Adaptive concurrent multiscale model for fracture and crack propagation in heterogeneous media

We introduce an adaptive concurrent multiscale methodology (ACM2) to handle situations in which both macroscopic and microscopic deformation fields strongly interact near the tip of a crack. The method is based on the balance between numerical and homogenization error; while the first type of error states that elements should be refined in regions of high deformation gradients, the second implies that element size may not be smaller than a threshold determined by the size of the unit cell representing the material’s microstructure. In this context, we build a finite element framework in which unit cells can be embedded in continuum region through appropriate macro–micro boundary coupling conditions. By combining the idea of adaptive refinement with the embedded unit cell technique, the methodology ensures that appropriate descriptions of the material are used adequately, regardless of the severity of deformations. We will then show that our computational technique, in conjunction with the extended finite element method, is ideal to study the strong interactions between a crack and the microstructure of heterogeneous media. In particular, it enables an explicit description of microstructural features near the crack tip, while a computationally inexpensive coarse scale continuum description is used in the rest of the domain. The paper presents several examples of crack propagation in materials with random microstructures and discuss the potential of the multiscale technique in relating microstructural details to material strength and toughness.