Michel Brunet

Analytical and experimental studies of necking in sheet metal forming processes

Abstract Two approaches are detailed for the determination of forming limit diagrams (FLD). The first one is experimental: a correlation technique has been developed for the displacement field measurement on a sheet. The second approach is theoretical: a necking criterion based on the load-instability and plane strain localization assumptions is proposed. It includes the possibility to introduce the modified Gurson–Tvergaard damage model taking account Hills or Barlat and Lians anisotropy. The criterion is written in an intrinsic form and is applicable to linear strain paths as well as to non-linear strain paths. Finally, the FLD for three aluminum sheets and a mild-steel sheet obtained by experimental and theoretical ways are compared.

Detailed formulation of the rotation‐free triangular element “S3” for general purpose shell analysis

Purpose – The aim of this paper is to present an enriched formulation of a rotation‐free (RF) triangular shell element in order to use it for shells of general shapes while, up to now, it is limited to shells without branching surfaces and progressive variations in terms of material behavior and thickness.Design/methodology/approach – The formulation keeps the main characteristic of Morleys element: bending effects can be expressed with three “bending angles” only. But, for a RF element, these angles are defined with the rigid body rotations of the element itself and those of its neighbours. This usual formulation of a RF shell element can be extended provided that curvatures‐displacements relation involves the material characteristics of the element itself and of its neighbours and the same goes for thickness.Findings – Numerous examples with regular and irregular meshes of structures involving branching surfaces point out convergence and accuracy. Large displacement analyses – including crash simulatio...

Modelling of a roll-forming process with a combined 2D and 3D FEM code

Abstract In roll-forming of steel sheets, flat strips are progressively deformed by successive sets of rotating rolls. A specific FE code, PROFIL, has been developed in order to analyse the complete strain history of the material, and it has the function to attain the optimisation of the design roll profiles. This design system is based on the elastic–plastic FEM, where a 2D cross-section analysis with moving boundary conditions is combined with a 3D analysis between a set of roll-stands. Deformed geometry and strain distributions predicted by simulations are compared with the results from previously conducted experiments. Channel sections of all types and complexity can be investigated.

Finite element modeling of the head skeleton with a new local quantitative assessment approach

The present study was undertaken to build a finite element model of the head skeleton and to perform a new assessment approach in order to validate it. The application fields for such an improved model are injury risk prediction as well as surgical planning. The geometrical reconstruction was performed using computed tomography scans and a total of 4680 shell elements were meshed on the median surface of the head skeleton with the particular characteristic of adapted mesh density and real element thickness. The assessment protocol of the finite element model was achieved using a quasi-static experimental compression test performed on the zygomatic bone area of a defleshed isolated head. Mechanical behavior of the finite element model was compared to the real one and the assessment approach was divided into two steps. First, the mechanical properties of the anatomical structure were identified using the simulation and then the simulated displacement field was compared to local displacement measurement performed during test using a digital correlation method. The assessment showed that the head skeleton model behaved qualitatively like the real structure. Quantitatively, the local relative error varied from 8% up to 70%.

A simplified triangular shell element with a necking criterion for 3-D sheet-forming analysis

A 3-node triangular shell element with only 3 translational degrees of freedom per node is presented, in which the out-of-plane displacement is the only d.o.f. considered for bending. The bending stiffness matrix of the element is derived by assuming constant curvature normal to the boundary with adjacent elements. An explicit dynamic time integration scheme is implemented for sheet forming analysis. The authors have incorporated in the numerical analysis their necking criterion based on the intrinsic Forming-Limit Stress Diagram.

A new quadrilateral shell element using 16 degrees of freedom

Purpose – The purpose of this paper is to present a quadrilateral shell element using 16 degrees of freedom (dof) (12 translations and four rotations) which makes a pair with Morleys triangle at 12 dof. This latter has been updated by Batoz who later proposed an extension to a quadrilateral (“DKQ16”) but only with special interpolation functions for an elastic behaviour of the material. Precisely, it is in order to release from this strong limitation that a completely different formulation is proposed here.Design/methodology/approach – The development of this new quadrilateral called “DKS16” involves three stages. The first one starts from Morleys triangle updated by Batoz (“DKT12”) to derive a rotation‐free (RF) triangular element (“S3”). The second stage consists in generalising this triangle to a RF quadrilateral (“S4”). During the final leg, the S4 and DKT12 main features are combined to give the quadrilateral “DKS16”.Findings – Other parameters being equal, the type of finite element chosen for the...

Sheet Forming with a specific Inverse Approach for a further Springback Analysis

During the design of pressed parts, an ‘incremental’ F.E. algorithm presents the major disadvantage of an important computation time and its substitution by a ‘one‐step’ simulation seems attractive. But, if a springback incremental implicit analysis starts with a stress state coming from an ordinary one‐step inverse computation, the final shape is not correct in general. To change this established fact, we propose an additional procedure which applies curvatures to elements located on a ‘curvature path’. This specific formulation is based on successive proportional loadings — even with a combined hardening — to keep the advantage of a short computation time.