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In traditional phase-field modeling of multiphase materials, a significant challenge arises from the non-local nature of fracture energy regularization, where interfacial toughness is inherently coupled with the properties of the…

Computational Physics · Physics 2026-04-14 Ye-Hang Qin , Ye Feng

We use the amplitude expansion in the phase field crystal framework to formulate an approach where the fields describing the microscopic structure of the material are coupled to a hydrodynamic velocity field. The model is shown to reduce to…

Statistical Mechanics · Physics 2016-01-20 V. Heinonen , C. V. Achim , J. M. Kosterlitz , See-Chen Ying , J. Lowengrub , T. Ala-Nissila

Heterostructured (HS) materials exhibit excellent mechanical properties, combining high strength and significant ductility. Hetero-deformation-induced (HDI) hardening and strain de-localization are key to their strength-ductility synergy.…

Materials Science · Physics 2025-12-03 Yukai Xiong , Jianfeng Zhao , Jinling Liu , Jie Wang , Michael Zaiser , Xu Zhang

Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits…

Soft Condensed Matter · Physics 2015-05-19 Hartmut Löwen

Engineering alloys generally exhibit multi-phase microstructures. For simulating their microstructure evolution during solid-state phase transformation, CALPHAD-guided multi-phase-field models coupled with micro-mechanics have proven to be…

Materials Science · Physics 2023-01-05 Sourav Chatterjee , Daniel Schwen , Nele Moelans

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

The phase field paradigm, in combination with a suitable variational structure, has opened a path for using Griffith's energy balance to predict the fracture of solids. These so-called phase field fracture methods have gained significant…

Computational Engineering, Finance, and Science · Computer Science 2022-03-08 P. K. Kristensen , C. F. Niordson , E. Martínez-Pañeda

The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…

Numerical Analysis · Mathematics 2023-09-27 Yerbol Palzhanov , Alexander Zhiliakov , Annalisa Quaini , Maxim Olshanskii

Using the recently developed theory of rigorously validated numerics, we address the Phase-Field-Crystal (PFC) model at the microscopic (atomistic) level. We show the existence of critical points and local minimizers associated with…

Numerical Analysis · Mathematics 2022-02-23 Gabriel Martine-La Boissoniere , Rustum Choksi , Jean-Philippe Lessard

A novel numerical formulation for solving fluid-structure interaction (FSI) problems is proposed where the fluid field is spatially discretized using smoothed particle hydrodynamics (SPH) and the structural field using the finite element…

Computational Engineering, Finance, and Science · Computer Science 2021-06-16 Sebastian L. Fuchs , Christoph Meier , Wolfgang A. Wall , Christian J. Cyron

The standard cement paste (C-43-St) was studied previously by static heating, SH, immediately after 1 month hydration at w/c = 0.4 [J. Therm. Anal. Calorim. 69 (2002) 187]. This paste after 5-year ageing (unprotected from contact with air)…

Materials Science · Physics 2024-01-26 E. T. Stepkowska , J. M. Blanes , F. Franco , C. Real , J. L. Perez-Rodrıguez

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

A phase-field formulation is introduced to simulate quantitatively microstructural pattern formation in alloys. The thin-interface limit of this formulation yields a much less stringent restriction on the choice of interface thickness than…

Materials Science · Physics 2016-08-31 Alain Karma

Mass concrete plays a crucial role in large-scale projects such as water conservancy hubs and transportation infrastructure. Due to its substantial volume and poor thermal conductivity, the accumulation of hydration heat during the curing…

Computational Physics · Physics 2025-04-01 Sana Ullah , Peng Wu , Ting Peng , Zujin Fan , Tianhao Long , Yuan Li

We present a systematic and reliable methodology, termed hierarchical mean-field theory (HMFT), to study and predict the behavior of strongly coupled many-particle systems. HMFT is a simple approximation, based upon group theoretical…

Strongly Correlated Electrons · Physics 2007-05-23 Gerardo Ortiz , Cristian D. Batista

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

This paper proposes a two-stage framework named ST-PAD for spatio-temporal fluid dynamics modeling in the field of earth sciences, aiming to achieve high-precision simulation and prediction of fluid dynamics through spatio-temporal physics…

Machine Learning · Computer Science 2024-03-22 Hao Wu , Fan Xu , Yifan Duan , Ziwei Niu , Weiyan Wang , Gaofeng Lu , Kun Wang , Yuxuan Liang , Yang Wang

This paper presents an innovative hierarchical meta-modelling approach for predicting the effective elastic properties of stone injected with composite cement grouts containing Carbon NanoTubes (CNTs) for structural rehabilitation purposes.…

Materials Science · Physics 2023-10-10 Rubén Rodríguez-Romero , Víctor Compán , Andrés Sáez , Enrique García-Macías

We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a…

Computational Engineering, Finance, and Science · Computer Science 2022-07-05 Andre Costa , Matteo Cusini , Tao Jin , Randolph Settgast , John Dolbow

A variational modeling framework for hydraulically induced fracturing of elastic-plastic solids is developed in the present work. The developed variational structure provides a global minimization problem. While fracture propagation is…

Numerical Analysis · Mathematics 2025-04-11 Daniel Kienle , Marc-Andre Keip
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