Analysis of heterogeneous microstructures by the Boundary Element Method considering plasticity
Luis Henrique R. Crozariol1; Amanda S. Furtado2; Matheus C. dos Santos2; Gabriela R. Fernandes2
1 UNESP -FEIS- Faculdade de Engenharia de Ilha Solteira; 2 Federal University of Goias - UFG
doi:10.20906/CPS/CILAMCE2017-0043
Resumo
A formulation of the Boundary Element Method (BEM) to perform elasto-plastic analysis of heterogeneous microstructures is presented. Inside the matrix can be defined voids or inclusions with different elastic properties and governed by different constitutive models. The microstructure is modelled by a zoned plate, where different values of Poisson's ratio and Young's modulus can be defined for each sub-region. To solve the domain integrals written in terms of in-plane displacements or plastic forces, the matrix and inclusions domains have to be discretized into cells where the displacements and forces are approximated. Thus, in this model, besides the boundary values for in-plane displacements and tractions, nodal values of in-plane displacements and plastic forces are defined in the domain. In the microstructure or RVE (representative volume element) the displacement field is defined as a sum of a linear part plus the displacement fluctuation, being its non-linear problem solved in terms of displacement fluctuations. Adopting homogenization techniques, the homogenized values for stress and constitutive tensor can be computed after solving the RVE equilibrium problem. In a future work, the multi-scale analysis could be performed using only the Boundary Element Method by coupling the proposed formulation to a BEM model adopted for the macro-continuum. Some numerical examples are presented whose results are compared to a finite element code to show the model accuracy.
Palavras-chave: boundary elements; stretching problem; zoned plates; Multi-scale analysis; plasticity; homogenization techniques