which can be trained to memorize and cycle through multiple configurations.

Although numerous working proofs of concepts have demonstrated promising capabilities in soft robotics, medical implants, textile, construction and automotive industries, 4D printing has yet to be part of the mainstream in manufacturing, as the transformations of the smart materials become less reliable over prolong usage. Such issues can be mitigated by developing 4D printing designs utilizing a mixture of different smart materials, and thus there is currently a pressing need to understand the interactions between different smart materials and how they influence the mechanical behavior of the overall structure.

In this proposal we plan to develop new mathematical models for thermally activated shape memory polymers (SMP) that can exhibit phase transitions, which is one of the more commonly used stimulus-responsive materials in 4D printing. The novelty of our approach is to describe the phase transition from one type of SMP to a second type with a diffuse interface ansatz. The resulting thermoelastic models seem to be amenable to further theoretical investigations, which motivates us to perform mathematical analysis for settings associated to specific types of elastic deformations (such as bending, elongation and twisting) that constitute the standard shape-shifting behaviors encountered in 4D printing applications. We envision the proposed models and accompanying analysis can contribute towards resolving other challenges in this fastgrowing interdisciplinary field.