Engineering › Mechanics of Materials

Numerical methods in engineering

Works Count: 58198

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Description

This cluster of papers represents advances in fracture mechanics modeling and simulation, focusing on topics such as fracture, meshless methods, extended finite element method, peridynamics, phase-field modeling, radial basis functions, crack propagation, brittle materials, discontinuities, and structural mechanics.

Keywords

Fracture; Meshless Methods; Extended Finite Element Method; Peridynamics; Phase-Field Modeling; Radial Basis Functions; Crack Propagation; Brittle Materials; Discontinuities; Structural Mechanics

The Mathematical Theory of Equilibrium Cracks in Brittle Fracture

1962-01-01

Г. И. Баренблатт

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Radial basis functions for multivariable interpolation: a review

1987-01-01

M. J. D. Powell

Boundary element methods in engineering science

1984-02-01

P. K. Banerjee , R. Butterfield

The boundary element method for engineers

1981-07-01

C. A. Brebbia

The Dual Reciprocity Boundary Element Method

1991-01-01

P. W. Partridge , C. A. Brebbia , L.C. Wrobel

A review on phase-field models of brittle fracture and a new fast hybrid formulation

2014-12-11

Marreddy Ambati , Tymofiy Gerasimov , Laura De Lorenzis

Meshless methods: A review and computer implementation aspects

2008-01-20

Vinh Phu Nguyen , Timon Rabczuk , Stéphane Bordas +1 more

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Extended finite element method for cohesive crack growth

2002-05-01

Nicolas Moës , Ted Belytschko

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Arbitrary discontinuities in finite elements

2001-01-01

Ted Belytschko , Nicolas Mo�s , Shuji Usui +1 more

A technique for modelling arbitrary discontinuities in nite elements is presented.Both discontinuities in the function and its derivatives are considered.Methods for intersecting and branching discontinuities are given.In all cases, the … A technique for modelling arbitrary discontinuities in nite elements is presented.Both discontinuities in the function and its derivatives are considered.Methods for intersecting and branching discontinuities are given.In all cases, the discontinuous approximation is constructed in terms of a signed distance functions, so level sets can be used to update the position of the discontinuities.A standard displacement Galerkin method is used for developing the discrete equations.Examples of the following applications are given: crack growth, a journal bearing, a non-bonded circular inclusion and a jointed rock mass.

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Extended finite element method for three-dimensional crack modelling

2000-01-01

N. Sukumar , Nicolas Mo�s , Brian J. Moran +1 more

An extended finite element method (X-FEM) for three-dimensional crack modelling is described. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to … An extended finite element method (X-FEM) for three-dimensional crack modelling is described. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Stress intensity factors (SIFs) for planar three-dimensional cracks are presented, which are found to be in good agreement with benchmark solutions. Copyright © 2000 John Wiley & Sons, Ltd.

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Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments

2009-05-05

Hanen Amor , Jean‐Jacques Marigo , Corrado Maurini

Linear elastic materials with voids

1983-07-01

Stephen C. Cowin , Jace W. Nunziato

A proposed standard set of problems to test finite element accuracy

1985-04-01

Richard H. MacNeal , R. L. Harder

A phase-field description of dynamic brittle fracture

2012-01-26

Michael J. Borden , Clemens V. Verhoosel , Michael A. Scott +2 more

Fracture mechanics for piezoelectric ceramics

1992-05-01

Zhigang Suo , Chung-Lun Kuo , D. M. Barnett +1 more

A generalized solid-state nudged elastic band method

2012-02-16

Daniel Sheppard , Penghao Xiao , William D. Chemelewski +2 more

A generalized solid-state nudged elastic band (G-SSNEB) method is presented for determining reaction pathways of solid–solid transformations involving both atomic and unit-cell degrees of freedom. We combine atomic and cell … A generalized solid-state nudged elastic band (G-SSNEB) method is presented for determining reaction pathways of solid–solid transformations involving both atomic and unit-cell degrees of freedom. We combine atomic and cell degrees of freedom into a unified description of the crystal structure so that calculated reaction paths are insensitive to the choice of periodic cell. For the rock-salt to wurtzite transition in CdSe, we demonstrate that the method is robust for mechanisms dominated either by atomic motion or by unit-cell deformation; notably, the lowest-energy transition mechanism found by our G-SSNEB changes with cell size from a concerted transformation of the cell coordinates in small cells to a nucleation event in large cells. The method is efficient and can be applied to systems in which the force and stress tensor are calculated using density functional theory.

