Discrete strain gap (DSG) solid finite elements at large deformations for non-linear analysis of shells and solids

We present a solid finite element for non-linear structural analysis, based on the Discrete Strain Gap (DSG) method, involving large deformations and non-linear material laws. For the linear case, the DSG method has proven to eliminate all geometric locking effects, such as shear locking, membrane locking, and trapezoidal locking, with one unique approach [1]. Satisfaction of the patch test ? which is violated in the original DSG formulation for solids ? may be ensured via a decomposition of strain modes into a constant part and higher order modes. However, this modification goes along with the appearance of trapezoidal locking (cf. ?MacNeal?s Dilemma? [12]). In the particular case of thin shell analysis with solid or solid-shell elements, this is of noticeable relevance. A way out of this dilemma is to choose the original, locking-free formulation for the ?out-of-plane? strain components while ensuring consistency via the mesh layout in transverse direction. The proposed method allows for an easy switch from 3-D structures to thin structures within one common element technology, and it is both consistent and locking-free in either case [2]. In order to remedy the material locking phenomenon of volumetric locking the DSG concept can be combined with the well-established Enhanced Assumed Strain (EAS) method. The DSG concept can be extended to large deformations. A 3-D solid element formulation based on the DSG concept is straight forward and well suited for nonlinear problems involving large deformations and material nonlinearities. While this paper concentrates on the linear case the presentation at the conference will focus also on the extension to non-linear problems.     «

We present a solid finite element for non-linear structural analysis, based on the Discrete Strain Gap (DSG) method, involving large deformations and non-linear material laws. For the linear case, the DSG method has proven to eliminate all geometric locking effects, such as shear locking, membrane locking, and trapezoidal locking, with one unique approach [1]. Satisfaction of the patch test ? which is violated in the original DSG formulation for solids ? may be ensured via a decomposition of str...     »