Shape optimization of an elasto-plastic body for the model with strain- hardening

This article is concerned with shape optimization of structures made of a material obeying Hencky's laws of plasticity, with the stress bound expressed by the von Mises effective stress. The ill-posedness of the model is circumvented by using two regularized versions of the mechanical problem. The first one is the classical Perzyna formulation which is regularized, the second one is a new regularized formulation proposed for the von Mises criterion. Shape gradients are calculated thanks to the adjoint method. The optimal shape is numerically computed by using the level set method. To illustrate the validity of the method, 2D examples are performed.

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Topology Optimization for Incremental Elastoplasticity: A Phase-Field Approach

Almi¹,

Stefanelli²

2021

SIAM J. Control Optim.

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Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined design of the macroscopic mechanical piece and its underlying microstructure. In this context, we investigate a topology optimization problem for an elastic medium featuring a periodic microstructure. The optimization problem is variationally formulated as a bilevel minimization of phase-field type. By resorting to Γ -convergence techniques, we characterize the homogenized problem and investigate the corresponding sharp-interface limit. First-order optimality conditions are derived, both at the homogenized phase-field and at the sharp-interface level.

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Shape optimization of an elasto-plastic body for the model with strain- hardening

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Cited by 3 publications

References 4 publications

Shape optimization of elasto-plastic structures and continua

Shape optimization of elasto-plastic structures and continua

Elasto-plastic Shape Optimization Using the Level Set Method

Topology Optimization for Incremental Elastoplasticity: A Phase-Field Approach

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