  A theoretical-computational framework is proposed for predicting the failure
behavior of two anisotropic brittle materials, namely, single crystal magnesium
and boron carbide. Constitutive equations are derived, in both small and large
deformations, by using thermodynamics in order to establish a fully coupled and
transient twin and crack system. To study the common deformation mechanisms
(e.g., twinning and fracture), which can be caused by extreme mechanical
loading, a monolithically-solved Ginzburg--Landau-based phase-field theory
coupled with the mechanical equilibrium equation is implemented in a finite
element simulation framework for the following problems: (i) twin evolution in
two-dimensional single crystal magnesium and boron carbide under simple shear
deformation; (ii) crack-induced twinning for magnesium under pure mode I and
mode II loading; and (iii) study of fracture in homogeneous single crystal
boron carbide under biaxial compressive loading. The results are verified by a
steady-state phase-field approach and validated by available experimental data
in the literature. The success of this computational method relies on using two
distinct phase-field (order) parameters related to fracture and twinning. A
finite element method-based code is developed within the Python-based
open-source platform FEniCS. We make the code publicly available and the
developed algorithm may be extended for the study of phase transformations
under dynamic loading or thermally-activated mechanisms, where the competition
between various deformation mechanisms is accounted for within the current
comprehensive model approach.
