In view of recent developments in advanced manufacturing and nanomaterial technologies, which have enabled realization of novel material architectures at small-scale, a mixed variational temperature-dependent rate-dependent thermo-viscoplastic continuum element is proposed and developed for elastic, plastic, and thermal wave propagation problems. The variational scheme is based on a Hamiltonian approach, while for the temporal and spatial discretization scheme a discrete calculus of variations approach is adopted. Within this framework, an exponential temperature dependence for material properties and second sound effects is included. The developed framework sets the foundations that can lead to new class of temperature dependent models for capturing thermoplastic behavior and wave propagation of different materials. The robustness of the proposed variational approach, and aspects of coupled dynamic temperature-dependent thermoplastic response are demonstrated through several case studies. Applications include elastic, plastic, and thermal wave propagation and reflection in semi-infinite and finite length space at small temporal scales.

鉴于先进制造和纳米材料技术的最新发展已实现了小规模新型材料结构的实现，提出并开发了一种用于弹性，塑料和热的混合变率依赖于速率的热粘塑性连续体元素。波传播问题。变分方案基于哈密顿方法，而对于时间和空间离散化方案，则采用离散变分方法。在此框架内，包括了材料特性和第二声音效果的指数温度依赖性。所开发的框架奠定了基础，可以导致新一类的温度相关模型来捕获热塑性行为和不同材料的波传播。通过几个案例研究，证明了所提出的变型方法的鲁棒性以及耦合的依赖温度的动态热塑性响应的各个方面。应用包括弹性波，塑性波和热波在小时间尺度上在半无限和有限长度空间中的传播和反射。