On the dynamic effects of explicit FEM in sheet metal forming analysis

Abstract

Since most of sheet metal forming process is done with a low tool velocity, it can be considered as a quasi-static process. Explicit dynamic FEM[1] has many advantages in treating severe nonlinearities such as nonlinear material, large deformation, instability and contact. In an explicit method, the time step is limited by the stability condition[2], so all solutions are essentially dynamic. Since contact algorithms used for explicit method[3] are more robust and straightforward than their implicit counterparts, explicit method are more attractive to simulate sheet metal forming [4,5]. Although there have been many researches on sheet metal forming analysis by an explicit method [4,5,[8][9][10][11][12][13][14], the dynamic effects are still not well-understood or quantified.To solve quasi-static problem in real time, a huge amount of computation time is necessary because of the small time step in an explicit method. Therefore when we use an explicit FEM for sheet metal forming analysis, it is conventional to convert the real problem to a virtual problem with a different time scale. In this context, time scaling and mass scaling techniques have been widely used in order to save computation time. If we use a large scaling factor with these methods, dynamic effects will increase and may cause incorrect results, especially for the stresses. In this situation, it is difficult to figure out how large the scaling should be to reduce computation time and still maintain the desired accuracy. The four node isoparametric shell element with one point integration with hourglass control is used by Belytschko and coworkers [6,7]. This shell element has been widely used to model sheet metal because of computational efficiency in explicit method.Several authors [5,8,9,13] have shown that the overall deformation and strain distribution can be predicted within acceptable accuracy if we use the scaling factor which yields a low ratio of total kinetic energy to total internal energy.

An automated solution for fixtureless sheet metal forming

“…To realise the relation between impact force and deformation, it is vital to understand the kinetic energy involved in deforming the material and dissipation of maximum kinetic energy onto workpiece [8].…”

Modeling of Size Dependent Failure in Cardiovascular Stent Struts under Tension and Bending

“…This is a consequence of using the explicit FE solver and is a well documented phenomenon. 3,18,43 It is not of concern in these analyses as it occurs following failure and does not affect the straining of the strut. Cuddy 4 found that intragranular ductile failure occurred in 316L stainless steel specimens in tension that had smaller grain sizes whereas intergranular failure was more common in large-grain annealed samples.…”

A comparative study of implicit and explicit FEM for the wrinkling prediction in the hydroforming process

“…In order to find a suitable scale factor, Belytschko et al suggested a new energy error estimate which identified where the dynamic effects are significant and how large the dynamic effects are [8,9]. From the suggested method, the error criterion e(t) for dynamic effects can be expressed simply by the ratio of the change of kinetic energy to the plastic work as follows:…”