Crack growth in anisotropic brittle and polycrystalline materials by adaptive phase field model using variable-node elements

Composite materials inherently own desirable properties including high strength, high stiffness and good toughness. The macroscopic mechanical properties of composite materials are generally anisotropic. Fracture in anisotropic or orthotropic materials has been widely concerned by researchers in the fields of computational mechanics, aviation, aerospace, construction, etc. The phase-field method (PFM) is a numerical method highly suitable for simulating crack propagation that has received extensive attention in recent years. This paper proposes an adaptive phase-field fracture model using finite elements associated with variable-node elements for orthotropic crack propagation. The directional effect is realized by adding a penalty term in the fracture energy density to prevent cracks propagating along the normal to the cleavage planes. The governing equations are solved with an effective staggered scheme. An adaptive algorithm is presented to improve the computational efficiency. The incompatibility between the elements due to local refinement is handled by the variable-node technology. The spatial discretization is locally refined based on a pre-defined threshold of phase-field variable. The accuracy and reliability of the developed adaptive orthotropic phase-field model are verified by examining four benchmark examples, consisting of a plate subjected to tensile load with an edge-crack and inclined center-crack respectively, a specimen with two staggered center-cracks under tension, and crack propagation in 2D polycrystalline materials.