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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…

The $\xi$-based spatially adaptive three-field variable phase-field model for quasi-static anti-plane crack propagation is introduced. A dynamically optimized regularization length is integrated to improve computational efficiency and…

Numerical Analysis · Mathematics 2025-06-17 Maria P. Fernando , S. M. Mallikarjunaiah

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

Accurately predicting when and how materials fail is critical to designing safe, reliable structures, mechanical systems, and engineered components that operate under stress. Yet, fracture behavior remains difficult to model across the…

Compressive-shear fracture is commonly observed in rock-like materials. However, this fracture type cannot be captured by current phase field models (PFMs), which have been proven an effective tool for modeling fracture initiation,…

Computational Engineering, Finance, and Science · Computer Science 2023-08-14 Shuwei Zhou , Xiaoying Zhuang , Timon Rabczuk

In this work, we describe our contribution to the Purdue-SANDIA-LLNL \emph{Damage Mechanics Challenge}. The phase field fracture model is adopted to blindly estimate the failure characteristics of the challenge test, an unconventional…

Computational Engineering, Finance, and Science · Computer Science 2024-03-28 Y. Navidtehrani , R. Duddu , E. Martínez-Pañeda

In this paper, a novel hybrid FEM and Peridynamic modeling approach proposed in Ni et al. (2020) is used to predict the dynamic solution of hydro-mechanical coupled problems. A modified staggered solution algorithm is adopted to solve the…

Numerical Analysis · Mathematics 2023-07-24 Tao Ni , Francesco Pesavento , Mirco Zaccariotto , Ugo Galvanetto , Bernhard A. Schrefler

In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an…

Analysis of PDEs · Mathematics 2013-12-09 Elena Bonetti , Christian Heinemann , Christiane Kraus , Antonio Segatti

Phase field method has been widely used because of its excellent ability to simulate fracture problems. At present, the implementation process is mainly based on commercial software, and the operation process is relatively complex. In this…

Materials Science · Physics 2023-02-06 Yuanfeng Yu , Xiaoya Zheng

Reproducing the key features of fracture behavior under multiaxial stress states is essential for accurate modeling. Experimental evidence indicates that three intrinsic material properties govern fracture nucleation in elastic materials:…

Numerical Analysis · Mathematics 2025-11-04 Eleonora Maggiorelli , Matteo Negri , Francesco Vicentini , Laura De Lorenzis

This paper proposes a phase field model (PFM) for describing hydraulic fracture propagation in transversely isotopic media. The coupling between the fluid flow and displacement fields is established according to the classical Biot…

Geophysics · Physics 2023-09-11 Shuwei Zhou , Xiaoying Zhuang

This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a…

Numerical Analysis · Mathematics 2020-02-19 Mats Kirkesæther Brun , Thomas Wick , Inga Berre , Jan Martin Nordbotten , Florin Adrian Radu

A continuum model of crack propagation is presented and discussed. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic and viscoelastic effects are…

Materials Science · Physics 2020-02-26 M. Fleck , D. Pilipenko , R. Spatschek , E. A. Brener

A series of recent papers have modified the classical variational phase-field fracture models to successfully predict both the nucleation and propagation of cracks in brittle fracture under general loading conditions. This is done through…

Materials Science · Physics 2025-01-03 Chockalingam Senthilnathan

We investigate dynamic fracture of heterogeneous materials experimentally by measuring displacement fields as a rupture propagates through a periodic array of obstacles of controlled fracture energy. Our measurements demonstrate the…

Soft Condensed Matter · Physics 2021-07-21 Gabriele Albertini , Mathias Lebihain , François Hild , Laurent Ponson , David S. Kammer

In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian framework. Here, the focus is on…

Numerical Analysis · Mathematics 2020-06-22 Amirreza Khodadadian , Nima Noii , Maryam Parvizi , Mostafa Abbaszadeh , Thomas Wick , Clemens Heitzinger

A phase field (PF) based electrochemical model is presented for simulation of galvanic corrosion. Distributions of electrolyte potential and current density on anode and cathode surfaces are obtained by coupling the phase field variable…

Materials Science · Physics 2018-04-24 Anahita Imanian , Mehdi Amiri

We address in this review unified analysis of phase-field models for cohesive fracture. Aiming to regularize the Barenblatt (1959) cohesive zone model, all the discussed models are distinguished by three characteristic functions, i.e., the…

Materials Science · Physics 2024-12-06 Jian-Ying Wu

We introduce a phenomenological continuum model for mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between…

Soft Condensed Matter · Physics 2009-11-07 Alain Karma , David A. Kessler , Herbert Levine

A phase-field model is used to capture the surfactant-driven formation of fracture patterns in particulate monolayers. The model is intended for the regime of closely-packed systems in which the mechanical response of the monolayer can be…

Soft Condensed Matter · Physics 2017-06-30 Christian Peco , Wei Chen , Yingjie Liu , M. M. Bandi , John E. Dolbow , Eliot Fried
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