On cracks in rectilinearly anisotropic bodies

1965-09-01

G. C. Sih , Paul C. Paris , G. R. Irwin

THE PARTITION OF UNITY METHOD

1997-02-28

Ivo Babuška , Jens Markus Melenk

A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved. This new method can … A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved. This new method can therefore be more efficient than the usual finite element methods. An additional feature of the partition-of-unity method is that finite element spaces of any desired regularity can be constructed very easily. This paper includes a convergence proof of this method and illustrates its efficiency by an application to the Helmholtz equation for high wave numbers. The basic estimates for a posteriori error estimation for this new method are also proved. © 1997 by John Wiley & Sons, Ltd.

Nonlocal Damage Theory

1987-10-01

Gilles Pijaudier‐Cabot , Zdeněk P. Bažant

In the usual local finite element analysis, strain softening causes spurious mesh sensitivity and incorrect convergence when the element is refined to vanishing size. In a previous continuum formulation, these … In the usual local finite element analysis, strain softening causes spurious mesh sensitivity and incorrect convergence when the element is refined to vanishing size. In a previous continuum formulation, these incorrect features were overcome by the imbricate nonlocal continuum, which, however, introduced some unnecessary computational complications due to the fact that all response was treated as nonlocal. The key idea of the present nonlocal damage theory is to subject to nonlocal treatment only those variables that control strain softening, and to treat the elastic part of the strain as local. The continuum damage mechanics formulation, convenient for separating the nonlocal treatment of damage from the local treatment of elastic behavior, is adopted in the present work. The only required modification is to replace the usual local damage energy release rate with its spatial average over the representative volume of the material whose size is a characteristic of the material. Avoidance of spurious mesh sensitivity and proper convergence are demonstrated by numerical examples, including static strain softening in a bar, longitudinal wave propagation in strain‐softening material, and static layered finite element analysis of a beam. In the last case, the size of the representative volume serving in one dimension as the averaging length for damage must not be less than the beam depth, due to the hypothesis of plane cross sections. It is also shown that averaging of the fracturing strain leads to an equivalent formulation, which could be extended to anisotropic damage due to highly oriented cracking.

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Mixed finite element methods — Reduced and selective integration techniques: A unification of concepts

1978-07-01

David S. Malkus , Thomas J.R. Hughes

Numerical experiments in revisited brittle fracture

2000-04-01

Blaise Bourdin , Gilles A. Francfort , Jean‐Jacques Marigo

Matrix fracture in fiber-reinforced ceramics

1986-01-01

Bernard Budiansky , John W. Hutchinson , A.G. Evans

Generalizing the finite element method: Diffuse approximation and diffuse elements

1992-01-01

Bernard Nayroles , Gilbert Touzot , Pierre Villon

Modeling holes and inclusions by level sets in the extended finite-element method

2001-09-01

N. Sukumar , David L. Chopp , Nicolas Moës +1 more

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Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—II solutions to parabolic, hyperbolic and elliptic partial differential equations

1990-01-01

E.J. Kansa

A class of mixed assumed strain methods and the method of incompatible modes

1990-06-01

J.C. Simo , M. S. Rifai

Abstract A three‐field mixed formulation in terms of displacements, stresses and an enhanced strain field is presented which encompasses, as a particular case, the classical method of incompatible modes. Within … Abstract A three‐field mixed formulation in terms of displacements, stresses and an enhanced strain field is presented which encompasses, as a particular case, the classical method of incompatible modes. Within this frame‐work, incompatible elements arise as particular ‘compatible’ mixed approximations of the enhanced strain field. The conditions that the stress interpolation contain piece‐wise constant functions and be L 2 ‐ortho‐gonal to the enhanced strain interpolation, ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation. The preceding conditions are formulated in a form particularly convenient for element design. As an illustration of the methodology three new elements are developed and shown to exhibit good performance: a plane 3D elastic/plastic QUAD, an axisymmetric element and a thick plate bending QUAD. The formulation described herein is suitable for non‐linear analysis.

