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Many geo-engineering applications, e.g., enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase-field…

Geophysics · Physics 2023-04-27 Fan Fei , Andre Costa , John E. Dolbow , Randolph R. Settgast , Matteo Cusini

In this article we propose a discrete lattice model to simulate the elastic, plastic and failure behaviour of isotropic materials. Focus is given on the mathematical derivation of the lattice elements, nodes and edges, in the presence of…

Optimization and Control · Mathematics 2015-05-12 Ioannis Dassios , Andrey Jivkov , Andrew Abu-Muharib , Peter James

In this work, we examine a numerical phase-field fracture framework in which the crack irreversibility constraint is treated with a primal-dual active set method and a linearization is used in the degradation function to enhance the…

Numerical Analysis · Mathematics 2023-07-05 Leon Maximilian Kolditz , Katrin Mang , Thomas Wick

A globally-adaptive curvilinear coordinate formalism is shown to be easily convertible to a class of curvilinear transformations locally optimized around atom sites by a few parameters. Parameter transferability is established for a…

Materials Science · Physics 2009-10-31 D. R. Hamann

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

We consider a phase-field fracture propagation model, which consists of two (nonlinear) coupled partial differential equations. The first equation describes the displacement evolution, and the second is a smoothed indicator variable,…

Numerical Analysis · Mathematics 2019-12-17 Christian Engwer , Iuliu Sorin Pop , Thomas Wick

This paper presents a phase-field model for simulating the three-dimensional deformation of vesicle membranes, incorporating area-difference elasticity, with constraints on bulk volume and surface area. We develop efficient numerical…

Numerical Analysis · Mathematics 2025-11-19 Yihong Liang , Emine Celiker , Ping Lin

In this paper, we extend a micromechanics-based phase-field framework for fatigue fracture to incorporate cyclic plasticity with ratcheting. This mechanism is particularly relevant for low-cycle fatigue, where the accumulation of inelastic…

Applied Physics · Physics 2026-02-05 Mina Sarem , Nuhamin Eshetu Deresse , Els Verstrynge , Stijn François

A constitutive model based on the combination of damage mechanics and plasticity is developed to analyse concrete structures subjected to dynamic loading. The aim is to obtain a model, which requires input parameters with clear physical…

Materials Science · Physics 2011-03-09 Peter Grassl , Ulrika Nystrom , Rasmus Rempling , Kent Gylltoft

A theoretical platform is developed for active elastic-wave sensing of (stationary and advancing) fractures along bi-material interfaces in layered composites. Damaged contact surfaces are characterized by a heterogeneous distribution of…

Numerical Analysis · Mathematics 2018-01-17 Fatemeh Pourahmadian , Irene de Teresa

In this paper, the performance of different structural models based on global approach in evaluating the static response of curvilinear fibre composite laminates is analyzed. A Co shear flexible Quad-8 element developed based on…

Materials Science · Physics 2014-07-29 Anand Venkatachari , Sundararajan Natarajan , K Ramajeyathilagam , M Ganapathi

Self-sensing conductive composites can reveal deformation and damage through measurable changes in electrical resistance, which makes them attractive for embedded diagnostics and learning-enabled structural health monitoring. This paper…

Computational Physics · Physics 2026-04-07 Aamir Dean , Betim Bahtiri

Extreme localization of damage in conventional brittle materials is the source of a host of undesirable effects. We show how artificially engineered metamaterials with all brittle constituents can be designed to ensure that every breakable…

Materials Science · Physics 2021-07-14 O. U. Salman , L. Truskinovsky

We propose a decomposition of constitutive relations into crack-driving and persistent portions, specifically designed for materials with anisotropic/orthotropic behavior in the phase field approach to fracture to account for the…

Numerical Analysis · Mathematics 2022-12-28 Vahid Ziaei-Rad , Mostafa Mollaali , Thomas Nagel , Olaf Kolditz , Keita Yoshioka

This paper presents an adaptive strategy for phase-field simulations with transition to fracture. The phase-field equations are solved only in small subdomains around crack tips to determine propagation, while an XFEM discretization is used…

Computational Engineering, Finance, and Science · Computer Science 2020-07-28 Alba Muixí , Onofre Marco , Antonio Rodríguez-Ferran , Sonia Fernández-Méndez

We introduce a new multilevel domain decomposition method (MDD) for electronic structure calculations within semi-empirical and Density Functional Theory (DFT) frameworks. This method iterates between local fine solvers and global coarse…

Computational Physics · Physics 2007-05-23 M. Barrault , E. Cances , W. W. Hager , C. Le Bris

Soft fracture in highly deformable solids involves both geometric and constitutive nonlinearities, necessitating advanced theoretical and computational frameworks for its accurate understanding. Tensile fractures subjected to mixed-mode…

We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-04 Melanie Tonarelli , Simone Riva , Pietro Benedusi , Fabrizio Ferrandi , Rolf Krause

A phase-field approach is proposed for interface failure between two possibly dissimilar materials. The discrete adhesive interface is regularised over a finite width. Due to the use of a regularised crack model for the bulk material, an…

Materials Science · Physics 2019-09-06 Arne Claus Hansen-Dörr , René de Borst , Paul Hennig , Markus Kästner

To mitigate the substantial computational costs associated with modeling the mechanical behavior of large-scale architected lattice structures, this work introduces a concurrent multiscale approach: the Generalized Non-local Quasicontinuum…

Numerical Analysis · Mathematics 2025-03-14 Zi Li , Fan Yang , Qingcheng Yang
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