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A theoretical-computational framework is proposed for predicting the failurebehavior of two anisotropic brittle materials, namely, single crystal magnesiumand boron carbide. Constitutive equations are derived, in both small and largedeformations, by using thermodynamics in order to establish a fully coupled andtransient twin and crack system. To study the common deformation mechanisms(e.g., twinning and fracture), which can be caused by extreme mechanicalloading, a monolithically-solved Ginzburg--Landau-based phase-field theorycoupled with the mechanical equilibrium equation is implemented in a finiteelement simulation framework for the following problems: (i) twin evolution intwo-dimensional single crystal magnesium and boron carbide under simple sheardeformation; (ii) crack-induced twinning for magnesium under pure mode I andmode II loading; and (iii) study of fracture in homogeneous single crystalboron carbide under biaxial compressive loading. The results are verified by asteady-state phase-field approach and validated by available experimental datain the literature. The success of this computational method relies on using twodistinct phase-field (order) parameters related to fracture and twinning. Afinite element method-based code is developed within the Python-basedopen-source platform FEniCS. We make the code publicly available and thedeveloped algorithm may be extended for the study of phase transformationsunder dynamic loading or thermally-activated mechanisms, where the competitionbetween various deformation mechanisms is accounted for within the currentcomprehensive model approach.

international journal of solids and structures

Thermodynamically-consistent derivation and computation of twinning and  fracture in brittle materials by means of phase-field approaches in the  finite element method