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This work presents a new adaptive approach for the numerical simulation of a phase-field model for fractures in nearly incompressible solids. In order to cope with locking effects, we use a recently proposed mixed form where we have a…

Numerical Analysis · Mathematics 2021-06-18 Katrin Mang , Mirjam Walloth , Thomas Wick , Winnifried Wollner

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

This is the second paper of a three-part work the main aim of which is to provide a unified consistent framework for the phase-field modelling of cohesive fracture. Building on the theoretical foundations of the first paper, where…

Analysis of PDEs · Mathematics 2025-07-17 Roberto Alessi , Francesco Colasanto , Matteo Focardi

This article proposes a multi-phase-field model using the Puck failure theory to predict the failure in fiber-reinforced composites (FRCs) laminates. Specifically, this work proposes a two-dimensional multi-field model in conjunction with a…

Computational Physics · Physics 2026-03-11 Pavan Kumar Asur Vijaya Kumar , Rafael Fleischhacker , Aamir Dean , Heinz E Pettermann

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

We introduce a new phase-field model which allows for simulation of incoherent solid/solid transformations. Contrary to previous models which impose coherency at the interface, the zero shear-stress condition characteristic of incoherent…

Materials Science · Physics 2007-05-23 Jerome Paret

Over the past few decades, the phase-field method for fracture has seen widespread appeal due to the many benefits associated with its ability to regularize a sharp crack geometry. Along the way, several different models for including the…

Computational Engineering, Finance, and Science · Computer Science 2023-05-15 Andre Costa , Tianchen Hu , John Dolbow

In the context of the Damage Mechanics Challenge, we adopt a phase-field model of brittle fracture to blindly predict the behavior up to failure of a notched three-point-bending specimen loaded under mixed-mode conditions. The beam is…

Computational Engineering, Finance, and Science · Computer Science 2024-12-17 Jonas Heinzmann , Pietro Carrara , Chenyi Luo , Manav Manav , Akanksha Mishra , Sindhu Nagaraja , Hamza Oudich , Francesco Vicentini , Laura De Lorenzis

We present a new mechanistic framework for corrosion-induced cracking in reinforced concrete that resolves the underlying chemo-mechanical processes. The framework combines, for the first time, (i) a model for reactive transport and…

Computational Engineering, Finance, and Science · Computer Science 2023-06-06 E. Korec , M. Jirasek , H. S. Wong , E. Martínez-Pañeda

Understanding how interparticle interactions govern phase behavior is central to controlling self-organization in multicomponent soft-matter systems. In particular, the role of cross-interactions between unlike components remains…

Soft Condensed Matter · Physics 2026-03-03 Umesh Dhumal

Cracking Elements Method (CEM) is a numerical tool to simulate quasi-brittle fractures, which does not need remeshing, nodal enrichment, or complicated crack tracking strategy. The cracking elements used in the CEM can be considered as a…

Computational Engineering, Finance, and Science · Computer Science 2024-07-25 Xueya Wang , Yiming Zhang , Minjie Wen , Herbert Mang

Thick adhesive layers have potential structural application in ship construction for the joining of a composite superstructure to a steel hull. The purpose of this study is to develop a mechanics model for the adhesive fracture of such lap…

Materials Science · Physics 2020-12-30 Sina Askarinejad , Emilio Martínez-Pañeda , I. Ivan Cuesta , Norman A. Fleck

In this paper we propose a notion of irreversibility for the evolution of cracks in presence of cohesive forces, which allows for different responses in the loading and unloading processes, motivated by a variational approximation with…

Analysis of PDEs · Mathematics 2020-12-30 Marco Bonacini , Sergio Conti , Flaviana Iurlano

One of the major shortcomings of discrete element modelling (DEM) is the computational cost required when the number of particles is huge, especially for fine powders and/or industry scale simulations. This study investigates the scaling of…

Soft Condensed Matter · Physics 2015-06-04 Subhash C. Thakur , Jin Y. Ooi , Hossein Ahmadian

A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…

Computational Engineering, Finance, and Science · Computer Science 2025-04-03 Jacopo Bonari , Maria R. Marulli , Nora Hagmeyer , Matthias Mayr , Alexander Popp , Marco Paggi

The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The…

Computational Engineering, Finance, and Science · Computer Science 2023-12-05 Sindhu Nagaraja , Mohamed Elhaddad , Marreddy Ambati , Stefan Kollmannsberger , Laura De Lorenzis , Ernst Rank

The accurate and efficient prediction of crack propagation in dielectric materials is a critical challenge in structural health monitoring and the design of smart systems. This work presents a hybrid modeling framework that combines an…

Computational Physics · Physics 2026-02-03 Aamir Dean , Jaykumar Mavani , Betim Bahtiri , Behrouz Arash , Raimund Rolfes

This work overviews a new, recent success of phase-field modelling: its application to predicting the evolution of the corrosion front and the associated structural integrity challenges. Despite its important implications for society,…

Chemical Physics · Physics 2024-06-24 E. Martínez-Pañeda

Phase field models have emerged as a powerful and flexible framework for simulating complex interface-driven phenomena across a wide range of scientific and engineering applications. In fracture mechanics, the phase field…

Numerical Analysis · Mathematics 2025-06-23 Md Mamun Miah , Ryuhei Wakida , Masato Kimura

We present a phase field-based electro-chemo-mechanical formulation for modelling mechanics-enhanced corrosion and hydrogen-assisted cracking in elastic-plastic solids. A multi-phase-field approach is used to present, for the first time, a…

Materials Science · Physics 2022-06-22 C. Cui , R. Ma , E. Martínez-Pañeda