<p>A micromorphic theory of elastoplasticity is developed within a Cauchy–Piola framework, following the first part, which was devoted to the purely elastic case. The formulation extends classical elastoplasticity to continua with microstructure by introducing independent microdistortion fields while preserving the geometric structure of standard continuum mechanics. Plastic evolution is described through mechanisms associated with microdomain reorganization and internal microstructural rearrangements, embedded in a unified energetic and variational setting. The resulting model provides a microscale continuum description of elastoplastic behavior without relying on scale separation, periodicity assumptions, or representative volume elements. A reduced elastic strain energy is obtained depending exclusively on the spatial variable, without exhibiting microscale coordinates, yielding a formulation defined on a single spatial domain and compatible with standard finite element discretizations. For a chosen material symmetry, the number of constitutive parameters is equal to that of classical continuum mechanics. The framework supports microscale analyses of elastoplastic response in heterogeneous and microstructured materials, including architectured metamaterials, polycrystalline media, and foams.</p>

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A Cauchy–Piola framework for micro-based micromorphic continua. Part II: a geometric theory of elastoplasticity

  • Gabriele La Valle,
  • Christian Soize

摘要

A micromorphic theory of elastoplasticity is developed within a Cauchy–Piola framework, following the first part, which was devoted to the purely elastic case. The formulation extends classical elastoplasticity to continua with microstructure by introducing independent microdistortion fields while preserving the geometric structure of standard continuum mechanics. Plastic evolution is described through mechanisms associated with microdomain reorganization and internal microstructural rearrangements, embedded in a unified energetic and variational setting. The resulting model provides a microscale continuum description of elastoplastic behavior without relying on scale separation, periodicity assumptions, or representative volume elements. A reduced elastic strain energy is obtained depending exclusively on the spatial variable, without exhibiting microscale coordinates, yielding a formulation defined on a single spatial domain and compatible with standard finite element discretizations. For a chosen material symmetry, the number of constitutive parameters is equal to that of classical continuum mechanics. The framework supports microscale analyses of elastoplastic response in heterogeneous and microstructured materials, including architectured metamaterials, polycrystalline media, and foams.