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Related papers: A virtual element method for isotropic hyperelasti…

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This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress…

Numerical Analysis · Mathematics 2025-10-08 Saugata Ghosh , Dambaru Bhatta , S. M. Mallikarjunaiah

In the context of adaptive remeshing, the virtual element method provides significant advantages over the finite element method. The attractive features of the virtual element method, such as the permission of arbitrary element geometries,…

Numerical Analysis · Mathematics 2023-08-16 Daniel van Huyssteen , Felipe Lopez Rivarola , Guillermo Etse , Paul Steinmann

In this thesis, a computational framework for microstructural modelling of transverse behaviour of heterogeneous materials is presented. The context of this research is part of the broad and active field of Computational Micromechanics,…

Computational Engineering, Finance, and Science · Computer Science 2021-10-05 Marco Lo Cascio

A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in [R. Oyarz\'ua and R. Ruiz-Baier, Locking-free finite element methods for poroelasticity, SIAM J. Numer.…

Numerical Analysis · Mathematics 2019-12-13 Raimund Bürger , Sarvesh Kumar , David Mora , Ricardo Ruiz-Baier , Nitesh Verma

In this study, the Virtual Fields Method (VFM) is applied to identify constitutive parameters of hyperelastic models from a heterogeneous test. Digital image correlation (DIC) was used to estimate the displacement and strain fields required…

Classical Physics · Physics 2019-07-08 A Tayeb , Jean-Benoit Le Cam , M. Grédiac , E. Toussaint , F. Canevet , E. Robin , X. Balandraud

This paper presents two approaches: the virtual element method (VEM) and the stabilization-free virtual element method (SFVEM) for analyzing thermomechanical behavior in electronic packaging structures with geometric multi-scale features.…

Numerical Analysis · Mathematics 2025-12-29 Yanpeng Gong , Sishuai Li , Fei Qin , Bingbing Xu

We study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a rigid channel. Through a careful investigation of the…

Numerical Analysis · Mathematics 2020-07-20 L. Beirão da Veiga , C. Canuto , R. H. Nochetto , G. Vacca

In this thesis, we investigate a novel local projection based stabilized conforming virtual element method for the generalized Oseen problem using equal-order element pairs on general polygonal meshes. To ensure the stability, particularly…

Numerical Analysis · Mathematics 2025-09-05 Sudheer Mishra , E Natarajan

We present the non-conforming Virtual Element Method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component…

Numerical Analysis · Mathematics 2016-09-07 Andrea Cangiani , Vitaliy Gyrya , Gianmarco Manzini

In this work, an efficient and robust isogeometric three-dimensional solid-beam finite element is developed for large deformations and finite rotations with merely displacements as degrees of freedom. The finite strain theory and…

Numerical Analysis · Mathematics 2023-12-13 Abdullah Shafqat , Oliver Weeger , Bai-Xiang Xu

In this paper, we propose a robust low-order stabilization-free virtual element method on quadrilateral meshes for linear elasticity that is based on the stress-hybrid principle. We refer to this approach as the Stress-Hybrid Virtual…

Numerical Analysis · Mathematics 2023-11-28 Alvin Chen , N. Sukumar

Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational…

Applied Physics · Physics 2019-10-22 Elias Karabelas , Gundolf Haase , Gernot Plank , Christoph M. Augustin

This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von K\'{a}rm\'{a}n equations that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete…

Numerical Analysis · Mathematics 2023-09-12 Devika Shylaja , Sarvesh Kumar

We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a low-order approximation of the displacement field, as well as…

Numerical Analysis · Mathematics 2023-07-19 L. Beirão da Veiga , C. Lovadina , D. Mora

We analyze and validate the virtual element method combined with a boundary correction similar to the one in [1,2], to solve problems on two dimensional domains with curved boundaries approximated by polygonal domains. We focus on the case…

Numerical Analysis · Mathematics 2024-08-02 Silvia Bertoluzza , Monica Montardini , Micol Pennacchio , Daniele Prada

A robust $C^0$-continuous nonconforming virtual element method (VEM) is developed for a boundary value problem arising from strain gradient elasticity in two dimensions, with the family of polygonal meshes satisfying a very general…

Numerical Analysis · Mathematics 2024-12-24 Jianguo Huang , Yue Yu

This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…

Numerical Analysis · Mathematics 2024-10-25 Yi Liu , Alessandro Russo

Virtual element methods (VEMs) without extrinsic stabilization in arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming VEM and a conforming VEM in arbitrary dimension. The key is to…

Numerical Analysis · Mathematics 2023-09-25 Chunyu Chen , Xuehai Huang , Huayi Wei

We introduce a nonconforming virtual element method for the Poisson equation on domains with curved boundary and internal interfaces. We prove arbitrary order optimal convergence in the energy and $L^2$ norms, and validate the theoretical…

Numerical Analysis · Mathematics 2023-03-28 Lourenco Beirão Da Veiga , Yi Liu , Lorenzo Mascotto , Alessandro Russo

We discuss the approximation of eigenvalue problems associated with elliptic partial differential equations using the virtual element method. After recalling the abstract theory, we present a model problem, describing in detail the features…

Numerical Analysis · Mathematics 2021-01-01 Daniele Boffi , Francesca Gardini , Lucia Gastaldi