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Mathematical Problems in Engineering
Volume 2017, Article ID 3861526, 14 pages
https://doi.org/10.1155/2017/3861526
Research Article

Simplified Qualitative Discrete Numerical Model to Determine Cracking Pattern in Brittle Materials by Means of Finite Element Method

1Departamento de Ingeniería Mecánica, Fundación Universidad de América, Bogotá, Colombia
2Departamento de Ingeniería Mecánica y Mecatrónica, Universidad Nacional de Colombia, Bogotá, Colombia
3Departamento de Ingeniería Civil y Agrícola, Universidad Nacional de Colombia, Bogotá, Colombia
4Universidad Politécnica de Cataluña, Barcelona, Spain

Correspondence should be addressed to J. Ochoa-Avendaño; oc.ude.lanu@aaohcofj

Received 16 March 2017; Accepted 31 May 2017; Published 2 July 2017

Academic Editor: Fabrizio Greco

Copyright © 2017 J. Ochoa-Avendaño et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents the formulation, implementation, and validation of a simplified qualitative model to determine the crack path of solids considering static loads, infinitesimal strain, and plane stress condition. This model is based on finite element method with a special meshing technique, where nonlinear link elements are included between the faces of the linear triangular elements. The stiffness loss of some link elements represents the crack opening. Three experimental tests of bending beams are simulated, where the cracking pattern calculated with the proposed numerical model is similar to experimental result. The advantages of the proposed model compared to discrete crack approaches with interface elements can be the implementation simplicity, the numerical stability, and the very low computational cost. The simulation with greater values of the initial stiffness of the link elements does not affect the discontinuity path and the stability of the numerical solution. The exploded mesh procedure presented in this model avoids a complex nonlinear analysis and regenerative or adaptive meshes.