Mixed Mode Fracture Modeling of Concrete Using a Modified Coulomb Law

Luciani N. Lens, Eduardo Bittencourt, Virgínia M. R. d’Avila


A 2D model for plain concrete that considers discrete cracks is here proposed. Zero thickness cohesive surface elements are introduced between all adjacent finite elements. Mixed-mode rupture can be captured using a modified Coulomb’s law. The classical zero thickness cohesive model was here modified in order to partially eliminate mesh dependency.
In this work, some well-known Mode I post-peak constitutive equations used in discrete fracture methodologies for concrete, are implemented in the cohesive surface method. The shape of these equations changes overall results and is linked with the development of the process zone. Pre-peak of
the equations was modified in order to reduce mesh dependency. On the other side, Mode II constitutive equations and properties are not well known or defined in general. This issue is addressed here and a modified Coulomb’s law is proposed to deal with mixed mode cases. The methodology is
simple and, besides pure Mode I fracture properties, requires only the definition of a coupling factor between Mode I and II. An elastic-predictor and plastic-correct type of algorithm is used to define cohesive surface tractions. Results presented here are only preliminary but show that the methodology is able to capture correctly crack morphology as well as peak load in a simple 4 point double notched beam.

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