Open Access

ARTICLE

Size Effects and Mesh Independence in Dynamic Fracture Analysis of Brittle Materials

by Letícia Fleck Fadel Miguel¹, Ignacio Iturrioz², Jorge Daniel Riera³

1 Department of Mechanical Engineering, UFRGS, Porto Alegre, Brazil. letffm@ufrgs.br
2 Department of Mechanical Eng., UFRGS, Porto Alegre, Brazil. ignacio@mecanica.ufrgs.br
3 Department of Civil Engineering, UFRGS, Porto Alegre, Brazil. jorge.riera@ufrgs.br

Computer Modeling in Engineering & Sciences 2010, 56(1), 1-16. https://doi.org/10.3970/cmes.2010.056.001

Abstract

Numerical predictions of the failure load of large structures, accounting for size effects, require the adoption of appropriate constitutive relations. These relations depend on the size of the elements and on the correlation lengths of the random fields that describe material properties. The authors proposed earlier expressions for the tensile stress-strain relation of concrete, whose parameters are related to standard properties of the material, such as Young's modulus or specific fracture energy and to size. Simulations conducted for a typical concrete showed that as size increases, the effective stress-strain diagram becomes increasingly linear, with a sudden rupture, while at the same time the coefficients of variation (CV) of the relevant parameters decrease to negligible values, situation that renders Linear Elastic Fracture Mechanics (LEFM) applicable. However, it was later observed that a hitherto unknown problem arises in the analysis of non-homogeneous materials, leading to lack of mesh objectivity: the need to know a priori the degree of fracturing. This should affect not only the truss-like Discrete Element Method (DEM) employed herein, but also finite element analysis, requiring a careful evaluation of the energy dissipated by fracture or other mechanisms in the course of the loading process. In the paper a tentative criterion is proposed to account for the effect in non-linear dynamic fracture analysis.

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Keywords

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