A gauge theory for brittle damage in solids and a peridynamics implementation

Pathrikar, Anil; Rahaman, Masiur; Roy, Debasish

doi:10.1016/j.cma.2021.114036

Cited by 6 publications

(3 citation statements)

References 60 publications

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“…The correctness of the proposed plane stress formula was verified through benchmark testing examples. Pathrikar et al [50] proposed a gauge field theory model for quantifying and evolving micro-crack defects in solid deformation. The model considers kinematic aspects of deformation and damage, describing various characteristics of brittle damage, such as tension-compression asymmetry, stiffness degradation, and energy functionals, including crack contributions.…”

Section: Research Progressmentioning

confidence: 99%

Advancements in Phase-Field Modeling for Fracture in Nonlinear Elastic Solids under Finite Deformations

Zhang,

Tang,

Chen

et al. 2023

Mathematics

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The prediction of failure mechanisms in nonlinear elastic materials holds significant importance in engineering applications. In recent years, the phase-field model has emerged as an effective approach for addressing fracture problems. Compared with other discontinuous fracture methods, the phase-field method allows for the easy simulation of complex fracture paths, including crack initiation, propagation, coalescence, and branching phenomena, through a scalar field known as the phase field. This method offers distinct advantages in tackling complex fracture problems in nonlinear elastic materials and exhibits substantial potential in material design and manufacturing. The current research has indicated that the energy distribution method employed in phase-field approaches significantly influences the simulated results of material fracture, such as crack initiation load, crack propagation path, crack branching, and so forth. This impact is particularly pronounced when simulating the fracture of nonlinear materials under finite deformation. Therefore, this review outlines various strain energy decomposition methods proposed by researchers for phase-field models of fracture in tension–compression symmetric nonlinear elastic materials. Additionally, the energy decomposition model for tension–compression asymmetric nonlinear elastic materials is also presented. Moreover, the fracture behavior of hydrogels is investigated through the application of the phase-field model with energy decomposition. In addition to summarizing the research on these types of nonlinear elastic body fractures, this review presents numerical benchmark examples from relevant studies to assess and validate the accuracy and effectiveness of the methods presented.

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Section: Research Progressmentioning

confidence: 99%

Advancements in Phase-Field Modeling for Fracture in Nonlinear Elastic Solids under Finite Deformations

Zhang,

Tang,

Chen

et al. 2023

Mathematics

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show abstract

“…As a remedy, (PD) was developed based on meshless nonlocal integral‐based theory by Silling, 18 in which singular spatial derivatives along the discontinuities will not present. Therefore, PD becomes an emerging, efficient method to model dynamic fracturing, damage, and failure process 19–21 …”

Section: Introductionmentioning

confidence: 99%

“…Therefore, PD becomes an emerging, efficient method to model dynamic fracturing, damage, and failure process. [19][20][21] In PD, a solid is discretized into a set of material points with certain volume and mass. Based on nonlocality concept in PD, each material point has an initial spherical neighborhood of adjacent material points with radius of "horizon."…”

Section: Introductionmentioning

confidence: 99%

“Touch‐aware” contact model for peridynamics modeling of granular systems

Mohajerani

Wang

2022

Numerical Meth Engineering

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This article presents an innovative "touch-aware" frictional contact model for peridynamics to efficiently simulate the contact behavior between irregularly shaped particles. Conventional short-range force contact model formulates the contact force field in such a way that leaves a large gap between particles, leading to a softer stiffness of contact and inaccurate simulation of densely packed granular materials. The developed "touch-aware" contact model initiates the contact force calculation when contacting bodies are in touch, which leaves no gap between contacting bodies and provides a stiffer contact in an accurate and efficient way. It simulates frictional contact behaviors and damping between contacting bodies with irregular shapes. Different examples are given to verify the touch-aware contact model with theoretical solutions such as Hertz theory of contact, Hertz theory of impact, Coulomb's law and damping formulation.The model is also compared with conventional peridynamics contact model and the discrete element method. Finally, the touch-aware contact model is used to simulate condensation of an aggregate of irregularly shaped particles.These examples demonstrate excellent capacity of the "touch-aware" model in simulating packed granular systems.

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Understanding the first-order inhomogeneous linear elasticity through local gauge transformations

Xiang

2022

Arch Appl Mech

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A gauge theory for brittle damage in solids and a peridynamics implementation

Cited by 6 publications

References 60 publications

Advancements in Phase-Field Modeling for Fracture in Nonlinear Elastic Solids under Finite Deformations

Advancements in Phase-Field Modeling for Fracture in Nonlinear Elastic Solids under Finite Deformations

“Touch‐aware” contact model for peridynamics modeling of granular systems

Understanding the first-order inhomogeneous linear elasticity through local gauge transformations

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