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Dynamic fragmentation simulations are essential for predicting material response at high strain rates, yet explicit dynamic simulations that combine an extrinsic cohesive-zone model (CZM) with penalty-based contact often exhibit severe…

Computational Physics · Physics 2025-11-19 Thibault Ghesquière-Diérickx , Jean-François Molinari , Guillaume Anciaux

Understanding the fracture mechanisms in composite materials across scales, from nano- to micro-scales, is essential for an in-depth understanding of the reinforcement mechanisms and designing the next generation of lightweight,…

Materials Science · Physics 2024-11-25 Qinghua Zhang , Navid Valizadeh , Mingpeng Liu , Xiaoying Zhuang , Bohayra Mortazavi

The present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach and clarifying some confusing points found…

A novel phase field material point method is introduced for robust simulation of dynamic fracture in elastic media considering the most general case of anisotropic surface energy. Anisotropy is explicitly introduced through a properly…

Numerical Analysis · Mathematics 2019-09-04 Emmanouil Kakouris , Savvas P. Triantafyllou

In this study, we address damage initiation and micro-crack formation in ductile failure of polycrystalline metals. We show how our recently published thermodynamic framework for ductile phase-field fracture of single crystals can be…

Numerical Analysis · Mathematics 2024-11-01 Kim Louisa Auth , Jim Brouzoulis , Magnus Ekh

Damage gradient models approximate fracture mechanics using a modulation of the material stiffness. To this aim a single scalar field, the damage, is used to degrade as a whole the elastic energy. If applied to the structural models of…

Classical Physics · Physics 2022-11-30 Giovanni Corsi , Antonino Favata , Stefano Vidoli

We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo. The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Rodica Toader

Environmentally assisted cracking phenomena are widespread across the transport, defence, energy and construction sectors. However, predicting environmentally assisted fractures is a highly cross-disciplinary endeavour that requires…

Materials Science · Physics 2021-08-03 Emilio Martínez-Pañeda

A theoretical-computational framework is proposed for predicting the failure behavior of two anisotropic brittle materials, namely, single crystal magnesium and boron carbide. Constitutive equations are derived, in both small and large…

Cracking of rocks and rock-like materials exhibits a rich variety of patterns where tensile (mode I) and shear (mode II) fractures are often interwoven. These mixed-mode fractures are usually cohesive (quasi-brittle) and frictional.…

Geophysics · Physics 2021-01-12 Fan Fei , Jinhyun Choo

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…

Phase field models are promising to tackle various fracture problems where a diffusive crack is introduced and modelled using the phase variable. Owing to the non-convexity of the energy functional, the derived partial differential…

Numerical Analysis · Mathematics 2022-12-28 Chenyi Luo

A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the…

Numerical Analysis · Mathematics 2018-01-17 Fei Zhang , Weizhang Huang , Xianping Li , Shicheng Zhang

A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the…

Statistical Mechanics · Physics 2007-05-23 Klaus Kassner , Chaouqi Misbah , Judith Mueller , Jens Kappey , Peter Kohlert

In this paper, a peridynamics-based finite element method (Peri-FEM) is proposed for the quasi-static fracture analysis, which is of the consistent computational framework with the classical finite element method (FEM). First, the integral…

Computational Engineering, Finance, and Science · Computer Science 2021-09-24 Fei Han , Zhibin Li

This paper presents an overview of the theories and computer implementation aspects of phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches to fracture is that PFM can elegantly simulate complicated…

Geophysics · Physics 2023-09-11 X. Zhuang , S. Zhou , G. D. Huynh , P. Areias , T. Rabczuk

This study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More…

Materials Science · Physics 2020-08-26 Sansit Patnaik , Fabio Semperlotti

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

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

Understanding crack propagation in structures subjected to fluid loads is crucial in various engineering applications, ranging from underwater pipelines to aircraft components. This study investigates the dynamic response of structures,…

Computational Engineering, Finance, and Science · Computer Science 2023-10-06 Md Rushdie Ibne Islam