A Micropolar Peridynamic Theory in Linear Elasticity

TL;DR

This paper introduces a micropolar peridynamic theory for linear elastic solids that incorporates micro-rotational degrees of freedom and material length scales, enhancing the modeling of size-dependent behaviors.

Contribution

It develops a novel micropolar peridynamic framework with constitutive correspondence and derives both 3D and beam models to capture length scale effects in elastic materials.

Findings

Models effectively analyze length scale effects in beam and plane-stress problems.

Numerical simulations validate the models' ability to capture size-dependent behaviors.

Abstract

A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant material length scale parameters into peridynamics. Non-ordinary type modeling via constitutive correspondence is adopted here to define the micropolar peridynamic material. Along with a general three dimensional model, homogenized one dimensional Timoshenko type beam models for both the proposed micropolar and the standard non-polar peridynamic variants are derived. The efficacy of the proposed models in analyzing continua with length scale effects is established via numerical simulations of a few beam and plane-stress problems.