A Penalty Method for Coupling of Finite‐Element and Peridynamic Models

A classical continuum mechanics model no longer fulfills its basic assumptions, when the deformations are not smooth or discontinuous. Peridynamics (PD) as an integral formulation could better overcome these issues. Therefore, it is suited to solve fracture problems such crack initiation, growth and formation of patterns. In PD magnitudes internal forces at a material point depend on collective interaction all points within subdomain called horizon. To take advances from formulation, typically implemented in mesh-free form. that case, easy separate interactions between different points. As consequence, relatively high resolution required describe continuous deformation functions and, consequently computationally expensive. application undamaged regions requires unnecessary effort for receiving sufficient accurate results. contrast, finite element method (FEM) mechanics-based approach, very efficient, if stress distributions can be assumed. Consequently, computational cost reduction achieved, applied local damaged zone only remaining area modeled analyzed with FEM. Realization approach coupling FEM subdomains. brief overview about approaches given. Then general Arlequin based presented. Here achieved via overlapping areas. The equations developed realized help Penalty method. considered alternative procedure Lagrange multiplier strategy without creating new unknowns, which essentially simplifies coupled PD-FEM approach. validity limits proposed technique demonstrated through analysis, where choice number discussed well artificial wave oscillations, caused by area.