FEM/BEM formulation for multi-scale analysis of stretched plates. (May 2015)

• Record Type: Journal Article
• Authors: Fernandes, G.R.; Pituba, J.J.C.; de Souza Neto, E.A.
• Is Part Of: Engineering analysis with boundary elements. Volume 54(2015:May)
• Page Start: 47
• Page End: 59
• Publication Date: 2015-05
• Subjects: Multi-scale modelling -- Homogenisation -- Boundary elements -- Stretching plate problem; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2015.01.005
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: A multi-scale modelling for analysing the stretching problem of plates composed of heterogeneous materials is presented. The BEM (Boundary Element Method) is adopted to model the macro-continuum (represented by the plate) while the equilibrium problem at micro-scale (represented by the Representative Volume Element – RVE) is solved by a FEM (Finite Element Method) formulation that takes into account the Hill–Mandel Principle of Macro-Homogeneity. After solving the equilibrium problem of the RVE, the micro-to-macro transition is made by applying the volume averaging hypothesis of strain and stress tensors. Some numerical examples are then analysed to show that the proposed formulation is a suitable tool for the analysis of stretched of plates composed of heterogeneous materials. To define the microstructure, different RVEs composed of an elasto-plastic matrix with inclusions or voids are considered. Besides, a quadratic rate of asymptotic convergence of the Newton–Raphson scheme has been achieved during the iterative procedure.