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The phase-field method is based on the energy minimization principle which is a geometric method for modeling diffusive cracks that are popularly implemented with irreversibility based on Griffith's criterion. This method requires a…

Optimization and Control · Mathematics 2025-04-01 Tim Suchan , Chaitanya Kandekar , Wolfgang E. Weber , Kathrin Welker

The immersed peridynamics (IPD) method is a fluid-structure interaction (FSI) model to simulate fluid-driven material damage and failure of an immersed structure, in which a peridynamic (PD) constitutive correspondence model is employed…

Numerical Analysis · Mathematics 2026-03-18 Keon Ho Kim , Boyce E. Griffith

A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…

Numerical Analysis · Mathematics 2025-05-20 Haifeng Ji , Zhilin Li

We present a phase field modeling framework for hydrogen assisted cracking. The model builds upon a coupled mechanical and hydrogen diffusion response, driven by chemical potential gradients, and a hydrogen-dependent fracture energy…

Numerical Analysis · Mathematics 2018-08-10 Emilio Martínez-Pañeda , Alireza Golahmar , Christian F. Niordson

The increasing use of polymer composites in industry asks for the creation of better, faster and cost-effective methods to detect the damage state of such materials. This work presents the investigation of the phase decay , $\Delta{\Phi}$,…

Applied Physics · Physics 2024-04-24 Matias Lasen , Dario Di Maio , Damaso De Bono , Michelle Peluzzo

In this work, we consider pressurized phase-field fracture problems in nearly and fully incompressible materials. To this end, a mixed form for the solid equations is proposed. To enhance the accuracy of the spatial discretization, a…

Numerical Analysis · Mathematics 2022-09-21 Seshadri Basava , Katrin Mang , Mirjam Walloth , Thomas Wick , Winnifried Wollner

Incompressible nonlinearly hyperelastic materials are rarely simulated in Finite Element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most…

Soft Condensed Matter · Physics 2020-09-07 Aisling Ni Annaidh , Michel Destrade , Michael D. Gilchrist , Jerry G. Murphy

Atherosclerotic plaque failure results from various pathophysiological events, with the existence of fibrous cap mode I tearing in the arterial wall, having the potential to block the aortic lumen and correspondingly induce serious clinical…

Tissues and Organs · Quantitative Biology 2018-06-14 Xiaochang Leng , Lindsey Davis , Xiaomin Deng , Tarek Shazly , Michael A. Sutton , Susan M. Lessner

We present a new phase-field model of solidification which allows efficient computations in the regime when interface kinetic effects dominate over capillary effects. The asymptotic analysis required to relate the parameters in the…

Condensed Matter · Physics 2007-05-23 Kalin Vetsigian , Nigel Goldenfeld

Metamaterials are a promising platform for a range of applications, from shock absorption to mechanical computing. These functionalities typically rely on floppy modes or mechanically frustrated loops, both of which are difficult to design.…

Soft Condensed Matter · Physics 2026-01-26 Wenfeng Liu , Tomer A. Sigalov , Corentin Coulais , Yair Shokef

The developed computational approach is capable of initiating and propagating cracks inside materials and along material interfaces of general multi-domain structures under quasi-static conditions. Special attention is paid to particular…

Computational Engineering, Finance, and Science · Computer Science 2023-08-23 Roman Vodička

Carbon fiber reinforced polymer (CFRP) composites offer a unique combination of in-plane specific strength and stiffness. They, however, suffer from a relatively poor out-of plane performance. Improving this requires a thorough…

Applied Physics · Physics 2017-12-13 Ali N Sarvestani , Mehran Tehrani

This paper explores the global Mode I fracture energy of a carbon fiber composite subject to a biaxial stress state at a crack tip, specifically in which one stress component is compressive and parallel to the crack. Based on an…

Materials Science · Physics 2022-07-27 Jeremy Brockmann , Marco Salviato

We present a generalised phase field-based formulation for predicting fatigue crack growth in metals. The theoretical framework aims at covering a wide range of material behaviour. Different fatigue degradation functions are considered and…

Computational Engineering, Finance, and Science · Computer Science 2021-11-24 Z. Khalil , A. Y. Elghazouli , E. Martínez-Pañeda

This article deals with the prediction of thermomechanical properties of fiber reinforced composites using several micromechanics models. These include strength of material approach, Halpin-Tsai equations, multi-phase mechanics of materials…

Applied Physics · Physics 2017-08-03 S. I. Kundalwal

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

A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…

Numerical Analysis · Mathematics 2025-12-29 S. M. Mallikarjunaiah

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

The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal model (APFC) allows for describing crystal lattice properties on…

Computational Physics · Physics 2019-04-25 Simon Praetorius , Marco Salvalaglio , Axel Voigt

We present creep experiments on fiber composite materials with controlled heterogeneity. Recorded strain rates and acoustic emission rates exhibit a power law relaxation in the primary creep regime (Andrade law) followed by a power law…

Materials Science · Physics 2009-11-10 H. Nechad , A. Helmstetter , R. El Guerjouma , D. Sornette
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