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Stress rate formulation for elastoplastic models with internal variables based on augmented Lagrangian regularisation

Abstract : The constitutive laws of elasto-plasticity with internal variables are described through the definition of suitable dual potentials, which include various hardening models. A family of variational principles for inelastic problems is obtained using convex analysis tools. The structural problem is analysed using the complementary energy (Prager-Hodge) functional. The functional is regularised introducing an Augmented Lagrangian Regularisation for the indicator function of the elastic domain so that a smooth optimisation problem is obtained. In the numerical solution the discretised problem is reformulated in a finite step form using a fully implicit integration scheme and the functional is redefined in the space of the self-equilibrated nodal stresses, after enforcing satisfaction of the equilibrium equations in a weak form. Numerical tests have shown good performance on the part of the algorithm, which approaches the converged solution for a considerably smaller number of elements as compared with other algorithms. The method is equally available for perfect or hardening plasticity.
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Massimo Cuomo, Loredana Contrafatto. Stress rate formulation for elastoplastic models with internal variables based on augmented Lagrangian regularisation. International Journal of Solids and Structures, Elsevier, 2000, 37, pp.3935 - 3964. ⟨hal-00913269⟩

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