B-bar virtual element method for nearly incompressible and compressible materials

Park, Kyoungsoo; Chi, Heng; Paulino, Gláucio H.

doi:10.1007/s11012-020-01218-x

Cited by 16 publications

(37 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, v h i,x , v h i,y , v h i,I and v h i,II are the coefficients of the basis functions in (19) and can thus be identified with the degrees of freedom of the method. Note, however, that the degrees of freedom of an enriched function v h X ∈ V h X (E) are no longer the values of v h X at the vertices of element E.…”

Section: Extended Virtual Element Space Elliptic Projection and Bilin...mentioning

confidence: 99%

“…which can be compared to (19). Accordingly, a generic virtual element function that belongs to the reduced space V h X (E) is described by 2N E + 2k E degrees of freedom instead of 4N E degrees of freedom.…”

Section: Partial Enrichmentmentioning

confidence: 99%

“…In recent years, the VEM has also been used to solve problems in solid mechanics, such as two-and three-dimensional linear elasticity [15,16], nearly incompressible elasticity [17][18][19], inelastic problems [20,21], mixed variational formulations for linear elasticity [22,23], linear elasticity on curvilinear elements [24], and elastodynamics [25][26][27]. However, very few studies have exploited the flexibility of the method to deal with meshes that are cut by discontinuities and/or contain interior singularities.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Extended virtual element method for two-dimensional linear elastic fracture

Benvenuti,

Chiozzi,

Manzini

et al. 2021

Preprint

View full text Add to dashboard Cite

In this paper, we propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture. This approach, which is an extension of the standard Virtual Element Method (VEM), facilitates mesh-independent modeling of crack discontinuities and elastic crack-tip singularities on general polygonal meshes. For elastic fracture in the X-VEM, the standard virtual element space is augmented by additional basis functions that are constructed by multiplying standard virtual basis functions by suitable enrichment fields, such as asymptotic mixed-mode crack-tip solutions. The design of the X-VEM requires an extended projector that maps functions lying in the extended virtual element space onto a set spanned by linear polynomials and the enrichment fields. An efficient scheme to compute the mixed-mode stress intensity factors using the domain form of the interaction integral is described. The formulation permits integration of weakly singular functions to be performed over the boundary edges of the element. Numerical experiments are conducted on benchmark mixed-mode linear elastic fracture problems that demonstrate the sound accuracy and optimal convergence in energy of the proposed formulation.

show abstract

Section: Extended Virtual Element Space Elliptic Projection and Bilin...mentioning

confidence: 99%

Section: Partial Enrichmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extended virtual element method for two-dimensional linear elastic fracture

Benvenuti,

Chiozzi,

Manzini

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…No additional degrees of freedom are introduced (displacement-based formulation). In the existing VEM approaches, the volumetric locking is alleviated by the B-bar formulation [1,2], mixed formulation [3], enhanced strain formulation [4], hybrid formulation [5], nonconforming formulations [6][7][8], or addition of degrees of freedom related to the normal components of the displacement field on the element's edges to satisfy the inf-sup condition [9].…”

Section: Introductionmentioning

confidence: 99%

A node-based uniform strain virtual element method for compressible and nearly incompressible elasticity

Ortiz-Bernardin¹,

Silva-Valenzuela²,

Salinas³

et al. 2022

Preprint

View full text Add to dashboard Cite

We propose a displacement-based approach to solve problems in compressible and nearly incompressible plane elasticity that combines a nodal integration technique and the virtual element method (VEM), wherein the strain is averaged around nodes from the strain of surrounding virtual elements. For the strain averaging procedure, a nodal averaging operator is constructed using a generalization to virtual elements of the node-based uniform strain approach for finite elements.We refer to these new elements as node-based uniform strain virtual elements (NVEM). A salient feature of the NVEM is that the stresses and strains become nodal variables just like displacements, which can be exploited in nonlinear simulations thereby providing room for further development of this novel approach. Through several benchmark problems in plane elasticity, we demonstrate that the NVEM is accurate and optimally convergent, and devoid of volumetric locking in the nearly incompressible limit.

show abstract

“…In connection with the phase-field method [1], Bijaya and Chowdhury [6] address fracture problems considering finite strains. The next group of papers addresses novel numerical methods in computational mechanics including the variational multiscale method (VMS) for incompressible flows by Kang and Masud [7], the virtual element method (VEM) for nearly incompressible materials by Park et al [8], the generalized finite element method (GFEM) for fracture of composites by Alves et al [9], and the Carrera Unified Formulation (CUF) for stress analysis by Filippi and Carrera [10].…”

mentioning

confidence: 99%