Peridynamics
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Dual‐horizon peridynamics Open
Summary In this paper, we develop a dual‐horizon peridynamics (DH‐PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’ issue. Therefore, the concept of dual horizon is introduced to consider…
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Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives Open
Since the first studies dedicated to the mechanics of deformable bodies (by Euler, D’Alembert, Lagrange) the principle of virtual work (or virtual velocities) has been used to provide firm guidance to the formulation of novel theories. Gab…
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Variable horizon in a peridynamic medium Open
Here, a notion of material homogeneity is proposed for peridynamic bodies with variable horizon but constant bulk properties. A relation is derived that scales the force state according to the position-dependent horizon while keeping the b…
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A comparative review of peridynamics and phase-field models for engineering fracture mechanics Open
Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models appl…
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A position-aware linear solid constitutive model for peridynamics Open
A position-aware linear solid (PALS) peridynamic constitutive model is proposed for isotropic elastic solids. The PALS model addresses problems that arise, in ordinary peridynamic material models such as the linear peridynamic solid (LPS),…
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Nonlinear mechanics of hybrid polymer networks that mimic the complex mechanical environment of cells Open
The mechanical properties of cells and the extracellular environment they reside in are governed by a complex interplay of biopolymers. These biopolymers, which possess a wide range of stiffnesses, self-assemble into fibrous composite netw…
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Roadmap for Peridynamic Software Implementation Open
The application of peridynamics for engineering analysis requires an efficient and robust software implementation. Key elements include processing of the discretization, the proximity search for identification of pairwise interactions, eva…
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A new peridynamic formulation with shear deformation for elastic solid Open
We propose a new peridynamic formulation with shear deformation for linear elastic solid. The key idea lies in subtracting the rigid body rotation part from the total deformation. Based on the strain energy equivalence between classic loca…
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A non-ordinary state-based peridynamics framework for anisotropic materials Open
Peridynamics (PD) represents a new approach for modelling fracture mechanics, where a continuum domain is modelled through particles connected via physical interactions. This formulation allows us to model crack initiation, propagation, br…
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Continuum-kinematics-inspired peridynamics. Mechanical problems Open
The main objective of this contribution is to develop a novel continuum-kinematicsinspired approach for peridynamics (PD), and to revisit PD’s thermodynamic foundations.
\nWe distinguish between three types of interactions, namely, one-nei…
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Ordinary state-based peridynamic modelling for fully coupled thermoelastic problems Open
An ordinary state-based peridynamic model is developed for transient fully coupled thermoelastic problems. By adopting an integral form instead of spatial derivatives in the equation of motion, the developed model is still valid at discont…
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Critical Comparison of Phase-Field, Peridynamics, and Crack Band Model M7 in Light of Gap Test and Classical Fracture Tests Open
The recently conceived gap test and its simulation revealed that the fracture energy Gf (or Kc, Jcr) of concrete, plastic-hardening metals, composites, and probably most materials can change by ±100%, depending on the crack-parallel stress…
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Modelling of Granular Fracture in Polycrystalline Materials Using Ordinary State-Based Peridynamics Open
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…
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Implementation of peridynamic beam and plate formulations in finite element framework Open
Peridynamic (PD) theory is a new continuum mechanics formulation introduced to overcome the limitations of classical continuum mechanics such as predicting crack initiation and propagation, and capturing nonlocal effects. PD theory is base…
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Mesoscale Fracture Analysis of Multiphase Cementitious Composites Using Peridynamics Open
Concrete is a complex heterogeneous material, and thus, it is important to develop numerical modeling methods to enhance the prediction accuracy of the fracture mechanism. In this study, a two-dimensional mesoscale model is developed using…
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Peridynamic model for visco-hyperelastic material deformation in different strain rates Open
This study presents a peridynamic (PD) constitutive model for visco-hyperelastic materials under homogenous deformation. The constitutive visco-hyperelastic model is developed in terms of Yeoh strain energy density function and Prony serie…
