Computational analysis of quasi-brittle fracture in fibre reinforced cementitious composites

Abstract

Prediction of quasi-brittle behaviour of structural components from fibre reinforced composites under mechanical loads should incorporate such physical processes as elastic, resp. plastic deformation, crack initiation, crack propagation in a matrix, pull out of fibres and rupture of fibres. The computational model for the practically most important case of cementitious composites containing short intentionally or quasi-randomly oriented steel, ceramic, resp. polymeric fibres with its primary import of suppression of tensile stresses in a matrix will be introduced. Its numerical approach relies on the modified eXtended Finite Element Method, open to the implementation of the cohesive traction separation law. This paper introduces the implementation of some integral-type nonlocal constitutive strain-stress relation. It pays attention namely to the Eringen model for the generation of the multiplicative damage factor, to the related quasi-static analysis, to the existence of a weak solution of the corresponding boundary and initial value problem with a parabolic system of partial differential equation and to the convergence of an algorithm based on 3 types of Rothe sequences. Thus, the article combines the possibilities of the two procedures for modeling crack propagation. Microstructural behavior is contained in the Eringen model, the effect of macro behavior in modified finite element method XFEM.