Abstract

In our present paper, we approach the mixed problem with initial and boundary conditions, in the context of thermoelasticity without energy dissipation of bodies with a dipolar structure. Our first result is a reciprocal relation for the mixed problem which is reformulated by including the initial data into the field equations. Then, we deduce a generalization of Gurtin’s variational principle, which covers our generalized theory for bodies with a dipolar structure. It is important to emphasize that both results are obtained in a very general context, namely that of anisotropic and inhomogeneous environments, having a center of symmetry at each point.

中文翻译：

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在不耗散偶极子能量的情况下，热固弹性的Gurtin变分原理的一般化

摘要

在本文中，我们在不考虑偶极结构体能量耗散的情况下，在热弹性的情况下研究了具有初始条件和边界条件的混合问题。我们的第一个结果是混合问题的倒数关系，该问题通过将初始数据包括在场方程中来重新公式化。然后，我们推导了古尔丁变分原理的推广，涵盖了我们对偶极结构体的推广理论。必须强调的是，这两个结果都是在非常普遍的情况下获得的，即各向异性和不均匀环境的结果，每个点都有一个对称中心。