Peridynamics is a non-local continuum theory that has shown promise in modeling the behavior of materials subjected to extreme deformation and complex material behaviors. Unlike classical continuum mechanics, peridynamics is based on integro-differential equations without partial derivatives in space and postulates that material points interact through pair-potentials (bond-based formulations) or multi-body potentials (state-based type formulations). This non-local character makes peridynamics particularly well-suited for modeling modern problems in mechanics involving the spontaneous formation of cracks/damage since the governing equations remain equally valid at points or surfaces of discontinuity. In the last decade, peridynamic equations have also been extended to diffusion-based problems and have successfully been applied to model coupled phenomena involving different physics, including corrosion damage, electrodeposition, etc. In this colloquium, we will discuss recent advances in peridynamics research, including the development of new constitutive models for complex materials such as soft tissues, porous media, and composites. An important space will be given to the recent developments and open problems in peridynamic modeling of material degradation and size-dependent behaviors. Furthermore, we will examine recent advancements in the numerical implementation of peridynamic models using meshfree or other discretization methods, including the development of GPU-based and parallel algorithms for large-scale simulations, and the use of machine learning techniques to improve the computational efficiency of peridynamics simulations. Finally, we will explore the potential future directions for peridynamics research, its applicability in areas such as biomechanics, structural health monitoring, and materials design, as well as its connection to other modeling approaches based on continuum mechanics (e.g., SPH, Phase-field, etc.).
Overall, this colloquium aims to provide a comprehensive overview of the recent advances in peridynamics, highlighting its potential to address fundamental challenges in materials science and engineering and to foster collaboration and exchange of ideas among researchers in this field.