An implicit numerical integration algorithm for Bai & Wierzbicki (2007) elasto-plastic model

Lucival Malcher, Francisco M. Andrade Pires, José M.A. César De Sá, Filipe X.C. Andrade

Department of Mechanical Engineering, Faculty of Engineering, University of Porto,Rua Dr. Roberto Frias, Porto 4200-465, Portugal.

DOI:

https://doi.org/10.7494/cmms.2009.2.0247

Abstract:

This contribution describes an implicit algorithm for numerical integration of a recently proposed model for metal plasticity and fracture [2]. The constitutive equations of the material model critically include both the effect of pressure through the triaxiality ratio and the effect of third deviatoric stress invariant through the lode angle in the description of material. These effects are directly introduced on the hardening rule of the material. The theoretical basis of the material model is presented in the first part of the paper. Then, the necessary steps required to implement the model within an implicit quasi-static finite element environment are discussed. In particular, the stress update procedure, which is based on the so-called operator split concept resulting in the standard elastic predictor/return mapping algorithm, and the computation of tangent matrix consistent with the stress update are described. Finally, the simulation of a flat grooved specimen subjected to tension [1] is presented to illustrate the robustness and efficiency of the proposed algorithm.

Cite as:

Malcher, L., Pires, F., De Sá, J. & Andrade, F. (2009). An implicit numerical integration algorithm for Bai & Wierzbicki (2007) elasto-plastic model. Computer Methods in Materials Science, 9(2), 309 – 315. https://doi.org/10.7494/cmms.2009.2.0247

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