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

Physically based multiscale-viscoplastic model for metals and steel alloys: theory and computation

The main requirement of large deformation problems such as high-speed machining, impact, and various primarily metal forming, is to develop constitutive relations which are widely applicable and capable of accounting for complex paths of deformation. Achieving such desirable goals for material like metals and steel alloys involves a comprehensive study of their microstructures and experimental observations under different loading conditions. In general, metal structures display a strong rate- and temperature-dependence when deformed non-uniformly into the inelastic range. This effect has important implications for an increasing number of applications in structural and engineering mechanics. The mechanical behavior of these applications cannot be characterized by classical (rate-independent) continuum theories because they incorporate no ‘material length scales’. It is therefore necessary to develop a rate-dependent (viscoplasticity) continuum theory bridging the gap between the classical continuum theories and the microstructure simulations. Physically based vicoplasticity models for different types of metals (body centered cubic, face centered cubic and hexagonal close-packed) and steel alloys are derived in this work for this purpose. We adopt a multi-scale, hierarchical thermodynamic consistent framework to construct the material constitutive relations for the rate-dependent behavior. The concept of thermal activation energy, dislocations interactions mechanisms and the role of dislocations dynamics in crystals are used in the derivation process taking into consideration the contribution of the plastic strain evolution of dislocation density to the flow stress of polycrystalline metals. Material length scales are implicitly introduced into the governing equations through material rate-dependency (viscosity). The proposed framework is implemented into the commercially well-known finite element software ABAQUS. The finite element simulations of material instability problems converge to meaningful results upon further refinement of the finite element mesh due to the successful incorporation of the material length scale in the model formulations. It is shown that the model predicted results compare very well with different experimental data over a wide range of temperatures (77K°-1000K°) and strain rates (10-3-104s-1). It is also concluded from this dissertation that the width of localization zone (shear band) exhibits tremendous changes with different initial temperatures (i.e., different initial viscosities and accordingly different length scales)

Application of the continuum shell finite element SHB8PS to sheet forming simulation using an extended large strain anisotropic elastic–plastic formulation

http://link.springer.com/article/10.1007%2Fs00419-012-0620-xThis paper proposes an extension of the SHB8PS solid–shell finite element to large strain anisotropic elasto-plasticity, with application to several non-linear benchmark tests including sheet metal forming simulations. This hexahedral linear element has an arbitrary number of integration points distributed along a single line, defining the "thickness" direction; and to control the hourglass modes inherent to this reduced integration, a physical stabilization technique is used. In addition, the assumed strain method is adopted for the elimination of locking. The implementation of the element in Abaqus/Standard via the UEL user subroutine has been assessed through a variety of benchmark problems involving geometric non-linearities, anisotropic plasticity, large deformation and contact. Initially designed for the efficient simulation of elastic–plastic thin structures, the SHB8PS exhibits interesting potentialities for sheet metal forming applications – both in terms of efficiency and accuracy. The element shows good performance on the selected tests, including springback and earing predictions for Numisheet benchmark problems

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&

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

Improved formulation for the stabilized enhanced strain solid-shell element (SHB8PS): geometric linear and nonlinear applications

In this study, the formulation of the SHB8PS solid-shell element is reviewed in order to eliminate some persistent membrane and shear locking phenomena. The resulting physically stabilized and locking-free finite element consists in a continuum mechanics shell element based on a purely three-dimensional formulation. In fact, this is a hexahedral element with eight nodes as well as five integration points, all distributed along the “thickness” direction. Consequently, it can be used for the modelling 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&

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

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

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&