Morphoelastic bodies are elastic materials that undergo complex shape changes due to intrinsic growth, remodelling, or active internal processes. In a theoretical context, these materials are typically represented by non-Euclidean material manifolds characterized by an evolving metric structure. In this work, we formulate remodelling on such manifolds through a gradient system, where the inertialess dynamics of the system are driven by the steepest descent of an energy functional within an appropriate metric space. We obtain a gradient flow equation by combining isotropic non-linear elasticity with growth-induced dissipative mechanisms and illustrate the formalism through numerical simulations of stress relaxation at fixed strain.

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A Gradient Structure for Isotropic Non-linear Morphoelastic Bodies

  • Adam Ouzeri

摘要

Morphoelastic bodies are elastic materials that undergo complex shape changes due to intrinsic growth, remodelling, or active internal processes. In a theoretical context, these materials are typically represented by non-Euclidean material manifolds characterized by an evolving metric structure. In this work, we formulate remodelling on such manifolds through a gradient system, where the inertialess dynamics of the system are driven by the steepest descent of an energy functional within an appropriate metric space. We obtain a gradient flow equation by combining isotropic non-linear elasticity with growth-induced dissipative mechanisms and illustrate the formalism through numerical simulations of stress relaxation at fixed strain.