Within the framework of the displacement-based virtual element method (VEM), namely, for plane elasticity, an important topic is the development of optimal techniques for the evaluation of the stress field. In fact, in the classical VEM formulation, the same projection operator used to approximate the strain field (and then evaluate the stiffness matrix) is employed to recover, via constitutive law, the stress field. Considering a first-order formulation, strains are locally mapped onto constant functions, and stresses are piecewise constant. However, the virtual displacements might engender more complex strain fields for polygons, which are not triangles. This leads to an undesirable loss of information with respect to the underlying virtual stress field. The recovery by compatibility in patches, originally proposed for finite element schemes, is here extended to VEM, aiming at mitigating such an effect. Stresses are recovered by minimizing the complementary energy of patches of elements over an assumed set of equilibrated stress modes. The procedure is simple, efficient, and can be readily implemented in existing codes. Numerical tests confirm the good performance of the proposed technique in terms of accuracy and indicate an increase of convergence rate with respect to the classical approach in many cases.

An equilibrium-based stress recovery procedure for the VEM / E. Artioli, S. de Miranda, C. Lovadina, L. Patruno. - In: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING. - ISSN 0029-5981. - 117:8(2019), pp. 885-900. [10.1002/nme.5983]

An equilibrium-based stress recovery procedure for the VEM

C. Lovadina;
2019

Abstract

Within the framework of the displacement-based virtual element method (VEM), namely, for plane elasticity, an important topic is the development of optimal techniques for the evaluation of the stress field. In fact, in the classical VEM formulation, the same projection operator used to approximate the strain field (and then evaluate the stiffness matrix) is employed to recover, via constitutive law, the stress field. Considering a first-order formulation, strains are locally mapped onto constant functions, and stresses are piecewise constant. However, the virtual displacements might engender more complex strain fields for polygons, which are not triangles. This leads to an undesirable loss of information with respect to the underlying virtual stress field. The recovery by compatibility in patches, originally proposed for finite element schemes, is here extended to VEM, aiming at mitigating such an effect. Stresses are recovered by minimizing the complementary energy of patches of elements over an assumed set of equilibrated stress modes. The procedure is simple, efficient, and can be readily implemented in existing codes. Numerical tests confirm the good performance of the proposed technique in terms of accuracy and indicate an increase of convergence rate with respect to the classical approach in many cases.
RCP; stress recovery; virtual element method
Settore MAT/08 - Analisi Numerica
2019
Article (author)
File in questo prodotto:
File Dimensione Formato  
Artioli_et_al-2019-International_Journal_for_Numerical_Methods_in_Engineering.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 2.02 MB
Formato Adobe PDF
2.02 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/668430
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 14
social impact