E.A. De Souza Neto, Djordje Perić and D.R.J. Owen
This work addresses the computational aspects of a model forelastoplastic damage at finite strains. The model is a modification of apreviously established model for large strain…
Abstract
This work addresses the computational aspects of a model for elastoplastic damage at finite strains. The model is a modification of a previously established model for large strain elastoplasticity described by Perić et al. which is here extended to include isotropic damage and kinematic hardening. Within the computational scheme, the constitutive equations are numerically integrated by an algorithm based on operator split methodology (elastic predictor—plastic corrector). The Newton—Raphson method is used to solve the discretized evolution equations in the plastic corrector stage. A numerical assessment of accuracy and stability of the integration algorithm is carried out based on iso‐error maps. To improve the stability of the local N—R scheme, the standard elastic predictor is replaced by improvedinitial estimates ensuring convergence for large increments. Several possibilities are explored and their effect on the stability of the N—R scheme is investigated. The finite element method is used in the approximation of the incremental equilibrium problem and the resulting equations are solved by the standard Newton—Raphson procedure. Two numerical examples are presented. The results are compared with those obtained by the original elastoplastic model.
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Andreas Heege, Pierre Alart and Eugenio Oñate
A consistent formulation for unilateral contact problems includingfrictional work hardening or softening is proposed. The approach is based onan augmented Lagrangian approach…
Abstract
A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach coupled to an implicit quasi‐static Finite Element Method. Analogous to classical work hardening theory in elasto‐plasticity, the frictional work is chosen as the internal variable for formulating the evolution of the friction convex. In order to facilitate the implementation of a wide range of phenomenological models, the friction coefficient is defined in a parametrised form in terms of Bernstein polynomials. Numerical simulation of a 3D deep‐drawing operation demonstrates the performance of the methods for predicting frictional contact phenomena in the case of large sliding paths including high curvatures.