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Materials 2017, 10(4), 434; doi:10.3390/ma10040434

Strain Localization of Elastic-Damaging Frictional-Cohesive Materials: Analytical Results and Numerical Verification

1
State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 510641, China
2
CIMNE, Technical University of Catalonia, Edificio C1, Campus Norte, Jordi Girona 1-3, 08034 Barcelona, Spain
*
Author to whom correspondence should be addressed.
Received: 9 March 2017 / Revised: 1 April 2017 / Accepted: 18 April 2017 / Published: 20 April 2017
(This article belongs to the Special Issue Computational Mechanics of Cohesive-Frictional Materials)
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Abstract

Damage-induced strain softening is of vital importance for the modeling of localized failure in frictional-cohesive materials. This paper addresses strain localization of damaging solids and the resulting consistent frictional-cohesive crack models. As a supplement to the framework recently established for stress-based continuum material models in rate form (Wu and Cervera 2015, 2016), several classical strain-based damage models, expressed usually in total and secant format, are considered. Upon strain localization of such damaging solids, Maxwell’s kinematics of a strong (or regularized) discontinuity has to be reproduced by the inelastic damage strains, which are defined by a bounded characteristic tensor and an unbounded scalar related to the damage variable. This kinematic constraint yields a set of nonlinear equations from which the discontinuity orientation and damage-type localized cohesive relations can be derived. It is found that for the “Simó and Ju 1987” isotropic damage model, the localization angles and the resulting cohesive model heavily depend on lateral deformations usually ignored in classical crack models for quasi-brittle solids. To remedy this inconsistency, a modified damage model is proposed. Its strain localization analysis naturally results in a consistent frictional-cohesive crack model of damage type, which can be regularized as a classical smeared crack model. The analytical results are numerically verified by the recently-proposed mixed stabilized finite element method, regarding a singly-perforated plate under uniaxial tension. Remarkably, for all of the damage models discussed in this work, the numerically-obtained localization angles agree almost exactly with the closed-form results. This agreement, on the one hand, consolidates the strain localization analysis based on Maxwell’s kinematics and, on the other hand, illustrates versatility of the mixed stabilized finite element method. View Full-Text
Keywords: localized failure; strain localization; damage; frictional-cohesive materials; constitutive behavior localized failure; strain localization; damage; frictional-cohesive materials; constitutive behavior
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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. (CC BY 4.0).

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Wu, J.-Y.; Cervera, M. Strain Localization of Elastic-Damaging Frictional-Cohesive Materials: Analytical Results and Numerical Verification. Materials 2017, 10, 434.

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