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In this paper, we introduce tensor involved peridynamics, a unified framework for simulating both isotropic and anisotropic materials. While traditional peridynamics models effectively simulate isotropic materials, they face challenges with…

Materials Science · Physics 2024-12-23 Hao Tian , Jinlong Shao , Chenguang Liu , Shuo Liu , Xu Guo

The immersed peridynamics (IPD) method is a fluid-structure interaction (FSI) model to simulate fluid-driven material damage and failure of an immersed structure, in which a peridynamic (PD) constitutive correspondence model is employed…

Numerical Analysis · Mathematics 2026-03-18 Keon Ho Kim , Boyce E. Griffith

Peridynamics provides a versatile tool for fracture modelling in materials where fracture pathways cannot be predicted beforehand, but must be envisaged as an emergent features of the deformation process. One class of materials where this…

Materials Science · Physics 2025-12-18 Shucheta Shegufta , Michael Zaiser

A particular failure mode of highly porous brittle materials consists in the propagation of cracks under uniaxial compressive loads. Such 'anticracks' have been observed in a range of materials, from snow and porous sandstone to brittle…

Soft Condensed Matter · Physics 2025-03-14 Shucheta Shegufta , Michael Zaiser

A thermo-mechanical fracture modeling is proposed to address thermal failure issues, where the temperature field is calculated by a heat conduction model based on classical continuum mechanics (CCM), while the deformation field with…

Computational Engineering, Finance, and Science · Computer Science 2025-09-03 Sitong Tao , Fei Han

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

We propose a decomposition of constitutive relations into crack-driving and persistent portions, specifically designed for materials with anisotropic/orthotropic behavior in the phase field approach to fracture to account for the…

Numerical Analysis · Mathematics 2022-12-28 Vahid Ziaei-Rad , Mostafa Mollaali , Thomas Nagel , Olaf Kolditz , Keita Yoshioka

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

Fracture involves interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From the…

Soft Condensed Matter · Physics 2022-02-04 Debdeep Bhattacharya , Patrick Diehl , Robert P. 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

Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely…

Materials Science · Physics 2023-01-12 Huaiqian You , Xiao Xu , Yue Yu , Stewart Silling , Marta D'Elia , John Foster

We propose a novel variational phase-field model for fracture in anisotropic materials. The model is specifically designed to allow a more flexible calibration of crack nucleation than existing anisotropic fracture formulations, while…

A field theory is presented for predicting damage and fracture in quasi brittle materials incorporating effects of irreversible (plastic) deformation as well as elastic moduli that soften with damage. The new observation made here is that…

Materials Science · Physics 2026-03-17 Hayden Bromley , Robert Lipton

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…

Materials Science · Physics 2022-05-18 Jing Han , Shaofan Li , Haicheng Yu , Jun Li , A-Man Zhang

Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Within the PUM global-local enrichment scheme [1, 2] different physical models can exist to…

Computational Engineering, Finance, and Science · Computer Science 2024-05-06 Matthias Birner , Patrick Diehl , Robert Lipton , Marc Alexander Schweitzer

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

Dual-continuum (DC) models can be tractable alternatives to explicit approaches for the numerical modelling of multiscale materials with multiphysics behaviours. This work concerns the conceptual and numerical modelling of poroelastically…

Geophysics · Physics 2020-12-02 Mark Ashworth , Florian Doster

Usage, manipulation, transport, delivery, and mixing of granular or particulate media, comprised of spherical or polyhedral particles, is commonly encountered in industrial sectors of construction (cement and rock fragments), pharmaceutics…

Computational Engineering, Finance, and Science · Computer Science 2021-02-25 Prashant K. Jha , Prathamesh S. Desai , Debdeep Bhattacharya , Robert Lipton

The goal of the current work is to explore direction-dependent damage initiation and propagation within an arbitrary anisotropic solid. In particular, we aim at developing anisotropic cohesive phase-field (PF) damage models by extending the…

Computational Engineering, Finance, and Science · Computer Science 2022-05-23 Shahed Rezaei , Ali Harandi , Tim Brepols , Stefanie Reese

This paper presents an improved non-ordinary state-based peridynamics (NOSB PD) framework for modelling the elastoplastic behaviour and damage of geomaterials, such as soil, rock, and concrete, under quasi static conditions. Conventional…

Materials Science · Physics 2025-03-21 Yixin Li , Xueyu Geng
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