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

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.