A uniquely defined multiplicative elasto-plasticity model with orthotropic yield function and plastic spin

• Published in: Computer methods in applied mechanics and engineering Vol. 374; p. 113565
• Main Authors: Ulz, Manfred H., Celigoj, Christian C.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2021; Elsevier BV
• Subjects: Configurations; Elastoplasticity; Isotropic material; Mathematical models; Metal sheets; Multiplicative plasticity; Numerical models; Orientational evolution; Orthotropy; Plastic spin; Substructures; Tensors; Unique intermediate configuration; Yield criteria; Orientational evolution; Plastic spin; Unique intermediate configuration; Multiplicative plasticity; Orthotropy
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113565

A rate-independent model for isotropic elastic–orthotropic plastic material behaviour including the plastic spin is presented in this paper. The plastic spin, as introduced by Dafalias, is the spin of the continuum relative to the material substructure. The model is based on a specific multiplicative decomposition of the deformation gradient tensor, which introduces a uniquely defined intermediate configuration as motivated by Casey. We focus our attention on metal sheets in forming processes, in which pre-existing preferred orientations govern the orthotropic plastic behaviour. As a result, we advocate a Hill-type yield criterion enriched by the notion of plastic spin to describe this material behaviour. Our formulation yields three key findings: firstly, the uniquely defined intermediate configuration, namely a plastically stretched intermediate configuration, allows for a neat implementation of the plastic spin; secondly, the algorithmic formulation is straightforward and shows no additional difficulties in the implementation; and thirdly, a good agreement of our numerical model with experimental and numerical results from in-plane sheet forming processes reported in the literature is achieved. •We develop a novel implementation of the notion of plastic spin into a multiplicative elastoplasticity setting.•A uniquely defined intermediate configuration is utilised, namely a plastically stretched intermediate configuration.•The unique decomposition allows for a neat implementation of the plastic spin for a plasticity induced evolution of anisotropy.•General isotropic hyperelasticity and an orthotropic Hill-type plasticity are considered at finite strains.•We use experimental data to calibrate our model and demonstrate the model’s performance by in-plane sheet forming simulations.