Limit-point buckling analyses using solid, shell and solid–shell elements

In this paper, the recently-developed solid-shell element SHB8PS is used for the analysis of a representative set of popular limit-point buckling benchmark problems. For this purpose, the element has been implemented in Abaqus/Standard finite element software and the modified Riks method was employed as an efficient path-following strategy. For the. benchmark problems tested, the new element shows better performance compared to solid elements and often performs as well as state-of-the-art shell elements. In contrast to shell elements, it allows for the accurate prescription of boundary conditions as applied to the actual edges of the structure.Agence Nationale de la Recherche, France (ANR-005-RNMP-007

Overview of the theoretical relations between necking and strain localization criteria.

Many criteria have been developed during last decades to predict diffuse or localized necking and shear banding. The lack of confrontation of these models with each other on relevant applications makes their choice difficult for the designer. It is proposed to reformulate these plastic instability criteria in an unified framework, to compare their theoretical bases to establish links between them and then to highlighten their limitations. In the case of diffuse necking, a comparison is made between the criteria based on bifurcation analysis and on those based on maximum force principle for elastic-plastic materials. In the case of localized modes, it is shown that the predictions of the Marciniak – Kuczynski approach, based on a multizone model, tend to those of the loss of ellipticity criterion when the initial defect size tends to zero (no initial defect introduced). In the case of elasto-viscoplastic behavior, an approach based on a linear stability analysis is mentioned

An improved assumed strain solid-shell element formulation with physical stabilization for geometric non-linear applications and elastic-plastic stability analysis

In this paper, the earlier formulation of the SHB8PS finite element is revised in order to eliminate some persistent membrane and shear locking phenomena. This new formulation consists of a solid-shell element based on a purely three-dimensional approach. More specifically, the element has eight nodes, with displacements as the only degrees of freedom, as well as an arbitrary number of integration points, with a minimum number of two, distributed along the 'thickness' direction. The resulting derivation, which is computationally efficient, can then be used for the modeling of thin structures, while providing an accurate description of the various through-thickness phenomena. A reduced integration scheme is used to prevent some locking phenomena and to achieve an attractive, low-cost formulation. The spurious zero-energy modes due to this in-plane one-point quadrature are efficiently controlled using a physical stabilization procedure, whereas the strain components corresponding to locking modes are eliminated with a projection technique following the assumed strain method. In addition to the extended and detailed formulation presented in this paper, particular attention has been focused on providing full justification regarding the identification of hourglass modes in relation to rank deficiencies. Moreover, an attempt has been made to provide a sound foundation to the derivation of the co-rotational coordinate frame, on which the calculations of the stabilization stiffness matrix and internal load vector are based. Finally to assess the effectiveness and performance of this new formulation, a set of popular benchmark problems is investigated, involving geometric non-linear analyses as well as elastic-plastic stability issues

Validation d’une nouvelle version de l’élément solide/coque “SHB8PS” sur des cas tests non linéaires

L’intérêt de disposer d’éléments finis volumiques capables de modéliser des structures minces est motivé par de nombreux problèmes industriels. Ainsi, ces dernières années, plusieurs travaux ont été réalisés dans ce domaine. Ces éléments coques épaisses ont de nombreux avantages : ils sont capables de représenter le comportement de structures minces avec une bonne prise en compte des phénomènes à travers l’épaisseur et avec un gain de temps de calcul significatif, ils permettent de mailler des géométries complexes où coques et solides doivent cohabiter sans les problèmes connus de raccordement de maillages. L’élément SHB8PS a été développé dans ce sens à partir d’une formulation purement tridimensionnelle. Récemment, une nouvelle version, libre de verrouillage (en membrane et cisaillement), a été formulée et validée en linéaire. Dans la présente étude, cette version revisitée est validée à travers de nombreux cas tests non linéaires.Contrat EDF R&

Locking-free formulation for the stabilized enhanced strain solid-shell element (SHB8PS): geometrically non-linear applications

In this work, a new locking-free and physically stabilized formulation of the SHB8PS solid-shell element is presented. The resulting finite element consists of a continuum mechanics shell element based on a purely three-dimensional approach. This eight-node hexahedron is integrated with a set of five Gauss points, all distributed along the “thickness” direction. Consequently, it can be used for the modeling of thin structures, while providing an accurate description of various through-thickness phenomena. The reduced integration has been used in order to prevent some locking phenomena and to increase its computational efficiency. The spurious zero-energy deformation modes due to the reduced integration are efficiently stabilized, whereas the strain components corresponding to locking modes are eliminated with a projection technique following the Enhanced Assumed Strain (EAS) method.Contrat EDF R&