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A novel and effective way to impose boundary conditions and to mitigate the surface effect in state‐based Peridynamics Open
Peridynamics is a nonlocal continuum theory capable of modeling effectively crack initiation and propagation in solid bodies. However, the nonlocal nature of this theory is the cause of two main problems near the boundary of the body: an u…
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Peridynamics modelling of coupled water flow and chemical transport in unsaturated porous media Open
A wide range of phenomena in natural or engineered systems emerge from strongly coupled hydraulic, chemical and mechanical processes involving a mix of clearly discrete and quasi-continuous mechanisms. Non-local formulations of these proce…
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Generalized reproducing kernel peridynamics: unification of local and non-local meshfree methods, non-local derivative operations, and an arbitrary-order state-based peridynamic formulation Open
State-based peridynamics is a non-local reformulation of solid mechanics that replaces the force density of the divergence of stress with an integral of the action of force states on bonds local to a given position, which precludes differe…
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Peridynamic simulation of brittle-ice crushed by a vertical structure Open
Sea ice is the main factor affecting the safety of the Arctic engineering. However, traditional numerical methods derived from classical continuum mechanics have difficulties in resolving discontinuous problems like ice damage. In this pap…
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A bond-level energy-based peridynamics for mixed-mode fracture in rocks Open
This paper deals with the numerical simulation of initiation and propagation of mixed mode fracture in rocks. A bond-level energy-based peridynamic model is developed by introducing a dilatation function to capture both volumetric and devi…
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Dynamic propagation of a macrocrack interacting with parallel small cracks Open
In this study, the effect of small cracks on the dynamic propagation of a macrocrack is investigated by using a new continuum mechanics formulation, peridynamics. Various combinations of small cracks with different number, location and den…
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Numerical experiments on the convergence properties of state-based peridynamic laws and influence functions in two-dimensional problems Open
Peridynamics is widely used as the theoretical basis for numerical studies of fracture evolution, propagation, and behavior. While the theory has been shown to converge to continuum mechanics in the theoretical limit, its behavior as a dis…
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The computational framework for continuum-kinematics-inspired peridynamics Open
Peridynamics (PD) is a non-local continuum formulation. The original version of PD was restricted to bond-based interactions. Bond-based PD is geometrically exact and its kinematics are similar to classical continuum mechanics (CCM). Howev…
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An ordinary state-based peridynamic model for the fracture of zigzag graphene sheets Open
This study develops an ordinary state-based peridynamic coarse-graining (OSPD-CG) model for the investigation of fracture in single-layer graphene sheets (SLGS), in which the peridynamic (PD) parameters are derived through combining the PD…
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Modelling soil desiccation cracking by peridynamics Open
Understanding of desiccation-induced cracking in soil has improved over the last 20–30 years through experimental studies, but progress in predictive modelling of desiccation cracking has been limited. The heterogeneous structure of soils …
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Quasi‐static fracture analysis by coupled three‐dimensional peridynamics and high order one‐dimensional finite elements based on local elasticity Open
This work investigates quasi‐static crack propagation in specimens made of brittle materials by combining local and non‐local elasticity models. The portion of the domain where the failure initiates and then propagates is modeled via three…
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Peridynamic modeling and simulation of thermo-mechanical de-icing process with modified ice failure criterion Open
De-icing technology has become an increasingly important subject in numerous applications in recent years. However, the direct numerical modeling and simulation the physical process of thermo-mechanical deicing is limited. This work is foc…
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A Non-Ordinary State-Based Peridynamic Formulation for Failure of Concrete Subjected to Impacting Loads Open
Strain hardening and strain rate play an important role in dynamic deformation and failure problems such as high-velocity impact cases. In this paper, a non-ordinary state-based peridynamic model for failure and damage of concrete material…
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Wellposedness of a nonlinear peridynamic model Open
We consider an evolution equation inspired by a model in peridynamics, with a singular pairwise interaction force term, and we give global in time existence, uniqueness and stability results for the Cauchy problem.