A meshfree method based on the peridynamic model of solid mechanics

2005-03-23

Stewart Silling , E. Askari

A stabilized conforming nodal integration for Galerkin mesh-free methods

2000-01-01

Jiun‐Shyan Chen , C.T. Wu , Sangpil Yoon +1 more

Domain integration by Gauss quadrature in the Galerkin mesh-free methods adds considerable complexity to solution procedures. Direct nodal integration, on the other hand, leads to a numerical instability due to … Domain integration by Gauss quadrature in the Galerkin mesh-free methods adds considerable complexity to solution procedures. Direct nodal integration, on the other hand, leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes. A strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration. For convergence, an integration constraint (IC) is introduced as a necessary condition for a linear exactness in the mesh-free Galerkin approximation. The gradient matrix of strain smoothing is shown to satisfy IC using a divergence theorem. No numerical control parameter is involved in the proposed strain smoothing stabilization. The numerical results show that the accuracy and convergent rates in the mesh-free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method. It is also demonstrated that the Gauss integration method fails to meet IC in mesh-free discretization. For this reason the proposed method provides even better accuracy than Gauss integration for Galerkin mesh-free method as presented in several numerical examples. Copyright © 2001 John Wiley & Sons, Ltd.

Cracking particles: a simplified meshfree method for arbitrary evolving cracks

2004-10-18

Timon Rabczuk , Ted Belytschko

Abstract A new approach for modelling discrete cracks in meshfree methods is described. In this method, the crack can be arbitrarily oriented, but its growth is represented discretely by activation … Abstract A new approach for modelling discrete cracks in meshfree methods is described. In this method, the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed. The crack is modelled by a local enrichment of the test and trial functions with a sign function (a variant of the Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centred at the particles in three dimensions, lines centred at the particles in two dimensions. The model is applied to several 2D problems and compared to experimental data. Copyright © 2004 John Wiley & Sons, Ltd.

Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress

2002-10-17

Zdeněk P. Bažant , Milan Jirásek

Modeling of the evolution of distributed damage such as microcracking, void formation, and softening frictional slip necessitates strain-softening constitutive models. The nonlocal continuum concept has emerged as an effective means … Modeling of the evolution of distributed damage such as microcracking, void formation, and softening frictional slip necessitates strain-softening constitutive models. The nonlocal continuum concept has emerged as an effective means for regularizing the boundary value problems with strain softening, capturing the size effects and avoiding spurious localization that gives rise to pathological mesh sensitivity in numerical computations. A great variety of nonlocal models have appeared during the last two decades. This paper reviews the progress in the nonlocal models of integral type, and discusses their physical justifications, advantages, and numerical applications.

Peridynamic States and Constitutive Modeling

2007-07-14

Stewart Silling , Michael A. Epton , Olaf Weckner +2 more

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Arbitrary branched and intersecting cracks with the extended finite element method

2000-01-01

Christophe Daux , Nicolas Mo�s , John E. Dolbow +2 more

Extensions of a new technique for the finite element modelling of cracks with multiple branches, multiple holes and cracks emanating from holes are presented. This extended finite element method (X-FEM) … Extensions of a new technique for the finite element modelling of cracks with multiple branches, multiple holes and cracks emanating from holes are presented. This extended finite element method (X-FEM) allows the representation of crack discontinuities and voids independently of the mesh. A standard displacement-based approximation is enriched by incorporating discontinuous fields through a partition of unity method. A methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed. Computation of the stress intensity factors (SIF) in different examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique. Copyright © 2000 John Wiley & Sons, Ltd.

