Some basic formulations of the virtual element method (VEM) for finite deformations
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Publication:2309085
DOI10.1016/j.cma.2016.12.020zbMath1439.74397OpenAlexW2566137435MaRDI QIDQ2309085
Heng Chi, Lourenco Beirão da Veiga, Glaucio H. Paulino
Publication date: 6 April 2020
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2016.12.020
Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
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Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- A variational formulation with rigid-body constraints for finite elasticity: theory, finite element implementation, and applications
- Equivalent projectors for virtual element methods
- Honeycomb Wachspress finite elements for structural topology optimization
- \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
- \texttt{PolyTop}: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes
- Polygonal finite element methods for contact-impact problems on non-conformal meshes
- Virtual element methods for plate bending problems
- A new \(I_{1}\)-based hyperelastic model for rubber elastic materials
- Variational and projection methods for the volume constraint in finite deformation elasto-plasticity
- Simulating the pervasive fracture of materials and structures using randomly close packed Voronoi tessellations
- Volume changes associated with the deformation of rubber-like solids
- Nearly isochoric elastic deformations: Application to rubberlike solids
- Mixed finite element methods - reduced and selective integration techniques: a unification of concepts
- On some mixed finite element methods for incompressible and nearly incompressible finite elasticity
- The virtual element method for discrete fracture network simulations
- On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes
- A virtual element method for contact
- A numerical approximation to the elastic properties of sphere-reinforced composites.
- A polygonal finite element method for modeling arbitrary interfaces in large deformation problems
- The nonlinear elastic response of suspensions of rigid inclusions in rubber. II: A simple explicit approximation for finite-concentration suspensions
- A paradigm for higher-order polygonal elements in finite elasticity using a gradient correction scheme
- Mean value coordinates
- Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons
- Mean value coordinates in 3D
- A virtual element method for elastic and inelastic problems on polytope meshes
- Virtual Element Method for general second-order elliptic problems on polygonal meshes
- Virtual Elements for Linear Elasticity Problems
- Basic principles of mixed Virtual Element Methods
- A displacement-based finite element formulation for general polyhedra using harmonic shape functions
- Reduction in mesh bias for dynamic fracture using adaptive splitting of polygonal finite elements
- Polygonal finite elements for finite elasticity
- Gradient correction for polygonal and polyhedral finite elements
- A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles
- Localmaximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods
- A $C^1$ Virtual Element Method for the Cahn--Hilliard Equation with Polygonal Meshes
- Polygonal finite elements for topology optimization: A unifying paradigm
- BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
- Polygonal finite elements for incompressible fluid flow
- The Hitchhiker's Guide to the Virtual Element Method
- New perspectives on polygonal and polyhedral finite element methods
- Addressing integration error for polygonal finite elements through polynomial projections: A patch test connection
- A virtual element method for the Steklov eigenvalue problem
- Gradient Bounds for Wachspress Coordinates on Polytopes
- A virtual element method with arbitrary regularity
