On the numerical integration in G/XFEM analysis for physically nonlinear problems and cohesive crack propagation

Resumo

This work presents a novel methodology to deal with some drawbacks related to crack propagation
in physically nonlinear problems in the context of the Generalized Finite Element Method (GFEM). The GFEM
associates Finite Element Method shape functions to local approximation functions that describe, for example,
the discontinuity from Fracture Mechanics cohesive crack problems. In this case, numerical integration must be
adapted for properly dealing with the non-polynomial integrand of the weak form of the boundary value problem.

A common alternative to consider the discontinuity is the employment of the subdivision of elements, in the inte-
gration points are changed according to the cited strategy. Although a very efficient procedure in linear problems,

it leads to the loss of the state constitutive variables history, responsible for indicating the degradation level in
physically nonlinear materials. A new strategy is here proposed, based on the nonlocal approach to recover the

evolution of the state constitutive variables in the integration points. A numerical example is provided to vali-
date and prove the efficiency of the proposed methodology. The computational implementation and analysis are

performed in the open source software INSANE (Interactive Structural Analysis Environment), developed by the
Structural Engineering Department of Federal University of Minas Gerais.