The constitutive laws of elasto-plasticity with internal variables are described through the de®nition 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 ®nite step form using a fully implicit integration scheme and the functional is rede®ned 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.
Stress Rate Formulation for Elastoplastic Models with Internal Variables Based on Augmented Lagrangian Regularisation
CUOMO M;CONTRAFATTO, Loredana Caterina
2000-01-01
Abstract
The constitutive laws of elasto-plasticity with internal variables are described through the de®nition 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 ®nite step form using a fully implicit integration scheme and the functional is rede®ned 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.File | Dimensione | Formato | |
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