# A rate-dependent and unconstrained phase-field model for brittle fracture

## Palavras-chave:

Phase-field, Fracture, Crack propagation, Residual stress, Finite elements## Resumo

This work deals with the formulation and numerical implementation of a rate-dependent model for

brittle fracture that allows for damage healing. The model formulation, which is carried out within the framework

of continuum mechanics, relies on the introduction of an extra independent kinematical descriptor, the phase field,

along with the corresponding force system, the microforce system. The governing equations of theory are obtained

by supplementing the standard and extra force balances with a constitutive theory consistent with a mechanical

version of the second law of thermodynamics. A particular version of the theory is singled out to provided a

regularization of a standard theory constrained by the assumption of damage irreversibility. The model shows a

derivation of an ”optimal” kinetic modulus function from an ”optimal” penalization of rate-independent model in

the literature, which made it capable to avoid healing at a level previously unknown for rate-dependent models of

that type. A few simulation results are shown for different problem parameters previously explored by other works.

To solve the equations of the model, we use the finite-element method, for spatial discretization, and a backward

Euler scheme, for the time integration, in a Python implementation aided by an open-source computing platform

FEniCS.