Discrete mathematics

Physics

Engineering

Mathematical analysis

Finite element method

Peridynamics

Horizon

Beam (structure)

Work (physics)

Materials science

Geometry

Equivalence (formal languages)

Point (geometry)

Mathematics

Mechanics

Structural engineering

Discretization

Mechanical engineering

Continuum mechanics

Theoretical and Applied Fracture Mechanics

Peridynamic models typically adopt regular point distributions and uniform horizons, limiting their flexibility and engineering applicability. In this work, a micropolar peridynamics approach with a non-uniform horizon (NHPD) is proposed. This approach is implemented in a conventional finite element framework using element-based discretization. Through modification of the dual-horizon approach in the preprocessing step, a point-dependent horizon and non-uniform beam-like bonds are built. By a domain correction strategy, the equivalence of the strain energy density is assured. Then, a novel energy–density-based failure criterion that directly relates the critical stretch to the mechanical strength is presented. The numerical results indicate the weak mesh dependency of NHPD and the effectiveness of the new failure criterion for Brazilian disk tests. Moreover, damage to solids with different nonlocal effects is shown to yield similar results through adjustment of only the mechanical strength.

A micropolar peridynamic model with non-uniform horizon for static damage of solids considering different nonlocal enhancements