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We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show…

Numerical Analysis · Mathematics 2018-06-27 Timo Heister , Thomas Wick

This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…

Computational Physics · Physics 2022-10-11 Tim Wallis , Philip T. Barton , Nikolaos Nikiforakis

This paper presents a modeling framework to describe the driving mechanisms of cyclic failure in brittle and ductile materials, including cyclic plasticity and fatigue crack growth. A variational model is devised using the energetic…

Numerical Analysis · Mathematics 2020-11-10 Jacinto Ulloa , Jef Wambacq , Roberto Alessi , Geert Degrande , Stijn François

Fracture of viscoelastic materials is considered to be a complex phenomenon due to their highly rate sensitive behavior. In this context, we are interested in the quasi-static response of a viscoelastic solid subjected to damage. This paper…

Computational Engineering, Finance, and Science · Computer Science 2023-05-15 Rajasekar Gopalsamy , Nicolas Chevaugeon , Olivier Chupin , Ferhat Hammoum

The phase-field method has become popular for the numerical modeling of fluid-filled fractures, thanks to its ability to represent complex fracture geometry without algorithms. However, the algorithm-free representation of fracture geometry…

Geophysics · Physics 2024-11-19 Fan Fei , Jinhyun Choo

Phase field models have emerged as a powerful and flexible framework for simulating complex interface-driven phenomena across a wide range of scientific and engineering applications. In fracture mechanics, the phase field…

Numerical Analysis · Mathematics 2025-06-23 Md Mamun Miah , Ryuhei Wakida , Masato Kimura

At present, there is an abundance of results showing that the phase-field approach to fracture in elastic brittle materials -- when properly accounting for material strength -- describes the \emph{nucleation} of fracture from large…

Soft Condensed Matter · Physics 2025-05-12 F. Kamarei , E. Breedlove , O. Lopez-Pamies

Phase-field fracture models are known to overestimate the crack area, a discrepancy that compromises the accuracy of fracture predictions. This issue stems from the diffuse crack representation and numerical artifacts, such as strain…

Materials Science · Physics 2026-05-06 M. Castillón , J. Segurado , I. Romero

The accurate and efficient prediction of crack propagation in dielectric materials is a critical challenge in structural health monitoring and the design of smart systems. This work presents a hybrid modeling framework that combines an…

Computational Physics · Physics 2026-02-03 Aamir Dean , Jaykumar Mavani , Betim Bahtiri , Behrouz Arash , Raimund Rolfes

In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but…

Computational Engineering, Finance, and Science · Computer Science 2018-08-01 M. K. Mudunuru , N. Panda , S. Karra , G. Srinivasan , V. T. Chau , E. Rougier , A. Hunter , H. S. Viswanathan

We present a hybrid-mixed finite element method for a novel hybrid-dimensional model of single-phase Darcy flow in a fractured porous media. In this model, the fracture is treated as an $(d-1)$-dimensional interface within the…

Numerical Analysis · Mathematics 2022-03-02 Guosheng Fu , Yang Yang

Fracture growth in a material is strongly influenced by the presence of inhomogeneities, which deviate crack trajectories from rectilinearity and deeply affect failure. Increasing crack tortuosity is connected to enhancement of fracture…

Materials Science · Physics 2022-07-20 Riccardo Cavuoto , Pietro Lenarda , Diego Misseroni , Marco Paggi , Davide Bigoni

In this work a generalized phase-field cohesive zone model ($\mu$PF-CZM) is proposed within the framework of the unified phase-field theory for brittle and cohesive fracture. With the introduction of an extra dissipation function for the…

Materials Science · Physics 2024-09-04 Jian-Ying Wu

This work presents a rigorous mathematical formulation for topology optimization of a macrostructure undergoing ductile failure. The prediction of ductile solid materials which exhibit dominant plastic deformation is an intriguingly…

Numerical Analysis · Mathematics 2023-03-22 Nima Noii , Hassan Ali Jahangiry , Haim Waisman

Failure in brittle materials led by the evolution of micro- to macro-cracks under repetitive or increasing loads is often catastrophic with no significant plasticity to advert the onset of fracture. Early failure detection with respective…

Computational Engineering, Finance, and Science · Computer Science 2020-03-25 Eduardo A. Barros de Moraes , Hadi Salehi , Mohsen Zayernouri

A three-dimensional SPH computational framework is presented for modeling fluid-structure interactions with structural deformation and failure. We combine weakly compressible SPH with a pseudo-spring-based SPH solver to capture the fluid…

Computational Engineering, Finance, and Science · Computer Science 2025-07-16 Vishabjeet Singh , Chong Peng , Md Rushdie Ibne Islam

The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns, but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands…

Numerical Analysis · Mathematics 2016-05-18 Patrick E. Farrell , Corrado Maurini

A novel variational framework to model the fatigue behavior of brittle materials based on a phase-field approach to fracture is presented. The standard regularized free energy functional is modified introducing a fatigue degradation…

Materials Science · Physics 2020-06-04 P. Carrara , M. Ambati , R. Alessi , L. De Lorenzis

The present contribution proposes a thermodynamically consistent model for the simulation of the ductile damage. The model couples the phase field method of fracture to the Armstrong-Frederick plasticity model with kinematic hardening. The…

Materials Science · Physics 2021-06-07 Serhat Aygün , Tillmann Wiegold , Sandra Klinge

In this work, we introduce a new Hybrid High-Order method for the numerical simulation of fracture propagation based on phase-field models. The proposed method supports general meshes made of polygonal/polyhedral elements, which provides…

Numerical Analysis · Mathematics 2025-11-20 Alessandra Crippa , Julien Coatléven , Daniele A. Di Pietro , Nicolas Guy , Yousef Soleiman
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