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Meshless methods: An overview and recent developments

1996-12-01

Ted Belytschko , Y. Krongauz , D. Organ +2 more

Radial basis functions

2000-01-01

M. D. Buhmann

Radial basis function methods are modern ways to approximate multivariate functions, especially in the absence of grid data. They have been known, tested and analysed for several years now and … Radial basis function methods are modern ways to approximate multivariate functions, especially in the absence of grid data. They have been known, tested and analysed for several years now and many positive properties have been identified. This paper gives a selective but up-to-date survey of several recent developments that explains their usefulness from the theoretical point of view and contributes useful new classes of radial basis function. We consider particularly the new results on convergence rates of interpolation with radial basis functions, as well as some of the various achievements on approximation on spheres, and the efficient numerical computation of interpolants for very large sets of data. Several examples of useful applications are stated at the end of the paper.

Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations

2010-03-22

Christian Miehé , Fabian Welschinger , Martina Hofacker

Abstract The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by a … Abstract The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by a diffusive crack modeling based on the introduction of a crack phase‐field. In this paper, we outline a thermodynamically consistent framework for phase‐field models of crack propagation in elastic solids, develop incremental variational principles and consider their numerical implementations by multi‐field finite element methods. We start our investigation with an intuitive and descriptive derivation of a regularized crack surface functional that Γ‐converges for vanishing length‐scale parameter to a sharp crack topology functional. This functional provides the basis for the definition of suitable convex dissipation functions that govern the evolution of the crack phase‐field. Here, we propose alternative rate‐independent and viscous over‐force models that ensure the local growth of the phase‐field. Next, we define an energy storage function whose positive tensile part degrades with increasing phase‐field. With these constitutive functionals at hand, we derive the coupled balances of quasi‐static stress equilibrium and gradient‐type phase‐field evolution in the solid from the argument of virtual power. Here, we consider a canonical two‐field setting for rate‐independent response and a time‐regularized three‐field formulation with viscous over‐force response. It is then shown that these balances follow as the Euler equations of incremental variational principles that govern the multi‐field problems. These principles make the proposed formulation extremely compact and provide a perfect base for the finite element implementation, including features such as the symmetry of the monolithic tangent matrices. We demonstrate the performance of the proposed phase‐field formulations of fracture by means of representative numerical examples. Copyright © 2010 John Wiley & Sons, Ltd.

The extended/generalized finite element method: An overview of the method and its applications

2010-04-23

Thomas‐Peter Fries , Ted Belytschko

Abstract An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, … Abstract An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non‐smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non‐smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi‐field problems. Copyright © 2010 John Wiley & Sons, Ltd.

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Element‐free Galerkin methods

1994-01-30

Ted Belytschko , Ye Lu , Linxia Gu

Abstract An element‐free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least‐squares interpolants … Abstract An element‐free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least‐squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least‐squares interpolants and the choices of the weight function are also discussed in this paper.

A finite element method for crack growth without remeshing

1999-09-10

Nicolas Mo�s , John E. Dolbow , Ted Belytschko

An improvement of a new technique for modelling cracks in the finite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous fields … An improvement of a new technique for modelling cracks in the finite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous fields and the near tip asymptotic fields through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique. Copyright © 1999 John Wiley & Sons, Ltd.

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A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics

1998-08-24

Satya N. Atluri , Tengteng Zhu

A point interpolation meshless method based on radial basis functions

2002-05-28

Jianguo Wang , G. R. Liu

Abstract A point interpolation meshless method is proposed based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity associated with the meshless methods based … Abstract A point interpolation meshless method is proposed based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis. This non‐singularity is useful in constructing well‐performed shape functions. Furthermore, the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least‐squares approximation. In addition, the partial derivatives of shape functions are easily obtained, thus improving computational efficiency. Examples on curve/surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high. Copyright © 2002 John Wiley & Sons, Ltd.

Elastic crack growth in finite elements with minimal remeshing

1999-06-20

Ted Belytschko , T. Howard Black

A minimal remeshing finite element method for crack growth is presented. Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack. This … A minimal remeshing finite element method for crack growth is presented. Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack. This method allows the crack to be arbitrarily aligned within the mesh. For severely curved cracks, remeshing may be needed but only away from the crack tip where remeshing is much easier. Results are presented for a wide range of two-dimensional crack problems showing excellent accuracy. Copyright © 1999 John Wiley & Sons, Ltd.

