Abstract

The paper builds a stable variational formulation for the non-ordinary state-based peridynamics (NOSB-PD). Firstly, a new force state vector is reformulated by introducing the first Piola-Kirchhoff stress in continuum mechanics. The consistency of the new governing equation of the proposed pridynamic model and classical continuum mechanics is proved. Secondly, a stable variational formulation of non-ordinary state based peridynamics is developed to unify the boundary conditions in peridynamcis and continuum mechanics. The zero mode oscillations of non-ordinary state based peridynamics is also eliminated by penalty method in numerical implementation. Numerical examples are illustrated to validate the proposed method. Numerical solutions obtained by the proposed method also indicate that the proposed method can well capture the general nonlinear behavior of solid materials.

Abstract

Abstract

This paper applies the peridynamic continuum mechanics theory on a new type of material known as harmonic-structured materials. Using the Peridigm software, rapid uniaxial elongation is simulated on a peridynamic model of a thin bimodal harmonic-structured metal sheet. Mechanical wave initiation, propagation, and reflection, as well as fracture initiation and propagation are successfully simulated.

Abstract

Metamaterials with engineered microstructures exhibit exceptional properties such as negative Poisson’s ratio, energy absorption, and bandgap. These materials can prevent propagation of elastic waves in certain range of frequency called bandgap. The microstructure of these materials affects the overall response of the structures. Microstructures may undergo significant rotations and their rotary inertia needs to be considered along with deformation. As the metamaterials in the study involve cracks, we develop a finite deformation micropolar peridynamics (PD) theory. The proposed PD micropolar theory is validated by comparing the results obtained from the boundary element solutions of plate with a hole. The response of metamaterials with periodic arrangement of holes and cracks is studied under static and dynamic loads and the results are compared with the nonpolar PD theory.

Abstract