Abstract

A mixed initial-boundary value problem is formulated for linear thermo-elastic relaxed micromorphic continuum with asymmetric micro-distortion tensor, micro-dislocation tensor and temperature field. First, Lagrange identity involving two admissible processes at different instants for the considered mixed initial-boundary value problem is established. Using this identity, four theorems are proved: (i) uniqueness of solution without recourse either to an energy conservation law or to any boundedness assumptions on the thermoelastic coefficients, (ii) continuous dependence of solution of the problem on loads, (iii) continuous dependence of solution of the problem on the initial data, and (iv) reciprocity relation. The use of positive definiteness conditions on the thermoelastic coefficients is also avoided.

摘要

提出了具有不对称微变形张量，微位移张量和温度场的线性热弹性松弛微形连续体的混合初边值问题。首先，针对所考虑的混合初边值问题，建立了涉及不同时刻两个可允许过程的拉格朗日恒等式。使用该恒等式，证明了四个定理：（i）不求助于能量守恒定律或热弹性系数的任何有界性假设的解的唯一性；（ii）对载荷的问题求解的连续依赖性；（iii）连续的问题的解决方案对初始数据的依赖性，以及（iv）互惠关系。也避免在热弹性系数上使用正定性条件。