A multiscale virtual element method for the analysis of heterogeneous media

[1]  C. F. Niordson,et al.  Size-effects on yield surfaces for micro reinforced composites , 2011 .

[2]  Joseph E. Bishop,et al.  Simulating the pervasive fracture of materials and structures using randomly close packed Voronoi tessellations , 2009 .

[3]  F. Brezzi,et al.  A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES , 2005 .

[4]  Glaucio H. Paulino,et al.  Addressing Integration Error for Polygonal Finite Elements Through Polynomial Projections: A Patch Test Connection , 2013, 1307.4423.

[5]  G. Paulino,et al.  PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab , 2012 .

[6]  Glaucio H. Paulino,et al.  On the Virtual Element Method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes , 2014 .

[7]  M. Shashkov,et al.  A new discretization methodology for diffusion problems on generalized polyhedral meshes , 2007 .

[8]  F. Brezzi,et al.  Basic principles of Virtual Element Methods , 2013 .

[9]  Qiang Du,et al.  Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations , 2006, SIAM J. Numer. Anal..

[10]  Glaucio H. Paulino,et al.  Gradient correction for polygonal and polyhedral finite elements , 2015 .

[11]  N. Sukumar,et al.  Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons , 2011 .

[12]  Glaucio H. Paulino,et al.  Polygonal finite elements for incompressible fluid flow , 2014 .

[13]  Hong-wu Zhang,et al.  Extended multiscale finite element method for mechanical analysis of heterogeneous materials , 2010 .

[14]  Glaucio H. Paulino,et al.  Polygonal finite elements for topology optimization: A unifying paradigm , 2010 .

[15]  Savvas P. Triantafyllou,et al.  A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials , 2014 .

[16]  Franco Dassi,et al.  High-order Virtual Element Method on polyhedral meshes , 2017, Comput. Math. Appl..

[17]  Pavel B. Bochev,et al.  Principles of Mimetic Discretizations of Differential Operators , 2006 .

[18]  Joseph E. Bishop,et al.  A displacement‐based finite element formulation for general polyhedra using harmonic shape functions , 2014 .

[19]  Carl T. Herakovich,et al.  Mechanics of composites: A historical review , 2012 .

[20]  Magdalena Ortiz,et al.  Local maximum‐entropy approximation schemes: a seamless bridge between finite elements and meshfree methods , 2006 .

[21]  Ahmed Alsaedi,et al.  Equivalent projectors for virtual element methods , 2013, Comput. Math. Appl..

[22]  M. Tootkaboni,et al.  A multi‐scale spectral stochastic method for homogenization of multi‐phase periodic composites with random material properties , 2010 .

[23]  Franco Dassi,et al.  Bricks for the mixed high-order virtual element method: Projectors and differential operators , 2018, Applied Numerical Mathematics.

[24]  Glaucio H. Paulino,et al.  PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes , 2012 .

[25]  Lourenco Beirao da Veiga,et al.  Stability Analysis for the Virtual Element Method , 2016, 1607.05988.

[26]  L. B. D. Veiga,et al.  A Mimetic discretization method for linear elasticity , 2010 .

[27]  Alexandre Ern,et al.  Analysis of Compatible Discrete Operator schemes for elliptic problems on polyhedral meshes , 2012, 1211.3354.

[28]  Charles E. Augarde,et al.  The use of Timoshenko's exact solution for a cantilever beam in adaptive analysis , 2008 .

[29]  J. E. Bolander,et al.  Voronoi-based Interpolants for Fracture Modelling , 2022 .

[30]  N. Sukumar,et al.  Conforming polygonal finite elements , 2004 .

[31]  Richard S. Falk,et al.  Basic principles of mixed Virtual Element Methods , 2014 .

[32]  A. Russo,et al.  New perspectives on polygonal and polyhedral finite element methods , 2014 .

[33]  Xuxin Tu,et al.  Multiscale framework for behavior prediction in granular media , 2009 .

[34]  Stéphane Bordas,et al.  Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping , 2009 .

[35]  Glaucio H. Paulino,et al.  Reduction in mesh bias for dynamic fracture using adaptive splitting of polygonal finite elements , 2014 .

[36]  Gianmarco Manzini,et al.  Hourglass stabilization and the virtual element method , 2015 .

[37]  DeroseTony,et al.  Harmonic coordinates for character articulation , 2007 .

[38]  Annalisa Buffa,et al.  Mimetic finite differences for elliptic problems , 2009 .

[39]  R. Eymard,et al.  A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS , 2008, 0812.2097.

[40]  Gianmarco Manzini,et al.  Mimetic finite difference method , 2014, J. Comput. Phys..

[41]  Alberto Taliercio,et al.  Macroscopic strength estimates for metal matrix composites embedding a ductile interphase , 2007 .

[42]  David J. Smith,et al.  Micro-mechanics of off-axis loading of metal matrix composites using finite element analysis , 2001 .

[43]  Matías Fernando Benedetto,et al.  An engineering perspective to the virtual element method and its interplay with the standard finite element method , 2019, Computer Methods in Applied Mechanics and Engineering.

[44]  Glaucio H. Paulino,et al.  Unstructured polygonal meshes with adaptive refinement for the numerical simulation of dynamic cohesive fracture , 2014, International Journal of Fracture.

[45]  Lourenço Beirão da Veiga,et al.  Virtual Elements for Linear Elasticity Problems , 2013, SIAM J. Numer. Anal..

[46]  Amir R. Khoei,et al.  A polygonal finite element method for modeling arbitrary interfaces in large deformation problems , 2012 .

[47]  E. Artioli,et al.  High-order virtual element method for the homogenization of long fiber nonlinear composites , 2018, Computer Methods in Applied Mechanics and Engineering.

[48]  Kai Hormann,et al.  A general construction of barycentric coordinates over convex polygons , 2006, Adv. Comput. Math..

[49]  Franco Brezzi,et al.  The Hitchhiker's Guide to the Virtual Element Method , 2014 .

[50]  Michael S. Floater,et al.  Gradient Bounds for Wachspress Coordinates on Polytopes , 2013, SIAM J. Numer. Anal..

[51]  Y. Kuznetsov,et al.  New mixed finite element method on polygonal and polyhedral meshes , 2005 .

[52]  Gianmarco Manzini,et al.  Arbitrary-Order Nodal Mimetic Discretizations of Elliptic Problems on Polygonal Meshes , 2011, SIAM J. Numer. Anal..

[53]  Bo Wang,et al.  Extended multiscale finite element method for small-deflection analysis of thin composite plates with aperiodic microstructure characteristics , 2017 .

[54]  Ivo Babuška,et al.  Homogenization Approach In Engineering , 1976 .

[55]  Lourenço Beirão da Veiga,et al.  Virtual element methods for parabolic problems on polygonal meshes , 2015 .

[56]  K. Lipnikov,et al.  The nonconforming virtual element method , 2014, 1405.3741.

[57]  Koulis Pericleous,et al.  A natural extension of the conventional finite volume method into polygonal unstructured meshes for CFD application , 1996 .

[58]  B. Schrefler,et al.  Multiscale Methods for Composites: A Review , 2009 .

[59]  L. Mascotto,et al.  Exploring high-order three dimensional virtual elements: Bases and stabilizations , 2017, Comput. Math. Appl..

[60]  N. Sukumar,et al.  Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons , 2013 .

[61]  N. Kikuchi,et al.  Simulation of the multi-scale convergence in computational homogenization approaches , 2000 .

[62]  Peter Wriggers,et al.  Polygonal finite element methods for contact-impact problems on non-conformal meshes , 2014 .