Multiscale Modelling of the Two-Dimensional Problem Using the Boundary Element Method

Autores

  • Gabriela Rezende Fernandes Federal University of Catalão (UFCAT)
  • Guilherme Bassi da Silva Pontes São Paulo State University – UNESP
  • Vitor Nascimento Oliveira Federal University of Catalão (UFCAT)

DOI:

https://doi.org/10.55592/cilamce.v6i06.8176

Palavras-chave:

Multi-scale modelling, RVE, boundary elements

Resumo

A full coupled multi-scale modelling using the Boundary Element Method for analysing the 2D problem of stretched plates composed of heterogeneous materials, where dissipative phenomena can be considered, is presented. Both the macro-scale and the micro-scale are modelled by BEM formulations where the consistent tangent operator (CTO) is used to achieve the equilibrium of the iterative procedures (see [1]). The equilibrium equation of the plate (macro-continuum) is written in terms of in-plane strains while the equilibrium problem of the microstructure, which is defined by the RVE (Representative Volume Element), is solved in terms of displacements fluctuations (see [2]-[5]). In this kind of modelling, the mechanical behaviour of the material is governed by the homogenized response of the RVE, obtained after solving its equilibrium problem. As this kind of modelling is expensive computationally, it is important to investigate other numerical methods to have faster formulations, but which are still accurate. To validate the presented model, the numerical results are compared to the ones where the material microstructure (RVE) is modelled by the FEM.
REFERENCES
[1] G. R. Fernandes and E. A. de Souza Neto, Self-consistent linearization of non-linear BEM formulations with quadratic convergence, Computational Mechanics, vol. 52, pp. 1125-1139, 2013.
[2] G. R. Fernandes, L. H. R. Crozariol, A. S. Furtado and M. C. Santos, A 2D boundary element method to model the constitutive behavior of heterogeneous microstructures considering dissipative phenomena Engineering Analysis with Boundary Elements, vol. 99, pp. 1-22, 2019.
[3] G. R. Fernandes, J. J. C. Pituba and E. A. de Souza Neto, FEM/BEM formulation for multi-scale analysis of stretched plates, Engineering Analysis with Boundary Elements, vol. 54, pp. 47-59, 2015.
[4] D. Peric, E. A. de Souza Neto, R. A. Feijóo, M. Partovi and A. J. C. Molina, On micro to macro transitions for multi scale analysis of non linear heterogeneous materials: unified variational basis and finite element implementation, Numerical Methods in Engineering, vol. 87, pp. 149-170, 2011.
[5] Somer D.D., de Souza Neto E.A., Dettmer W.G., Peric D., A sub-stepping scheme for multi-scale analysis of solids, Comput. Methods Appl. Mech. Engrg., v. 198, p. 10061016, 2009.

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Publicado

2024-12-02

Edição

Seção

Boundary element and mesh-reduced methods