Multiscale modeling of material failure: Theory and computational methods

Material behavior and microstructure geometries at small scales strongly influence the physical behavior at higher scales. For example, defects like cracks and dislocations evolve at lower scales and will strongly impact the material properties (mechanical, electrical, thermal, and chemical) at the macroscale. We summarize the recent developments in computational methods to simulate material behavior on multiple scales. We provide details on different techniques at various length scales: quantum, atomistic and coarse-grained models, and various continuum-based models. Furthermore, multiscale methods are broadly divided into: hierarchical, semiconcurrent, and concurrent techniques, and we review a number of modern hierarchical and semiconcurrent multiscale methods such as virtual atom cluster model, homogenization techniques, representative volume element-based methods and structural reconstruction based on Wang tiles. We also go through popular concurrent multiscale methods for fracture applications, such as extended bridging scale and extended bridging domain methods and discuss in detail adaptivity, coarse graining techniques, and their interactions. Computer implementation aspects of specific problems in the context of molecular as well as multiscale framework are also addressed for two- and three-dimensional crack growth problems. The chapter ends with conclusions and future prospects of multiscale methods.