ʹSolid-shellʹ elements with linear and quadratic shape functions at large deformations with nearly incompressible materials

Efficient computation in sheet metal forming or car crash analysis is obtained only by using shell elements instead of fully three-dimensional solid elements. However, many requirements in the investigations in particular when looking at edges and special situations like large stretching and bending with small radii – strains and stresses in thickness direction and general three-dimensional material laws – cannot be provided by shell elements even if they are based on the well-known degeneration concept. Therefore in Hauptman [Int. J. Numer. Meth. Engng. 42 (1998) 49] among others as Schoop [Ingenieur-Archiv 56 (1986) 427]; Parisch [Int. J. Numer. Meth. Engng. 38 (1995) 1855]; Miehe [Comp. Meth. Appl. Mech. Engng. 155 (1998) 193] a so-called `Solid-Shellʹ formulation which is described briefly in the following section, was proposed. It must be noted also that in the solid-shell formulation the use of rotational degrees of freedom can be avoided and it is based instead on displacement degrees of freedom belonging to the upper and lower shell surfaces. Thus a simple combination with solid elements is obtained and no problems concerning large rigid body motions appear.