大应变扩散下带电弹性体的动力学
Dynamics of charged elastic bodies under diffusion at large strains
摘要：
我们提出了一个模型，在大应变单极排斥长程（静电）相互作用的弹性或多孔弹性体的动力学。我们的模型尊重（仅）局部的非自互穿条件，但可以应付可能的全球自互穿，从而产生一定的理由，大多数工程计算忽略这些影响的弹性结构的分析。这些模型必须结合拉格朗日（物质）描述与欧拉（实际）演变的配置随时间演变。采用非局部非简单材料的概念，应用Lipschitz-连续映射的变量变换公式，并借助于Healey和Kroemer的结果，利用形变梯度行列式的正性，研究动力学问题.
英文摘要：
We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope with possible global self-interpenetration, yielding thus a certain justification of most of engineering calculations which ignore these effects in the analysis of elastic structures. These models necessarily combine Lagrangian (material) description with Eulerian (actual) evolving configuration evolving in time. Dynamical problems are studied by adopting the concept of nonlocal nonsimple materials, applying the change of variables formula for Lipschitz-continuous mappings, and relying on the positivity of the determinant of the deformation gradient thanks to a result by Healey and Kroemer.
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