Improving Nagata patch interpolation applied for tool surface description in sheet metal forming simulation

Abstract

The contact surface description is a very important field in the numerical simulation of problems involving frictional contact, which are among the most difficult ones in continuum mechanics, as is the case of sheet metal forming simulation. In this paper, a methodology to control the Nagata patch interpolation of piecewise linear meshes is proposed, in order to improve its applicability for tool surface description used in the numerical simulation of sheet metal forming processes. The interpolation can be applied either to triangular and quadrilateral Nagata patches, as well as structured and unstructured patches. The normal vectors needed for the Nagata interpolation are obtained through two distinct strategies. The first uses the information available in the CAD surface model, while the second resorts only to the piecewise linear mesh model information. In order to evaluate the interpolation accuracy, the Nagata patch is applied to describe a sheet metal forming complex shape part tool geometry. The results obtained show that, regardless of the strategy used to evaluate the surface normal vectors, the use of the proposed Nagata patch interpolation enables a large improvement in the geometric accuracy when compared with the models composed by piecewise linear elements. The use of CAD surface geometry to evaluate the surface normal vectors leads to the best Nagata patch interpolation in terms of shape and normal vector field accuracy.