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A 2D Boundary Element Method (BEM) Formulation to obtain the constitutive response of heterogeneous materials based on the Representative Volume Element (RVE) concept is developed to deal with dissipative phenomena over the domain and the phase debonding on the interface zone. Despite the formulation is written within a multiscale framework, in this work the analyses are performed only at microstructure level, but if a full coupled multiscale analysis is performed the computational cost becomes very expensive. Usually this kind of modelling is performed considering the Finite Element Method (FEM), but it is important to find other numerical solutions which are less expensive, but still accurate. To analyse metal matrix composites the RVEs are assumed to contain a ductile matrix, rigid inclusions and an interface zone where the phase debonding is modelled by a cohesive fracture model using embedded cohesive contact finite elements into the boundary element mesh. The RVE domain is discretized into cells to compute the domain integral written in terms of the inelastic forces, which have a part related to the plasticity phenomenon and another one referred to the cohesive-contact problem. The homogenized results are compared to a FEM model in order to validate the proposed formulation. [ABSTRACT FROM AUTHOR]

Abstract A boundary element formulation to obtain the constitutive response of heterogeneous microstructures is proposed, considering a RVE-based multiscale theory. The sub-region technique is adopted to model the RVE (Representative Volume Element), where voids and inclusions can be defined inside the matrix and different elastic properties and constitutive models can be assumed for each phase. Triangular cells are adopted to approximate the dissipative forces over the RVE domain, where they are assumed constant. After a strain vector is imposed to the microstructure boundary, its elastic forces field is obtained and the respective strain field computed. Then, according to the RVE-based multiscale theory, the RVE equilibrium problem must be solved what requires an iterative procedure to find the displacement fluctuations field that auto-equilibrates the microstructure stress field. After the RVE solution, the boundary tractions must be recalculated to consider the displacement fluctuations field as well as the dissipative forces. Then, from the boundary tractions the homogenized stress vector can be computed. The homogenized constitutive tensor is evaluated considering the constitutive tensors of all cell nodes and also the consistent tangent operator. To validate the proposed model, the homogenized responses of different microstructures are compared to the responses obtained via finite element model. [ABSTRACT FROM AUTHOR]

Abstract: In this work, a plate bending formulation of the boundary element method (BEM) based on the Reissner''s hypothesis to perform linear analysis of plates reinforced by rectangular beams is extended to consider the beams not displayed over their middle surface. Therefore eccentricity effects are taken into account. The building floor structure is modelled as a stiffened plate which is treated as a single body without dividing it into beam and plate elements. Moreover the equilibrium and compatibility conditions are automatically imposed by the integral equations. In the proposed model the final system of equation is obtained by coupling the bending problem to the stretching problem. Besides, in order to reduce the number of degrees of freedom, both the displacements and tractions are approximated along the beam width, leading to a model where the values are defined on the beams axis. In order to validate the proposed formulation, the numerical results are compared to a well know finite element code. [Copyright &y& Elsevier]