Numerical evaluation of failure theories for brittle materials

This paper will concentrate on the problem-the numerical evaluation of failure theories. The theories can be divided into two categories: those that incorporate volume integrals and those that use surface integrals. For complex geometries and stress states, the integrals are usually calculated by postprocessing the results from a finite element analysis. A common method is to use the centroidal stresses, which are assumed uniform throughout an element. For surface-type failures, shell elements are commonly employed in the analysis. However, it will be shown in the paper that by adopting a different integration procedure, Gaussian Quadrature, results can be obtained more accurately and efficiently. This requires the sampling of stresses at various Gauss points within an element. Also, the use of shell elements to evaluate the surface integrals will be shown to be unnecessary. In both cases, the quality of the results in terms of accuracy and speed of convergence with respect to the number of elements and the number of stress-sampling points will be considered for a range of failure theories and a wide range of component shapes. It will be shown that by using the postprocessor written by the authors, the errors are generally less than those associated with finite element analysis.