Ordinary State-based Peridynamics Research Articles

A discussion on failure criteria for ordinary state-based peridynamics

Peridynamics is a recently proposed nonlocal theory of continuum particularly suitable to describe fracture mechanics, since it employs an integral formulation which remains valid whenever discontinuities are present. In this paper, mixed-mode fracture cases are taken into consideration to numerically evaluate three failure criteria of the nonlocal interaction, called bond, between two material particles. These criteria are related to the maximum stretch of a bond or to the maximum energy that can be stored in a deformed bond. Their advantages and shortcomings are presented and discussed.

Mixed-mode dynamic stress intensity factors evaluation using ordinary state-based peridynamics

Mixed-mode dynamic stress intensity factors (DSIFs) for two-dimensional (2D) elastic cracked solids are evaluated employing ordinary state-based peridynamics (OSPD) theory. The interaction integral is adopted in the evaluation of the DSIFs. Because the displacement derivative cannot be evaluated in the standard OSPD theory, the derivative components in the interaction integral are derived based on the moving least-squares approximation (MLSA). In addition, the diffraction method is introduced in the MLSA to accurately evaluate the field variables around the crack. Several 2D mixed-mode crack problems are solved and evaluated DISFs for regular and irregular particle arrangements. High accuracy and path-independent mixed-mode DSIFs are achieved by this present formulation and discretization.

Ordinary state-based peridynamics for thermoviscoelastic deformation

This study presents the ordinary state-based peridynamic (PD) constitutive relations for viscoelastic deformation under mechanical and thermal loads. The behavior of the viscous material is modeled in terms of Prony series. The constitutive constants are the same as those of the classical history-integral model, and they are also readily available from relaxation tests. The state variables are conjugate to the PD elastic stretch measures; hence, they are consistent with the kinematic assumptions of the elastic deformation. The PD viscoelastic deformation analysis successfully captures the relaxation behavior of the material. The numerical results concern first the verification problems, and subsequently, a double-lap joint with a viscoelastic adhesive where failure nucleates and grows.

Modelling of Granular Fracture in Polycrystalline Materials Using Ordinary State-Based Peridynamics.

An ordinary state-based peridynamic formulation is developed to analyse cubic polycrystalline materials for the first time in the literature. This new approach has the advantage that no constraint condition is imposed on material constants as opposed to bond-based peridynamic theory. The formulation is validated by first considering static analyses and comparing the displacement fields obtained from the finite element method and ordinary state-based peridynamics. Then, dynamic analysis is performed to investigate the effect of grain boundary strength, crystal size, and discretization size on fracture behaviour and fracture morphology.

Ordinary state-based peridynamicsによる動的応力拡大係数評価に関する研究

Ordinary state-based peridynamicsによる動的応力拡大係数評価に関する研究

Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening

This study presents the ordinary state-based peridynamic constitutive relations for plastic deformation based on von Mises yield criteria with isotropic hardening. The peridynamic force density–stretch relations concerning elastic deformation are augmented with increments of force density and stretch for plastic deformation. The expressions for the yield function and the rule of incremental plastic stretch are derived in terms of the horizon, force density, shear modulus, and hardening parameter of the material. The yield surface is constructed based on the relationship between the effective stress and equivalent plastic stretch. The validity of peridynamic predictions is established by considering benchmark solutions concerning a plate under tension, a plate with a hole and a crack also under tension.

Mixed-Mode Crack Patterns in Ordinary State-Based Peridynamics

A new nonlocal theory of continuum, called Peridynamics, was introduced in 2000. While the classical theory of solid mechanics employs spatial derivatives in order to solve the motion equation and consequently requires the derivability of the displacement field, Peridynamics employs an integral formulation of the equation of motion which leads to the possibility to analyze structures without specific techniques whenever discontinuities, such as cracks or inhomogeneities, are involved. Peridynamics has proven to be able to handle several phenomena concerning crack propagation. There are two variants of the theory, bond-based and state-based. The former is a particular case of the latter, which can also be found in two versions, the ordinary, in which the interaction force between two nodes is aligned with their current relative position, and the non-ordinary, in which interaction forces can have different directions and classical models can be directly introduced in the formulation, even though in this variant numerical integration problems arise (spurious mode deformation). In this study, fracture patterns for mixed-mode crack propagation cases are investigated while varying two fundamental parameters of Peridynamics, the maximum length of interaction, called horizon, and the ratio between the grid spacing and the horizon, called m-ratio. An ordinary state-based Peridynamics formulation is adopted and numerical results are compared with experimental evidences.