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This study proposes a multi-field asymptotic homogenization for the analysis of thermo-piezoelectric materials with periodic microstructures. The effect of the microstructural heterogeneity is taken into account by means of periodic…

Materials Science · Physics 2017-01-13 Francesca Fantoni , Andrea Bacigalupo , Marco Paggi

Modeling the propagation of cracks at the microscopic level is fundamental to understand the effect of the microstructure on the fracture process. Nevertheless, microscopic propagation is often unstable and when using phase field fracture…

Materials Science · Physics 2024-12-24 Pedro Aranda , Javier Segurado

In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…

Mathematical Physics · Physics 2015-12-31 A. Bacigalupo , L. Morini , A. Piccolroaz

A multifield asymptotic homogenization technique for periodic thermo-diffusive elastic materials is provided in the present study. Field equations for the first-order equivalent medium are derived and overall constitutive tensors are…

Fluid Dynamics · Physics 2020-02-27 Francesca Fantoni , Andrea Bacigalupo

The failure of heterogeneous materials with microstructures is a complex process of damage nucleation, growth and localisation. This process spans multiple length scales and is challenging to simulate numerically due to its high…

Materials Science · Physics 2023-05-24 Philip P. Müller , Falk K. Wittel , David S. Kammer

The favored phase field method (PFM) has encountered challenges in the finite strain fracture modeling of nearly or truly incompressible hyperelastic materials. We identified that the underlying cause lies in the innate contradiction…

Numerical Analysis · Mathematics 2022-05-04 Fucheng Tian , Jun Zeng , Mengnan Zhang , Liangbin Li

The phase field fracture method is attracting significant interest. Phase field approaches have enabled predicting - on arbitrary geometries and dimensions - complex fracture phenomena such as crack branching, coalescence, deflection and…

Computational Engineering, Finance, and Science · Computer Science 2021-04-19 Yousef Navidtehrani , Covadonga Betegón , Emilio Martínez-Pañeda

In this contribution we investigate the application of phase-field fracture models on non-linear multiscale computational homogenization schemes. In particular, we introduce different phase-fields on a two-scale problem and develop a…

Computational Engineering, Finance, and Science · Computer Science 2023-12-21 Felix Schmidt , Stefan Schuß , Christian Hesch

This study addresses ductile fracture of single grains in metals by modeling of the formation and propagation of transgranular cracks. A proposed model integrates gradient extended hardening, phase-field modeling for fracture, and crystal…

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

This paper proposes a phase field model for fracture in poroelastic media. The porous medium is modeled based on the classical Biot poroelasticity theory and the fracture behavior is controlled by the phase field model. Moreover, the…

Geophysics · Physics 2019-02-27 Shuwei Zhou , Xiaoying Zhuang , Timon Rabczuk

A multiscale (micro-to-macro) analysis is proposed for the prediction of the finite strain behavior of composites with hyperelastic constituents and embedded localized damage. The composites are assumed to possess periodic microstructure…

Materials Science · Physics 2020-10-20 Nathan Perchikov , Jacob Aboudi

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

Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…

Analysis of PDEs · Mathematics 2023-07-10 Stefano Almi , Ulisse Stefanelli

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 propagation of a 3D crack in an heterogeneous material is studied using a phase field model. It is shown that in the case of randomly distributed inclusions of soft material in a matrix, the nature of the distribution has little effect…

Materials Science · Physics 2025-03-11 Hervé Henry

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

Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…

Numerical Analysis · Mathematics 2021-08-10 Fabrizio Greco , Lorenzo Leonetti , Paolo Lonetti , Raimondo Luciano , Andrea Pranno

A new approach is developed for computational modelling of microstructure evolution problems. The approach combines the phase-field method with the recently-developed laminated element technique (LET) which is a simple and efficient method…

Numerical Analysis · Mathematics 2024-02-29 Jedrzej Dobrzanski , Stanislaw Stupkiewicz

We investigate the fragmentation process of solid materials with crystalline and amorphous phases using the discrete element method. Damage initiates inside spherical samples above the contact zone in a region where the circumferential…

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