Use of improved Westergaard stress functions to adequately simulate the stress field around crack tips

Elvis Yuri Mamani¹; Ney Augusto Dumont¹

¹ Pontifical Catholic University of Rio de Janeiro

doi:10.20906/CPS/CILAMCE2015-0840

Resumo

In the traditional boundary element methods, the numerical modeling of cracks is usually carried out by means of hypersingular fundamental solutions. A more natural procedure should make use of fundamental solutions (Green's functions) that represent the square-root singularity of the gradient field around the crack tip, which at most leads to improper integrals. Such a representation is best accomplished in a variationally-based framework that also addresses a convenient means of evaluating results at internal points. This is the subject of the present paper, with the use of generalized Westergaard stress functions for the numerical simulation of two-dimensional problems that may be completely unrelated to fracture mechanics. Problems of general topology can be modeled, such as in the case of unbounded and multiply-connected domains. The formulation is naturally applicable to notches and generally curved cracks. It also provides an easy means of approximating stress intensity factors. For a general-purpose code, Kelvin's and Westergaard-type fundamental solutions can be combined. It is shown that fundamental solutions corresponding to crack openings given by Hermitian polynomials lead to a better description of the stress field caused by a crack than as previously developed by the authors. A basic, validating numerical example is presented.

Palavras-chave: Hybrid boundary elements; Fracture mechanics; Generalized Westergaard functions; Variational methods