Triangles and tetrahedra in explicit dynamic codes for solids

Abstract

Explicit dynamic codes which are used currently for the study of plastic deformations in impact, or with some modification for metal forming, suffer two serious limitations. First, only quadrilateral or hexahedral linear elements can be used thus limiting the possibilities of adaptive refinement and adaptive meshing. Second, even with the use of such elements, special devices such as reduced integration must be introduced to avoid locking and reduce costs. These necessitate complex hour glass control, mending‐type procedures. The main difficulties are those due to the need of treatment of (almost) incompressible deformation modes. Recently, similar difficulties have been overcome in the context of fluid dynamics soil dynamics and we show here how the processes introduced there can be adopted effectively to the present problem, thus allowing an almost unrestricted choice of element interpolations. © 1998 John Wiley & Sons, Ltd.

Stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications

“…For an in-depth description of this method the reader should consult Reference [2] as only a brief summary of the technique will be presented here. For clarity purposes, this will be done using the same notation employed for the ANP method rather than the notation used in Reference [2].…”

“…For clarity purposes, this will be done using the same notation employed for the ANP method rather than the notation used in Reference [2]. In addition, the following minor di erence will be introduced in the formulation.…”

“…For this purpose, a linear interpolation of both p and v * over each element is used and the surface term is assumed to vanish [2]. Simple algebra then yieldsJ…”

“…The resulting element formulation is easily implemented in a standard type of explicit code and has been used successfully in complex human body simulations. A second approach has been presented by Zienkiewic et al [2] using the fractional step or split algorithm ÿrst introduced by Chorin [4]. In this method a rate form of the volumetric constitutive equations is used in terms of the pressure and the divergence of the velocity.…”

Numerical simulations of strain localization in inelastic solids using mesh-free methods

“…However, technical di culties have remained in the context of explicit ÿnite element method. The commonly used Delaunay triangulation will certainly destroy the much needed quadrilateral (or hexahedral) pattern, and consequently the reÿned mesh is not suitable for explicit calculation anymore, though there is a recent attempt to store the triangle (or tetrahedra) element in explicit computation (see [39]); nevertheless, triangle element mesh is highly mesh-alignment-sensitive to the shear-band formation. On the other hand, mesh-free methods enjoy an amazing simplicity in the h-adaptive procedure.…”