SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1070-1087, January 2021.
We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of the pressure in the deformed configuration. We also provide a convex relaxation of the problem together with its dual formulation, based on measure valued mappings, which coincides with the original problem under our condition.

中文翻译：

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非线性弹性问题中的隐凸性

SIAM数学分析杂志，第53卷，第1期，第1070-1087页，2021年1月。
我们在一般情况下研究可压缩和不可压缩的非线性弹性变化问题。我们的主要结果就变形构造中压力的凸度特性而言，为平衡成为全局能量最小化提供了充分的条件。我们还基于度量值映射提供了问题的凸松弛及其对偶表示，这与我们条件下的原始问题一致。