Related papers: Peridynamic stress is the static first Piola-Kirch…
The peridynamic stress tensor proposed by Lehoucq and Silling (2008) is cumbersome to implement in numerical computations. In this note, we show that the peridynamic stress tensor has the mathematical expression of a weighted static Virial…
We re-examine the notion of stress in peridynamics. Based on the idea of traction we define two new peridynamic stress tensors $\mathbf{P}^{\mathbf{y}}$ and $\mathbf{P}$ which stand, respectively, for analogues of the Cauchy and 1st…
The microscopic definition for the Cauchy stress tensor has been examined in the past from many different perspectives. This has led to different expressions for the stress tensor and consequently the "correct" definition has been a subject…
Irving and Kirkwood formulism (IK formulism) provides a way to compute continuum mechanics quantities at certain location in terms of molecular variables. To make the approach more practical in computer simulation, Hardy proposed to use a…
A stress equilibration procedure for hyperelastic material models is proposed andanalyzed in this paper. Based on the displacement-pressure approximation computed with a stable finite element pair, it constructs, in a vertex-patch-wise…
A force-based optimization method is proposed to apply the first and second kind of Piola-Kirchhoff stresses in molecular statics simulation. This method is important for finite deformation problems in which the atomistic behavior can be…
Crack-tip stress evaluation has always been a problem in the frame of classical elasticity theory. Peridynamics has been shown to have great advantages in dealing with crack problems. In the present study, we present a peridynamic crack-tip…
In this work, we developed a bond-based cohesive peridynamics model (CPDM) and apply it to simulate inelastic fracture by using the meso-scale Xu-Needleman cohesive potential . By doing so, we have successfully developed a bond-based…
Material strength is a classical concept with renewed importance in fracture mechanics, particularly in crack nucleation in brittle solids. We formulate material strength in finite elasticity and examine its geometric, constitutive, and…
We propose a fully mixed virtual element method for the numerical approximation of the coupling between stress-altered diffusion and linear elasticity equations with strong symmetry of total poroelastic stress (using the Hellinger--Reissner…
We introduce conformal mixed finite element methods for $2$D and $3$D incompressible nonlinear elasticity in terms of displacement, displacement gradient, the first Piola-Kirchhoff stress tensor, and pressure, where finite elements for the…
Stress testing, and in particular, reverse stress testing, is a prominent exercise in risk management practice. Reverse stress testing, in contrast to (forward) stress testing, aims to find an alternative but plausible model such that under…
This study proposes a novel Modified Bond-Based PeriDynamic (MBB-PD) model based on the bonds' classification. This classification of bonds is performed on the basis of the equivalent hypothetical local strains and falls into three…
Peridynamics formulates the balance of linear momentum as an integro-differential equation, making it naturally suited for fracture modeling without special treatment of discontinuities. The bond-associated correspondence formulation…
This work proposes a novel, general and robust method of determining bond micromoduli for anisotropic linear elastic bond-based peridynamics. The problem of finding a discrete distribution of bond micromoduli that reproduces an anisotropic…
Predicting residual stresses has always been a topic of significance due to its implications in the development of enhanced materials and better processing conditions. In this work, an analytical model for prediction of residual stresses is…
A first-principles method is presented to calculate elastic constants up to the fourth order of crystals with the cubic and hexagonal symmetries. The method relies on the numerical differentiation of the second Piola-Kirchhoff stress tensor…
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…
We address several issues regarding the derivation and implementation of the Cauchy-Born approximation of the stress at finite temperature. In particular, an asymptotic expansion is employed to derive a closed form expression for the first…
In the present work, we first introduce a general framework for modelling complex multiscale fluids and then focus on the derivation and analysis of a new hybrid continuum-kinetic model. In particular, we combine conservation of mass and…