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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

Recent advancements in computations have enabled the application of various modeling approaches to predict fracture and failure, such as the gradient-damage (phasefield) method. Several existing studies have leveraged the heat equation…

Soft Condensed Matter · Physics 2026-01-14 Keven Alkhoury , Shawn A. Chester , Vikas Srivastava

We present a novel, generalised formulation to treat coupled structural integrity problems by combining phase field and multi-physics modelling. The approach exploits the versatility of the heat transfer equation and is therefore well…

Computational Engineering, Finance, and Science · Computer Science 2025-06-27 Y. Navidtehrani , C. Betegón , E. Martínez-Pañeda

This manuscript presents a practical method for incorporating trained Neural Networks (NNs) into the Finite Element (FE) framework using a user material (UMAT) subroutine. The work exemplifies crystal plasticity, a complex inelastic…

Computational Physics · Physics 2024-10-14 Yuqing He , Yousef Heider , Bernd Markert

We present a wrapper that allows Abaqus user material subroutines (UMATs) to be used as an External Material library in the software COMSOL Multiphysics. The wrapper, written in C language, transforms COMSOL's external material subroutine…

Computational Engineering, Finance, and Science · Computer Science 2024-02-22 S. Lucarini , E. Martínez-Pañeda

Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure.…

Mesoscale and Nanoscale Physics · Physics 2025-06-06 Vinamra Agrawal , Brandon Runnels

Fracture mechanics is crucial for many fields of engineering, as precisely predicting failure of structures and parts is required for efficient designs. The simulation of failure processes is, from a mechanical and a numerical point of…

Materials Science · Physics 2022-06-15 Sebastian Pech , Markus Lukacevic , Josef Füssl

We investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling. Several paradigmatic boundary value problems are addressed, spanning the fields of…

Numerical Analysis · Mathematics 2019-12-19 Philip K. Kristensen , Emilio 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

This paper presents an overview of the theories and computer implementation aspects of phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches to fracture is that PFM can elegantly simulate complicated…

Geophysics · Physics 2023-09-11 X. Zhuang , S. Zhou , G. D. Huynh , P. Areias , T. Rabczuk

The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of…

Applied Physics · Physics 2020-11-17 P. K. Kristensen , C. F. Niordson , E. Martínez-Pañeda

Phase field method has been widely used because of its excellent ability to simulate fracture problems. At present, the implementation process is mainly based on commercial software, and the operation process is relatively complex. In this…

Materials Science · Physics 2023-02-06 Yuanfeng Yu , Xiaoya Zheng

In this paper, we discuss the implementation of a cell based smoothed finite element method (CSFEM) within the commercial finite element software Abaqus. The salient feature of the CSFEM is that it does not require an explicit form of the…

This work investigates the existing capabilities and limitations in numerical modeling of fracture problems in functionally graded materials (FGMs) by means of the well-known finite element code ABAQUS. Quasi-static crack initiation and…

Materials Science · Physics 2017-11-02 Emilio Martínez-Pañeda , Rafael Gallego

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 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

This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling…

Computational Engineering, Finance, and Science · Computer Science 2019-03-01 Jacinto Ulloa , Patricio Rodríguez , Cristóbal Samaniego , Esteban Samaniego

We present a phase field formulation for fracture in functionally graded materials (FGMs). The model builds upon homogenization theory and accounts for the spatial variation of elastic and fracture properties. Several paradigmatic case…

Materials Science · Physics 2019-04-19 Hirshikesh , Sundararajan Natarajan , Ratna K. Annabattula , Emilio Martínez-Pañeda

We present a new phase field framework for modelling fracture and fatigue in Shape Memory Alloys (SMAs). The constitutive model captures the superelastic behaviour of SMAs and damage is driven by the elastic and transformation strain energy…

Computational Engineering, Finance, and Science · Computer Science 2020-12-02 Marlini Simoes , Emilio Martínez-Pañeda

A novel phase field material point method is introduced for robust simulation of dynamic fracture in elastic media considering the most general case of anisotropic surface energy. Anisotropy is explicitly introduced through a properly…

Numerical Analysis · Mathematics 2019-09-04 Emmanouil Kakouris , Savvas P. Triantafyllou
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