惯性热粘弹性材料的率无关损伤
Rate-independent damage in thermo-viscoelastic materials with inertia
摘要：
本文提出了一个考虑惯性和热效应的粘弹性材料的率无关、单向、部分损伤模型。损伤过程是通过一个内部变量，由速率无关的流动规则。热方程和动量平衡的位移耦合在一个高度非线性的方式。我们对相应的能量泛函的假设也包括Ambrosio-Tortorelli相场模型的情况下（没有通过脆性极限）。我们讨论了一个合适的弱制定和证明的存在性定理的援助（部分）解耦的时间离散计划和变分收敛方法。我们还进行了渐近分析，为零的粘度和惯性，并获得一个完全率无关的位移和损伤的极限模型，这是独立于温度。
英文摘要：
We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is independent of temperature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
