Estratégias baseadas na partição da unidade para simulação do comportamento de meios parcialmente frágeis

Abstract

Meshfree Methods have been used as alternatives to the Finite Element Method, due to their flexibility in building conforming approximations. Another attractive feature is the capacity of obtaining approximate solutions of high regularity. Such characteristics can be successfully used to describe state variables based on derivatives of the problem solution and responsible for representing the nonlinear behavior of structures made of quasi-brittle material. On the other hand, the lack of the Kronecker-delta property, a more complex computation of the shape functions, and numerical integration issues represent drawbacks that can overburden the computational analysis. In a nonlinear analysis, the processing time becomes an important issue to be considered. Aiming to conciliate the efficiency of the finite element analysis with the flexibility of meshfree methods, coupling techniques for both methods have been proposed, especially in cases where the nonlinear phenomenon is confined in a small part of the structure. Here, a new coupling strategy based on the Global-local Generalized Finite Element Method (GFEM-gl) to simulate damage propagation in quasi-brittle media is proposed. The global domain of the structure is represented by a coarse mesh of finite elements. The region of damage propagation defines the local domain, represented by a set of nodes of the meshfree approach called Element Free Galerkin Method (EFG). This local discretization is responsible for providing a numerically obtained function used to enrich the approximate solution of the global problem. Numerical examples in two-dimensional domain are presented to discuss how the meshfree method can efficiently describe the damage propagation, while the global behavior of the structure is represented by the enriched finite element solution.