A physically stabilized and locking-free formulation of the (SHB8PS) solid-shell element

In this work, the formulation of the SHB8PS finite element is reviewed in order to eliminate some persistent membrane and shear locking phenomena. This is a solid-shell element based on a purely three-dimensional formulation. In fact, the element has eight nodes as well as five integration points, all distributed along the "thickness" direction. Consequently, it can be used for the modeling of thin structures, while providing an accurate description of the various through-thickness phenomena. The reduced integration has been used in order to prevent some locking phenomena and to increase computational efficiency. The spurious zero-energy modes due to the reduced integration are efficiently stabilized, whereas the strain components corresponding to locking modes are eliminated with a projection technique following the Enhanced Assumed Strain (EAS) method.Dans cette étude, la formulation de l’élément SHB8PS est revisitée dans le but d’éliminer certains blocages persistants en membrane et cisaillement transverse. Rappelons que cet élément est de type coque épaisse obtenue à partir d’une formulation purement tridimensionnelle. Il possède donc huit noeuds et cinq points d’intégration répartis selon la direction de l’épaisseur. Ainsi, il peut être utilisé pour modéliser des structures minces tout en prenant correctement en compte les différents phénomènes à travers l’épaisseur. Afin d’améliorer ses performances de calcul et d’éviter certains blocages, l’intégration réduite a été employée. Les modes de hourglass générés par la sous-intégration sont efficacement stabilisés et les modes de blocages persistants sont éliminés par une technique de projection pouvant se mettre sous le formalisme de la « méthode de déformation postulée »

A new locking-free formulation for the SHB8PS solid–shell element: non-linear benchmark problems

In this work, a new physically stabilized and locking-free formulation of the SHB8PS element is presented. This is a solid-shell element based on a purely 3D formulation. It has eight nodes as well as five integration points, all distributed along the “thickness” direction. Consequently, it can be used for the modeling of thin structures, while providing an accurate description of the various through-thickness phenomena. The reduced integration has been used in order to prevent some locking phenomena and to increase computational efficiency. The spurious zero-energy deformation modes due to the reduced integration are efficiently stabilized, whereas the strain components corresponding to locking modes are eliminated with a projection technique following the Enhanced Assumed Strain (EAS) method.Contrat EDF R&

Numerical Investigation of the Limit Strains in Sheet Forming Involving Bending

In this work, the finite element method is used to simulate a typical FLD test over tools of different radii. Parameters like the mesh density, element type, numerical determination of the onset of strain localization, limit strain definition etc. have been investigated. Finally, the limit strain for plane strain tension has been determined as a function of the thickness vs. tool radius (t/R) ratio. These simulations confirm that increasing the curvature of the tool increases the value of the limit strains. They also reveal that, as soon as bending becomes important, the practical relevance of the limit strains diminishes - At least with their current definition. The need for new strain localization models is emphasized, together with some of the associated challenges.Projet ANR FORME

Limit-point buckling analyses using solid, shell and solid–shell elements

International audienceIn this paper, the recently-developed solid-shell element SHB8PS is used for the analysis of a representative set of popular limit-point buckling benchmark problems. For this purpose, the element has been implemented in Abaqus/Standard finite element software and the modified Riks method was employed as an efficient path-following strategy. For the. benchmark problems tested, the new element shows better performance compared to solid elements and often performs as well as state-of-the-art shell elements. In contrast to shell elements, it allows for the accurate prescription of boundary conditions as applied to the actual edges of the structure

New prismatic solid-shell element : Assumed strain formulation and hourglass mode analysis

The formulation of a six-node solid-shell called SHB6, which is a linear, isoparametric element, is discussed. An eigenvalue analysis of the element stiffness matrix is first carried out. Several modifications are introduced into the formulation of the SHB6 element following the assumed strain method adopted by Belytschko and Bindeman. SHB6's coordinates and displacements are related to the nodal coordinates and displacements through the linear shape functions. Applying the simplified form of the Hu-Washizu nonlinear mixed variational principle, in which the assumed stress field is chosen to be orthogonal to the difference between the symmetric part of the displacement gradient and the assumed strain field, the formula is obtained. The newly developed SHB6 element was implemented into the finite element codes INCA and ASTER. It represents some improvement since it converges well and performs much better than the PRI6 six-node three-dimensional element in all of the benchmark problems tested