A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits

2010-05-08

Christian Miehé , Martina Hofacker , Fabian Welschinger

Peridynamic Theory and Its Applications

2013-10-21

Erdogan Madenci , Erkan Oterkus

Meshfree Approximation Methods with Matlab

2007-04-01

Gregory E. Fasshauer

The boundary element method for engineers

1978-11-01

P. Ward

The Fourier transform and its applications

1980-04-01

M. L. J. Hautus

A three-dimensional large deformation meshfree method for arbitrary evolving cracks

2007-03-05

Timon Rabczuk , Ted Belytschko

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The Variational Approach to Fracture

2008-03-14

Blaise Bourdin , Gilles A. Francfort , Jean‐Jacques Marigo

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Fractional-Order Derivative, Bounding Surface Plasticity–Based Anisotropic NorSand: Formulation and Validation

2025-06-26

Hadi Hasanzadehshooiili , Jean-Marie Konrad , Jean Côté | Journal of Geotechnical and Geoenvironmental Engineering

Numerical simulation and shear strength research of reinforced concrete beam based on peridynamics

2025-06-25

Zhongwen Gong , Ergang Xiong , Shang Wang +2 more | Frontiers of Structural and Civil Engineering

A Newton-Krylov-based implicit integration algorithm for single and multisurface plasticity

2025-06-25

Rafael Abreu , Eleazar Cristian Mejía Sanchez , Deane Roehl | Computers & Structures

A phase field model for hydraulic fracture: Drucker–Prager driving force and a hybrid coupling strategy

2025-06-24

Yousef Navidtehrani , Covadonga Betegón , Javier Vallejos +1 more | Computer Methods in Applied Mechanics and Engineering

Simulation of the Mesoscale Cracking Processes in Concrete Under Tensile Stress by Discrete Element Method

2025-06-24

Zhenyu Zhu , Bintang Mas Mediamartha , Shuyang Yu +3 more | Materials

Material scientists face a critical challenge in characterizing the mesoscopic damage evolution of concrete under tensile loading, as traditional experimental and theoretical approaches struggle to resolve the complexities of its … Material scientists face a critical challenge in characterizing the mesoscopic damage evolution of concrete under tensile loading, as traditional experimental and theoretical approaches struggle to resolve the complexities of its multiphase heterogeneous structure. This study addresses this gap by employing the Discrete Element Method (DEM) with PFC2D to model concrete’s mesoscopic cracking, integrating aggregates, mortar, interfacial transition zones (ITZ), and pores. Through parameter calibration against experimental data, uniaxial tensile simulations reveal how aggregate percentages (30–45%) and pore percentages (1–6%) influence crack propagation and tensile strength. Specifically, when the aggregate percentage increased from 30% to 40%, the peak tensile strength decreased by 26%, while increasing from 40% to 45% led to a recovery in strength. With porosity increasing from 2% to 4%, the peak strength dropped by approximately 3%, and further to 6% caused a 14% reduction, demonstrating the quantitative impact of microstructural parameters on concrete performance. Simulation results align closely with experimental data, validating DEM’s efficacy in modeling mesoscopic cracking. This work provides a mesoscopic theoretical foundation for optimizing concrete’s tensile properties and underscores the need to incorporate realistic mesoscopic features in future simulations.

Iterative coupling of DDM and FEM for planar hydraulic fracturing under non-uniform confining stresses

2025-06-24

Luis Fernando Paullo Muñoz , Eleazar Cristian Mejía Sanchez , Julio Rueda +1 more | Computers and Geotechnics

Fractional double-phase problems with Kirchhoff-type operators and variable exponents

2025-06-23

Mohamed El Khayr Boukraa , Mohamed Saad Bouh Elemine Vall | Journal of Elliptic and Parabolic Equations

Novel multidimensional Gaidai hypersurface reliability design concept incorporating material manufacturing imperfections

2025-06-23

Oleg Gaidai , Jinlu Sheng , Shicheng He +6 more | Australian Journal of Multi-Disciplinary Engineering

