有限应变弹塑性力学中高对比度介质的均匀化
Homogenization of high-contrast media in finite-strain elastoplasticity
AI总结：
本文利用变分技术研究有限应变弹塑性高对比度复合材料的均匀化问题，克服软夹杂导致的强制性缺失，证明能量泛函的Γ-极限为两组件贡献之和，并得出能量最小化构型的收敛性。
摘要：
本研究致力于分析非弹性固体中内部变量与高对比度微结构之间的相互作用。作为一个具体案例，我们借助变分技术推导出弹塑性介质的宏观描述。具体而言，我们考虑一种复合材料，它通过用软夹杂填充周期性穿孔刚性基体中的空洞而获得。我们研究了当周期趋于零时相关能量泛函的Γ-收敛。主要挑战在于软部分材料特性的退化所导致的强制性缺失。我们证明了在合适的收敛概念下计算出的Γ-极限，是两个组件各自贡献的总和。最终，获得了能量最小化构型的收敛性。
英文摘要：
This work is devoted to the analysis of the interplay between internal variables and high-contrast microstructure in inelastic solids. As a concrete case-study, by means of variational techniques, we derive a macroscopic description for an elastoplastic medium. Specifically, we consider a composite obtained by filling the voids of a periodically perforated stiff matrix by soft inclusions. We study the $Γ$-convergence of the related energy functionals as the periodicity tends to zero. The main challenge is posed by the lack of coercivity brought about by the degeneracy of the material properties in the soft part. We prove that the $Γ$-limit, which we compute with respect to a suitable notion of convergence, is the sum of the contributions resulting from each of the two components separately. Eventually, convergence of the energy minimizing configurations is obtained.
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