Beyond polyconvexity: an existence result for a class of quasiconvex hyperelastic materials
Beyond polyconvexity: an existence result for a class of quasiconvex hyperelastic materials
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超越多凸性：一类拟凸超弹性材料的存在结果
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发表时间：
2017
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通讯作者：
M. Schneider
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文献类型：
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作者：
M. Schneider
本文给出了一类满足材料不可穿透性条件的拟凸储能函数的存在性结果，这主要阻碍了经典技术从向量变分到非线性弹性力学的应用。可逆性的基本概念是以欧拉和拉格朗日观点所固有的基本二元性为特征的非线性弹性理论的起点。在这一概念的启发下，分裂拟凸存储能量函数表现出了从数学角度非常隐含的性质。例如，任何具有有限能量的函数都自动是Sobolev同胚；极小子的存在是容易建立的，并且第一变分公式成立。版权所有©2016 John Wiley&Sons，Ltd.
This article contains an existence result for a class of quasiconvex stored energy functions satisfying the material non‐interpenetrability condition, which primarily obstructs applying classical techniques from the vectorial calculus of variations to nonlinear elasticity. The fundamental concept of reversibility serves as the starting point for a theory of nonlinear elasticity featuring the basic duality inherent to the Eulerian and Lagrangian points of view. Motivated by this concept, split‐quasiconvex stored energy functions are shown to exhibit properties, which are very alluding from a mathematical point of view. For instance, any function with finite energy is automatically a Sobolev homeomorphism; existence of minimizers can be readily established and first variation formulae hold. Copyright © 2016 John Wiley & Sons, Ltd.