A Sparse Hierarchical hp-Finite Element Method on Disks and Annuli

2025-06-23

Ioannis P. A. Papadopoulos , Sheehan Olver | Journal of Scientific Computing

Peridynamics model of viscoelasticity for shells and metasurfaces

2025-06-23

Kundan Kumar , Nilesh Choudhary , Sajal +2 more | Computer Methods in Applied Mechanics and Engineering

Mathematical solutions for moving generalized electric-magnetic-polarization saturation models in magneto-electro-elastic materials via weight functions

2025-06-21

Sandeep Singh | Mechanics Research Communications

Effect of bedding structures on hydraulic fracture propagation behavior investigated using a coupled thermo-hydraulic-mechanical numerical model based on the phase-field cohesive zone method

2025-06-21

Xun Gong , Zhijun Jin , Xinhua Ma +2 more | Computers and Geotechnics

Finite block method with automatic differentiation algorithm for Reissner plate nonlinear analysis

2025-06-20

Xiaopeng Li , S.M Liu , Weilin Huang +1 more | Engineering Analysis with Boundary Elements

Mindlin’s Problem for a Surface-Stiffened Exponentially-Graded Transversely Isotropic Half-Space

2025-06-19

Parham Samea , S. Farzad Ahmadi | Journal of Elasticity

Implementation of a Non-Intrusive Primal–Dual Method with 2D-3D-Coupled Models for the Analysis of a DCB Test with Cohesive Zones

2025-06-19

Raquel Villar-Hernández , Jorge Hinojosa , Ignacio Fuenzalida-Henríquez +1 more | Applied Sciences

This study explores a global–local non-intrusive computational strategy to address problems in computational mechanics, specifically applied to a double cantilever beam (DCB) with cohesive interfaces. The method aims to reduce … This study explores a global–local non-intrusive computational strategy to address problems in computational mechanics, specifically applied to a double cantilever beam (DCB) with cohesive interfaces. The method aims to reduce computational requirements while maintaining accuracy. The DCB, representing two plates connected by a cohesive zone simulating delamination, was modeled with a 3D representation using the cohesive zone method for crack propagation. Different mesh configurations were tested to evaluate the strategy’s effectiveness. The results showed that the global–local strategy successfully provided solutions that were comparable to monolithic models. Mesh size had a significant impact on the results, but even with a simplified local model that did not fully represent the plate thickness, the structural deformation and crack displacement were accurately captured. The interface near the study area influenced the stress distribution. Although effective, the strategy requires careful mesh selection due to its sensitivity to mesh size. Future research could optimize mesh configurations, expand the strategy to other structures, and explore the use of orthotropic materials. This research introduces a computational approach that reduces costs while simulating delamination and crack propagation, highlighting the importance of mesh configuration for real-world applications.

An adaptive phase-field model integrated with multi-patch isogeometric analysis and adaptive cycle jump scheme for thermo-electro-mechanical fatigue fracture in flexoelectric solids

2025-06-19

Haozhi Li , Tiantang Yu , Zhaowei Liu +2 more | Computer Methods in Applied Mechanics and Engineering

Bulk penetration of edge properties in two-dimensional materials

2025-06-18

NULL AUTHOR_ID | Physical review. B./Physical review. B

A new formulation of SBFEM and its application to SIF computation of 3D crack

2025-06-18

Yuguang Fu , Xin Xu , Zhiqiang Hu +1 more | Engineering Fracture Mechanics

Dislocation stress-field and solute-strengthening predictions based on minimal ab-initio input

2025-06-18

Davide Fioravanti , J.P.M. Hoefnagels , E. van der Giessen +1 more | Computational Materials Science

