A micropolar peridynamic theory in linear elasticity

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.

A new peridynamic formulation with shear deformation for elastic solid

“…Amani et al [17] implemented the Johnson-Cook (JC) and damage model based on NOSB peridynamics. Apart from the applications for solid, peridynamics has also been extended to other fields, heat diffusion [18,19,20], plates and shells [21,22,23], composite materials [24] and the nonlocal vector calculus [25].…”

A bond‐based peridynamic model considering effects of particle rotation and shear influence coefficient

“…The SPD model removes the limitation of Poisson's ratio in the original PD theory. Additionally, the SPD model was used to describe the continuous and discontinuous behavior of more comprehensive materials in applications, such as thermoplastic, viscoelasticity, plasticity, visioplasticity, thermoviscoelastic, and finite deformation problems …”

“…Additionally, the SPD model was used to describe the continuous and discontinuous behavior of more comprehensive materials in applications, such as thermoplastic, 12 viscoelasticity, 13 plasticity, 14 visioplasticity, 15 thermoviscoelastic, 16 and finite deformation problems. 17 As described by Huang et al 18 and Wang et al, 19 the BPD model still has a wide range of applications because of its simplicity compared to the SPD model, and it can be realized more easily in program implementation. In order to overcome the limitation of Poisson's ratio, many scholars proposed extended PD models based on the classical BPD model.…”

A hierarchy of dynamic equations for solid isotropic micropolar circular cylinders

“…Among these Ramezani et al [17] adopt a more general series expansion approach. A mathematical approach for deriving static torsional and Timoshenko like models based on asymptotic theories is given in [19], while [20] studies a non-local micropolar Timoshenko beam theory.…”