Journal of Applied & Computational Mathematics

Boundary Element Method and Tangent Operator Technique applied in the Multi Crack Propagation Modelling of Concrete Structures

Abstract

Ferreira Cordeiro SG and Leonel ED

The cohesive crack model has demonstrated its accuracy in the simulation of crack growth phenomena in concrete structures. Moreover, the Boundary Element Method (BEM) is recognised as a robust and efficient numerical technique for addressing fracture problems. In this context, the present study aims at coupling the cohesive crack model to a BEM formulation to simulate the mechanical behaviour of cracked concrete structure. The cohesive cracks are modelled mechanically through the sub-region BEM approach. Because the tractions values along the fractured interfaces depend on the crack opening displacements, this problem is solved in the context of nonlinear solutions. The nonlinear system of equations is solved using the Tangent Operator (TO) technique, in which tangent prevision and tangent correction steps are required. Such scheme assures better convergence and accuracy than the classical Newton approach. The determination of the TO terms is the main contribution of this study. To validate the proposed formulation, it was applied in the simulation of crack growth in concrete structures. The results achieved were compared to numerical and experimental responses available in the literature. Apart from the strong agreement among the results obtained, faster convergence was verified using TO instead of the classical scheme.