Nonlocal phase field approach for modeling damage in brittle materials

In this work, we present a nonlocal phase field model for damage in brittle materials. We define a nonconservative 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.

Automated summary

This work presents a nonlocal phase field model for damage in brittle materials, incorporating a nonconservative order parameter and a new degradation function for damage evolution. The hypothesis of strain equivalence and strain energy equivalence are adopted to predict damage evolution, and a conjugate force to damage is derived. The modified Arc-length method is used to solve the nonlinear system of coupled equations, demonstrating the effectiveness of the proposed damage model through numerical examples.