Phase-field modeling of fracture via homogenization

2025-06-18

Gerard Villalta , A. Ferrer , F. Otero | International Journal of Fracture

Abstract This study presents a novel phase-field modeling approach for brittle fracture that incorporates computational homogenization techniques to characterize the microstructural degradation of the material. Traditional phase-field models often implement … Abstract This study presents a novel phase-field modeling approach for brittle fracture that incorporates computational homogenization techniques to characterize the microstructural degradation of the material. Traditional phase-field models often implement degradation and dissipation functions in terms of the phase-field variable that, despite offering satisfactory results, their physical interpretation and their extension to anisotropic fracture behavior is not always clear. To address this challenge, we develop a framework inspired by the nucleation, growth, and coalescence of microstructural voids to model macroscopic fracture. The proposed approach employs homogenization techniques to calculate the effective material properties when introducing voids of varying sizes and shapes. By solving the homogenization problem for different void geometries, we obtain degradation functions that relate the size of microstructural voids to the homogenized constitutive tensor. These degradation functions provide a direct link between microscale damage mechanisms and macroscale fracture behavior. Comparative analyses with conventional AT1 and AT2 models reveal strong correlations between their response and those obtained via homogenization techniques. This relationship highlights the ability of homogenized models to not only replicate established results but also provide a new understanding of the phase-field variable.

Thermo‐Mechanical Crack Growth Investigation in Foam Core Graphite Epoxy Laminated Sandwich Structure Using Phase Field Method

2025-06-18

Manish Singh Rajput , Raj Kiran , Himanshu Pathak | Advanced Theory and Simulations

Abstract Foam core sandwich composite structures have wide structural applications in aerospace; they are subjected to thermo‐mechanical loading environments during their service life. Therefore, it is necessary to predict the … Abstract Foam core sandwich composite structures have wide structural applications in aerospace; they are subjected to thermo‐mechanical loading environments during their service life. Therefore, it is necessary to predict the fracture behavior of these composite structures accurately. In this work, a computational framework based on the well‐proven, computationally efficient hybrid PFM associated with an orthogonal decomposition scheme is presented and implemented to predict the thermo‐mechanical crack growth phenomena in an orthotropic multi‐material layered system (foam core graphite epoxy laminated composite sandwich structure) under the combined effect of mechanical loading and thermal environment (heating or cooling). The thermo‐mechanical fracture response of the laminated composite sandwich structure (LCSS) is analyzed for crack initiation, crack growth, and load‐bearing capacity. Both the crack intersection and crack merging phenomena are captured during the failure of LCSS under thermal cooling and thermal heating, accompanied by mechanical load. The performance of the LCSS is analyzed by comparing the structural load capacity, crack nucleation threshold, and fracture energy of the structure in multiple numerical cases. The presented methodology, based on a hybrid phase field method and orthogonal strain decomposition scheme, is validated for structural problems from existing literature under the thermo‐mechanical loading and further extended to LCSS structure cases.

A peridynamic biochemo-mechanical model for Alzheimer’s Disease

2025-06-17

Lianfu Qiu , Xiaofei Wang , Zhen Wei +1 more | Engineering Analysis with Boundary Elements

Modeling the Formation and Propagation of Equidistant Fractures in Layered Rock Masses Using the Advanced Peridynamic Method

2025-06-16

Pengfei Ma , Yichen Zhang , Yuancheng Li +2 more | Rock Mechanics and Rock Engineering

Numerical Method and Analysis for the Coupled Sine‐Gordon Equations on Unbounded Domains

2025-06-16

Hongwei Li , Xinyue Chen | Numerical Methods for Partial Differential Equations

ABSTRACT In this article, we delve into the efficient artificial boundary method, specifically focusing on its application in solving the coupled sine‐Gordon equations on unbounded domains, which are widely used … ABSTRACT In this article, we delve into the efficient artificial boundary method, specifically focusing on its application in solving the coupled sine‐Gordon equations on unbounded domains, which are widely used in a variety of scientific fields. By incorporating the operator splitting approach, we have designed local artificial boundary conditions that effectively address the challenges posed by the unbounded nature of the physical domain and the intricate nonlinearities involved. These conditions are specifically developed for the coupled sine‐Gordon equations, ensuring that wave outgoing boundaries are achieved without any reflections. An initial boundary value problem on a bounded computational domain is obtained, and the finite difference method is adopted to discretize the reduced problem. Rigorous analysis of the stability and convergence of the reduced problem is conducted through the introduction of an energy function. Some numerical examples are presented to demonstrate the accuracy and effectiveness of the method.

