Nonlocal phase field approach for modeling damage in brittle materials

Karthik, S. and Rajagopal, A. and Reddy, J.N. (2021) Nonlocal phase field approach for modeling damage in brittle materials. Mechanics of Materials, 157. p. 103797. ISSN 01676636

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Abstract

In this work, we present a nonlocal phase field model for damage in brittle materials. We define a non-conservative order parameter for representing the damage. The Helmholtz free energy functional of the Ginzburg-Landau type that incorporates a new degradation function for the elastic strain energy is considered. The hypothesis of strain equivalence and strain energy equivalence from continuum damage mechanics are adopted to predict the evolution of damage. A conjugate force to damage is derived for both these hypothesis to arrive at a damage criterion. The strong interrelation between phase field models and gradient damage models has been brought out. The solution of the nonlinear system of coupled equation is achieved by a change in the modified Arc-length method and considering a staggered approach. In this approach a linearization of the Crisfield Arc-length quadratic equation for calculation of load increment factor results in an unique root. Numerical examples are presented to demonstrate the usefulness of the proposed damage model.

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IITH Creators:
IITH CreatorsORCiD
Karthik, S.UNSPECIFIED
Rajagopal, A.UNSPECIFIED
Item Type: Article
Uncontrolled Keywords: Arc length method; Continuum damage; Damage modelling; Damage-mechanics; Gradient enhanced damage model; Helmholtz; Nonlocal; Ordering parameter; Phase field models; Phase-field approaches
Subjects: Civil Engineering
Divisions: Department of Civil Engineering
Depositing User: . LibTrainee 2021
Date Deposited: 19 Jul 2021 10:00
Last Modified: 19 Jul 2021 10:00
URI: http://raiith.iith.ac.in/id/eprint/8433
Publisher URL: http://doi.org/10.1016/j.mechmat.2021.103797
OA policy: https://v2.sherpa.ac.uk/id/publication/13707
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