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In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws…

Numerical Analysis · Mathematics 2019-05-22 Nima Noii , Thomas Wick

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 paper a second-order homogenization approach for periodic material is derived from an appropriate representation of the down-scaling that correlates the microdisplacement field to the macro-displacement field and the macro-strain…

Materials Science · Physics 2014-01-31 Andrea Bacigalupo

In this work, we consider fracture propagation in nearly incompressible and (fully) incompressible materials using a phase-field formulation. We use a mixed form of the elasticity equation to overcome volume locking effects and develop a…

Numerical Analysis · Mathematics 2022-02-10 Timo Heister , Katrin Mang , Thomas Wick

In this article, a failure mode dependent and thermodynamically consistent continuum damage model with polynomial-based damage hardening functions is proposed for continuum damage modeling of laminated composite panels. The damage model…

Computational Physics · Physics 2025-09-24 Shubham Rai , Badri Prasad Patel

Review of selected fundamental topics on the interaction between phase transformations, fracture, and other structural changes in inelastic materials is presented. It mostly focuses on the concepts developed in the author's group over last…

Materials Science · Physics 2021-08-24 Valery I. Levitas

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

Micro-structured materials consisting of an array of microstructures are engineered to provide the specific material properties. This present work investigates the design of cellular materials under the framework of level set, so as to…

Computational Engineering, Finance, and Science · Computer Science 2018-11-13 Jie Gao , Hao Li , Zhen Luo , Liang Gao , Peigen Li

We present a microstructural model of permeability in fractured solids, where the fractures are described in terms of recursive families of parallel, equidistant cohesive faults. Faults originate upon the attainment of a tensile or shear…

Computational Physics · Physics 2017-04-26 Maria Laura De Bellis , Gabriele Della Vecchia , Michael Ortiz , Anna Pandolfi

In the hydraulic fracturing of natural rocks, understanding and predicting crack penetrations into the neighboring layers is crucial and relevant in terms of cost-efficiency in engineering and environmental protection. This study…

Geophysics · Physics 2023-07-24 Xiaoying Zhuang , Shuwei Zhou , Mao Sheng , Gensheng Li

A novel FFT-based phase-field fracture framework for modelling fatigue crack initiation and propagation at the microscale is presented. A damage driving force is defined based on the stored energy and dislocation density, relating…

Computational Engineering, Finance, and Science · Computer Science 2023-04-04 Sergio Lucarini , Fionn P. E. Dunne , Emilio Martínez-Pañeda

This work presents a rigorous prediction of the effective equations governing the paramagnetic-ferromagnetic phase transition in a perforated three-dimensional body. Assuming a periodic distribution of perforations, we investigate the…

Analysis of PDEs · Mathematics 2025-08-29 Catherine Choquet , Mohamed Ouhadan , Mouhcine Tilioua

Thermal fracture is prevalent in many engineering problems and is one of the most devastating defects in metal additive manufacturing. Due to the interactive underlying physics involved, the computational simulation of such a process is…

Materials Science · Physics 2022-12-28 Hui Ruan , Shahed Rezaei , Yangyiwei Yang , Dietmar Gross , Bai-Xiang Xu

This paper reviews the current state-of-the-art in the simulation of the mechanical behavior of polycrystalline materials by means of computational homogenization. The key ingredients of this modelling strategy are presented in detail…

Materials Science · Physics 2018-11-22 J. Segurado , R. A. Lebensohn , J. LLorca

We present a novel computational framework to simulate the electromechanical response of self-sensing carbon nanotube (CNT)-based composites experiencing fracture. The computational framework combines electrical-deformation-fracture finite…

Computational Engineering, Finance, and Science · Computer Science 2023-02-22 L. Quinteros , E. García-Macías , E. Martínez-Pañeda

We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…

Numerical Analysis · Mathematics 2026-04-09 Erik Burman , Peter Hansbo , Mats G. Larson , Karl Larsson , Shantiram Mahata

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

Stress distributions and the corresponding fracture patterns and evolutions in the microstructures strongly influence the load-carrying capabilities of composite structures. This work introduces an enhanced phase-field fracture model…

Computational Engineering, Finance, and Science · Computer Science 2024-11-19 Yanran Wang , Yichun Tang , Jing Du , Mike Hillman , J. S. Chen

We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain computational efficiency. By using a conveniently constructed…

Numerical Analysis · Mathematics 2024-10-24 Omar Richardson , Omar Lakkis , Adrian Muntean , Chandrasekhar Venkataraman

In our previous papers we have described efficient and reliable methods of generation of representative volume elements (RVE) perfectly suitable for analysis of composite materials via stochastic homogenization. In this paper we profit from…

Computational Engineering, Finance, and Science · Computer Science 2015-04-10 Vladimir Salnikov , Sophie Lemaitre , Daniel Choï , Philippe Karamian-Surville
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