Electromagnetic–Thermal–Mechanical–Damage Coupling Simulation of Rock Under Microwave Irradiation Based on the COMSOL–Peridynamics Method

2025-06-16

Luming Zhou , Zhihong Zhao , Zhibo Duan +2 more | Rock Mechanics and Rock Engineering

Interface strength and crack propagation mechanisms in sintered copper nanoparticles

2025-06-13

Leiming Du , Weiping Jiao , Olof Bäcke +6 more | Acta Materialia

Tension-compression asymmetry based on different energy decompositions within a gradient-extended two-surface damage-plasticity framework

2025-06-13

Jian Zhang , Jike Han , Qinghua Zhang +2 more | Computational Mechanics

An Extrapolated Second-Order BDF Combined with Local Meshfree Radial Point Interpolation Method for Numerical Simulation of Multi-Dimensional Regularized Long Wave Equation Emerging in Fluids

2025-06-13

Ömer Oruç | Journal of Scientific Computing

Abstract This study proposes, an accurate method based on a unification of second-order BDF and a local meshfree method to obtain numerical solutions of one-, two-, three- and four-dimensional regularized … Abstract This study proposes, an accurate method based on a unification of second-order BDF and a local meshfree method to obtain numerical solutions of one-, two-, three- and four-dimensional regularized long wave equations. The regularized long wave equation is a frequently used important nonlinear partial differential equation in modelling of fluids. The proposed method discretize the temporal variable via a second-order extrapolated BDF approach in first stage. In second stage, space variables are discretized via local meshfree radial point interpolation method based on thin plate splines. In this way, a full discrete scheme is obtained for getting numerical solution of the considered problem. The use of local radial point interpolation method is promising approach for large scale problems due to sparse matrices obtained in discretization of space variables. The stability and convergence analysis of time discrete scheme are investigated through the medium of energy method. To assess performance of the proposed method, acquired numerical outcomes are subjected to comparisons with analytical solutions and with over ten different existing methods in literature such as finite difference, finite element, meshfree and wavelet methods. The numerical outcomes and their comparisons confirm accuracy and reliability of the proposed method.

A polynomial-augmented RBF collocation method using ghost points for 2D elliptic problems with nonlocal boundary conditions

2025-06-12

Ömer Oruç | Computational Particle Mechanics

Extended Galerkin Neural Network Approximation of Singular Variational Problems with Error Control

2025-06-12

Mark Ainsworth , Justin Dong | SIAM Journal on Scientific Computing

Retraction Note to “A new criterion for modeling multiple discontinuities passing through an element using XIGA”

2025-06-11

I.V. Singh , Gagandeep Bhardwaj , B. K. Mishra | Journal of Mechanical Science and Technology

Application of radial basis functions augmented by polynomials in the boundary element method to solve problems governed by the Laplace equation

2025-06-11

Filipe Lopes Cruzeiro , Lucas Silveira Campos , Luciano de Oliveira Castro Lara | Engineering Computations

Purpose Radial basis function interpolation is a highly valuable tool in the field of numerical methods, and its polynomially augmented version holds promise in addressing some limitations of the traditional … Purpose Radial basis function interpolation is a highly valuable tool in the field of numerical methods, and its polynomially augmented version holds promise in addressing some limitations of the traditional formulation. In this article, we aim to analyze the performance of the boundary element method, which employs an alternative approach to traditional boundary discretization with the aid of radial basis functions. Design/methodology/approach This work presents the complete mathematical formulation along with the associated theory, as well as a comparison of errors between the proposed formulation and the traditional formulation, which uses polynomial interpolation. Additionally, a processing time analysis was conducted and is presented. Findings The proposed method yielded the lowest error across all examples with straight geometries. However, its performance was less effective in the problem involving a circular section, likely due to challenges in accurately representing this type of geometry. Originality/value The study presents an interpolation technique that can aid in mesh generation and can be extended to three-dimensional applications. Moreover, the lower errors observed in certain easily identifiable geometries suggest that this approach could be a good option for problems requiring higher accuracy.

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