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An estimate of the effective toughness of heterogeneous materials is proposed based on the Phase Field Fracture model implemented in an FFT homogenization solver. The estimate is based on the simulation of the deformation of representative…

Materials Science · Physics 2025-08-12 Pedro Aranda , Javier Segurado

A numerical framework for simulating progressive failure under high-cycle fatigue loading is validated against experiments of composite quasi-isotropic open-hole laminates. Transverse matrix cracking and delamination are modeled with a…

Computational Engineering, Finance, and Science · Computer Science 2024-05-06 P. Hofman , F. P. van der Meer , L. J. Sluys

This paper is concerned with the energy decomposition of various nonlocal models, including elasticity, thin plates, and gradient elasticity, to arrive at bond-based nonlocal models in which the bond force depends only on the deformation of…

Classical Physics · Physics 2023-07-24 Huilong Ren , Timon Rabczuk , Xiaoying Zhuang , Zhiyuan Li

We address a three-dimensional model capable of describing coupled damage and plastic effects in solids at finite strains. Formulated within the variational setting of {\it generalized standard materials}, the constitutive model results…

Analysis of PDEs · Mathematics 2020-12-30 David Melching , Michael Neunteufel , Joachim Schöberl , Ulisse Stefanelli

Following the so-called Cracking Elements Method (CEM), recently presented in \cite{Yiming:14,Yiming:16}, we propose a novel Galerkin-based numerical approach for simulating quasi-brittle fracture, named Global Cracking Elements Method…

Computational Engineering, Finance, and Science · Computer Science 2019-08-20 Yiming Zhang , Herbert A. Mang

This study develops a polygonal cell-based smoothed finite element method (CSFEM) for two-dimensional seepage analyses in porous media, covering steady-state, transient, and free-surface problems. Wachspress interpolation on convex…

Numerical Analysis · Mathematics 2026-02-19 Yang Yang , Mingjiao Yan , Zongliang Zhang , Yinpeng Yin , Qiang Liu , You liang Li

The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…

Numerical Analysis · Mathematics 2014-01-21 Carsten Carstensen , Asha K. Dond , Neela Nataraj , Amiya K. Pani

Nonlinearities and instabilities in mechanical structures have shown great promise for embedding advanced functionalities. However, simulating structures subject to nonlinearities can be challenging due to the complexity of their behavior,…

Soft Condensed Matter · Physics 2025-10-23 Paul Ducarme , Bart Weber , Martin van Hecke , Johannes T. B. Overvelde

We consider a Stokes problem posed on a 2D surface embedded in a 3D domain. The equations describe an equilibrium, area-preserving tangential flow of a viscous surface fluid and serve as a model problem in the dynamics of material…

Numerical Analysis · Mathematics 2018-01-23 Maxim A. Olshanskii , Annalisa Quaini , Arnold Reusken , Vladimir Yushutin

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

This paper constructs the first mixed finite element for the linear elasticity problem in 3D using $P_3$ polynomials for the stress and discontinuous $P_2$ polynomials for the displacement on tetrahedral meshes under some mild mesh…

Numerical Analysis · Mathematics 2023-08-22 Jun Hu , Rui Ma , Yuanxun Sun

In this paper we present a new H(div)-conforming unfitted finite element method for the mixed Poisson problem which is robust in the cut configuration and preserves conservation properties of body-fitted finite element methods. The key is…

Numerical Analysis · Mathematics 2024-09-04 Christoph Lehrenfeld , Tim van Beeck , Igor Voulis

This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear…

Numerical Analysis · Mathematics 2014-01-29 Douglas N. Arnold , Gerard Awanou , Ragnar Winther

The extended finite element method (XFEM) was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to be split by a discontinuity, strong…

Numerical Analysis · Mathematics 2017-10-13 M Surendran , S Natarajan , SPA Bordas , GS Palani

In this work we aim to develop a unified mathematical framework and a reliable computational approach to model the brittle fracture in heterogeneous materials with variability in material microstructures, and to provide statistic metrics…

Materials Science · Physics 2022-08-10 Yiming Fan , Huaiqian You , Xiaochuan Tian , Xiu Yang , Xingjie Li , Naveen Prakash , Yue Yu

Within the framework of the displacement-based Virtual Element Method (VEM) for plane elasticity a significant problem is represented by an accurate evaluation of the stress field. In particular, in the classical VEM formulation, a suitable…

Numerical Analysis · Mathematics 2018-02-20 Edoardo Artioli , Stefano de Miranda , Carlo Lovadina , Luca Patruno

A mix-mode cohesive fracture model considering tension, compression and shear material behaviour is presented, which has wide applications to geotechnical problems. The model considers both elastic and inelastic displacements. Inelastic…

Computational Engineering, Finance, and Science · Computer Science 2015-01-19 Yilin Gui , Ha H. Bui , Jayantha Kodikara

Successful scientific applications of large-scale molecular dynamics often rely on automated methods for identifying the local crystalline structure of condensed phases. Many existing methods for structural identification, such as Common…

Materials Science · Physics 2016-05-24 Peter Mahler Larsen , Søren Schmidt , Jakob Schiøtz

The eXtended Finite Element Method (XFEM) is used to solve interface problems with an unfitted mesh. We present an implementation of the XFEM in the FEM-library deal.II. The main parts of the implementation are (i) the appropriate…

Numerical Analysis · Mathematics 2015-07-16 Thomas Carraro , Sven Wetterauer

The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with…