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<p>In this paper, we extend our study of the relaxation and homogenization of unbounded singular integral functionals, previously developed in Anza Hafsa et al. (AMBP 24:135–193, 2017; AA 74:123–134, 2011) where we examined the case of integrands whose quasiconvexification has polynomial growth. Here, we focus on the more general case where the quasiconvexification has convex growth. The distinguishing feature of this study is that such a singularity on the integrands is compatible with the fundamental constraint of hyperelasticity which says that compressing a volume of matter to a point requires an infinite amount of energy. However, our framework is not consistent with the constraint of noninterpenetration of matter.</p>

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New results on relaxation and homogenization of unbounded singular integrals

  • 期刊论文

  • 发表日期：

    2025年1月30日

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  • Omar Anza Hafsa,
  • Mohamed Lamine Leghmizi,
  • Jean-Philippe Mandallena

摘要

In this paper, we extend our study of the relaxation and homogenization of unbounded singular integral functionals, previously developed in Anza Hafsa et al. (AMBP 24:135–193, 2017; AA 74:123–134, 2011) where we examined the case of integrands whose quasiconvexification has polynomial growth. Here, we focus on the more general case where the quasiconvexification has convex growth. The distinguishing feature of this study is that such a singularity on the integrands is compatible with the fundamental constraint of hyperelasticity which says that compressing a volume of matter to a point requires an infinite amount of energy. However, our framework is not consistent with the constraint of noninterpenetration of matter.