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Related papers: Nonlocal elastodynamics and fracture

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A simple nonlocal field theory of peridynamic type is applied to model brittle fracture. The fracture evolution is shown to converge in the limit of vanishing nonlocality to classic plane elastodynamics with a running crack. The kinetic…

Analysis of PDEs · Mathematics 2020-07-30 Robert Lipton , Prashant K. Jha

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

The dynamics of rapid brittle cracks is commonly studied in the framework of linear elastic fracture mechanics where nonlinearities are neglected. However, recent experimental and theoretical work demonstrated explicitly the importance of…

Materials Science · Physics 2009-11-13 Eran Bouchbinder , Ting-Shek Lo

Peridynamics is a nonlocal continuum-mechanical theory based on minimal regularity on the deformations. Its key trait is that of replacing local constitutive relations featuring spacial differential operators with integrals over differences…

Analysis of PDEs · Mathematics 2018-05-23 Martin Kružík , Carlos Mora-Corral , Ulisse Stefanelli

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

The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of…

Numerical Analysis · Mathematics 2021-03-17 Huilong Ren , Xiaoying Zhuang , Erkan Oterkus , HeHua Zhu , Timon Rabczuk

Integral-type nonlocal damage models describe the fracture process zones by regular strain profiles insensitive to the size of finite elements, which is achieved by incorporating weighted spatial averages of certain state variables into the…

Materials Science · Physics 2014-06-16 Peter Grassl , Dimitrios Xenos , Milan Jirásek , Martin Horák

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

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

We consider the nonlocal formulation of continuum mechanics described by peridynamics. We provide a link between peridynamic evolution and brittle fracture evolution for a broad class of peridynamic potentials associated with unstable…

Analysis of PDEs · Mathematics 2013-06-20 Robert Lipton

We develop a novel nonlocal model of dislocations based on the framework of peridynamics. By embedding interior discontinuities into the nonlocal constitutive law, the displacement jump in the Volterra dislocation model is reproduced,…

Computational Engineering, Finance, and Science · Computer Science 2020-05-20 Teng Zhao , Yongxing Shen

We argue that nucleation of brittle cracks in initially flawless soft elastic solids is preceded by a nonlinear elastic instability, which cannot be captured without accounting for geometrical precise description of finite elastic…

Soft Condensed Matter · Physics 2024-06-17 D. Riccobelli , P. Ciarletta , G. Vitale , C. Maurini , L. Truskinovsky

We investigate phase-field modeling of brittle fracture in a one-dimensional bar featuring a continuous variation of elastic and/or fracture properties along its axis. Our main goal is to quantitatively assess how the heterogeneity in…

Applied Physics · Physics 2022-11-22 Francesco Vicentini , Pietro Carrara , Laura De Lorenzis

This work addresses an efficient Global-Local approach supplemented with predictor-corrector adaptivity applied to anisotropic phase-field brittle fracture. The phase-field formulation is used to resolve the sharp crack surface topology on…

Numerical Analysis · Mathematics 2020-02-19 Nima Noii , Fadi Aldakheel , Thomas Wick , Peter Wriggers

Motivated by the existing complications of finding solutions of Eringen nonlocal model, an alternative model is developed here. The new formulation of the nonlocal elasticity is centered upon expressing the dynamic equilibrium requirements…

Applied Physics · Physics 2018-10-11 Mohamed Shaat

A mechanical model is introduced for predicting the initiation and evolution of complex fracture patterns without the need for a damage variable or law. The model, a continuum variant of Newton's second law, uses integral rather than…

Analysis of PDEs · Mathematics 2016-02-02 Robert Lipton , Stewart Silling , Richard Lehoucq

Peridynamics (PD), as a nonlocal theory, is well-suited for solving problems with discontinuities, such as cracks. However, the nonlocal effect of peridynamics makes it computationally expensive for dynamic fracture problems in large-scale…

Computational Engineering, Finance, and Science · Computer Science 2024-03-07 Zhong Jiandong , Han Fei , Du Zongliang , Guo Xu

Extreme localization of damage in conventional brittle materials is the source of a host of undesirable effects. We show how artificially engineered metamaterials with all brittle constituents can be designed to ensure that every breakable…

Materials Science · Physics 2021-07-14 O. U. Salman , L. Truskinovsky

The interaction of crack fronts with asperities is central to the criteria of fracture in heterogeneous materials and for predicting fracture surface formation. It is known how dynamic crack fronts respond to small, 1st-order,…

Soft Condensed Matter · Physics 2025-09-17 Itamar Kolvin , Mokhtar Adda-Bedia

In the phase-field modeling of brittle fracture, anisotropic constitutive assumptions for the degradation of stored elastic energy due to fracture are crucial to preventing cracking in compression and obtaining physically sound numerical…

Numerical Analysis · Mathematics 2018-05-22 Fei Zhang , Weizhang Huang , Xianping Li , Shicheng Zhang
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