Peridynamiclike

Peridynamiclike refers to a class of modeling approaches in continuum mechanics that resemble peridynamics in using nonlocal interactions to describe material response, including fracture and damage. The term is not a single theory but a label for frameworks that generalize or modify the core ideas of peridynamics, often by altering the interaction laws, horizon definition, or constitutive relations.

Mathematically, peridynamiclike models typically represent the body as a nonlocal domain where the acceleration or deformation at a point depends on integrals over a finite neighborhood, rather than solely on local gradients. A common formulation involves an integral of a nonlocal force density over a horizon around each material point, optionally coupled with state or history variables that capture damage, anisotropy, or nonlinear elasticity. The exact form of the kernel, horizon size, and bond or state dependencies distinguish peridynamiclike models from classical or standard peridynamics.

Relation to peridynamics and distinctions: peridynamics itself uses either bond-based or state-based nonlocal interactions. Peridynamiclike models extend these ideas by allowing more general kernels, direction-dependent interactions, evolving damage laws, or variable horizons. They may incorporate additional physics, such as anisotropic damage, rate effects, or coupling with other nonlocal theories, while retaining the nonlocal character that enables robust fracture modeling.

Applications and considerations: these models are used for fracture, damage prediction, and failure analysis in solids, including composites and metamaterials. Practical use involves calibrating horizon size and kernel parameters, managing computational cost, and handling nonlocal boundary conditions. The term reflects a broad, evolving landscape of nonlocal continuum modeling rather than a single established framework.