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As a nonlocal extension of continuum mechanics, peridynamics has been widely and effectively applied in different fields where discontinuities in the field variables arise from an initially continuous body. An important component of the…

Numerical Analysis · Mathematics 2021-09-22 Xiao Xu , Marta D'Elia , John T. Foster

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…

Computational Engineering, Finance, and Science · Computer Science 2026-04-13 Kai Partmann , Christian Wieners , Michael Ortiz , Kerstin Weinberg

This paper presents a unified framework for bond-associated peridynamic material correspondence models that were proposed to inherently address the issue of material instability or existence of zero-energy modes in the conventional…

Materials Science · Physics 2024-10-03 Xuan Hu , Hailong Chen , Yichi Zhang , Zening Wang

Peridynamic (PD) theories have gained widespread diffusion among various research areas, due to the ability of modeling discontinuities formation and evolution in materials. Bond-Based Peridynamics (BB-PD), notwithstanding some modeling…

Numerical Analysis · Mathematics 2022-10-12 Nunzio Dimola , Alessandro Coclite , Giuseppe Fanizza , Tiziano Politi

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…

Computational Engineering, Finance, and Science · Computer Science 2023-02-08 Alireza Masoumi , Mohammad Ravandi , Manouchehr Salehi

This paper is concerned with the energy decomposition of various nonlocal models, including elasticity, thin plates, and gradient elasticity, to arrive at bond-based nonlocal models in which the bond force depends only on the deformation of…

Classical Physics · Physics 2023-07-24 Huilong Ren , Timon Rabczuk , Xiaoying Zhuang , Zhiyuan Li

This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an…

Numerical Analysis · Mathematics 2023-10-19 Keon Ho Kim , Amneet P. S. Bhalla , Boyce E. Griffith

Most peridynamics models adopt regular point distribution and unified horizon, limiting their flexibility and engineering applications. In this work, a micropolar peridynamics approach with non-unified horizon (NHPD) is proposed. This…

Computational Engineering, Finance, and Science · Computer Science 2020-09-18 Yiming Zhang , Xueqing Yang , Xiaoying Zhuang

In this paper, we propose two approaches to apply boundary conditions for bond-based peridynamic models. There has been in recent years a renewed interest in the class of so-called non-local models, which include peridynamic models, for the…

Computational Engineering, Finance, and Science · Computer Science 2020-10-02 Serge Prudhomme , Patrick Diehl

We study the quasistatic evolution of a linear peridynamic Kelvin-Voigt viscoelastic material. More specifically, we consider the gradient flow of a nonlocal elastic energy with respect to a nonlocal viscous dissipation. Following an…

Analysis of PDEs · Mathematics 2024-02-27 Manuel Friedrich , Manuel Seitz , Ulisse Stefanelli

The convergence of a peridynamic model for solid mechanics inside heterogeneous media in the limit of vanishing nonlocality is analyzed. It is shown that the operator of linear peridynamics for an isotropic heterogeneous medium converges to…

Analysis of PDEs · Mathematics 2014-11-27 Bacim Alali , Max Gunzburger

We prove that that for nonlinear elastic energies with strong enough energetic control of the outer distortion of admissible deformations, almost everywhere global invertibility as constraint can be obtained in the $\Gamma$-limit of the…

Analysis of PDEs · Mathematics 2022-06-29 Stefan Krömer , Philipp Reiter

This contribution presents a concept to dynamic fracture with continuum-kinematics-based peridynamics. Continuum-kinematics-based peridynamics is a geometrically exact formulation of peridynamics, which adds surface- or volumetric-based…

Computational Engineering, Finance, and Science · Computer Science 2022-09-21 Kai Friebertshäuser , Christian Wieners , Kerstin Weinberg

We formulate a nonlocal cohesive model for calculating the deformation state inside a cracking body. In this model a more complete set of physical properties including elastic and softening behavior are assigned to each point in the medium.…

Analysis of PDEs · Mathematics 2015-07-14 Robert Lipton

The peridynamic model of a solid does not involve spatial gradients of the displacement field and is therefore well suited for studying defect propagation. Here, bond-based peridynamic theory is used to study the equilibrium and steady…

Computational Physics · Physics 2018-05-09 Linjuan Wang , Rohan Abeyaratne

We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal strain that describes deformation based on pairwise…

Analysis of PDEs · Mathematics 2023-06-28 Tadele Mengesha , James M. Scott

The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and non-locality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems.…

Numerical Analysis · Mathematics 2021-06-01 Xue Liang , Linjuan Wang , Jifeng Xu , Jianxiang Wang

In this paper, we introduce a novel bond-based peridynamic model that utilizes a Gaussian kernel function. Previous peridynamic models, when directly discretized, have exhibited a lack of asymptotically compatibility with their…

Mathematical Physics · Physics 2025-12-15 Chenguang Liu , Hao Tian , Jinlong Shao

Peridynamics is a nonlocal generalization of continuum mechanics theory which adresses discontinuous problems without using partial derivatives and replacing its by an integral operator. As a consequence, it finds applications in the…

Numerical Analysis · Mathematics 2022-09-07 Luciano Lopez , Sabrina Francesca Pellegrino

A nonlocal model of peridynamic type for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inelastic phase depends on material strength. Existence and…

Analysis of PDEs · Mathematics 2024-04-02 Robert P. Lipton , Debdeep Bhattacharya
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