A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of metal ring compression. The point collocation method is a true meshfree method without the employment of a background mesh. It is shown that, in a point collocation approach, the remesh problem because of the mesh distortion in FEM （finite element method） and the low efficiency in Galerkin-based meshfree method are avoided. The corrected kernel functions are introduced to the stabilization of free-surface boundary conditions. The solution of symmetric ring compression problem is compared with a conventional finite element solution, and reasonable results have been obtained.
This paper suggested to reformulate cylindrical deep drawing parameters with dimensionless form. A diagram, in which a feasible zone is drawn to bound both the maximal allowable tension and compression stress during the deep drawing process, was established. Since it is presented in a dimensionless form, it may be applied for both conventional and micro deep drawing. Cylindrical cup deep drawing was taken as an example to show the dimensionless process design method. In addition, the size effects should be taken into account. Two kinds of size effects on micro deep drawing were investigated, which can be explained by surface layer model and strain gradient model. Numerical simulations were carried out to compare the strain distribution with or without consideration of size effect.
