Energy return in running surfaces

Running surfaces are estimated to account for up to one percent of the en-ergy necessary for running. How much of this energy is dissipated in the surface and how much is returned to the runner is not known. A method has been designed to calculate the energy that is absorbed and returned by a running surface. In this method the time of energy return is of importance. Energy can only be returned if this return coïncides with the take off phase. A two dimensional finite element model (FEM) was generated to calculate the energy. Linear elastic, plane strain elements with linear Rayleigh damp-ing were used. Data obtained by a force platform for toe running were used as input for the model. The FEM consisted of two layers of surface of which the stiffness was varied independently. Additionally, the Rayleigh damp-ing ratio for the whole model was varied. The results indicate that there are combinations of top layer stiffness, bottom layer stiffness and damping ratio for which the performance of the surface from an energy standpoin

Shape prediction for complex polymer extrudates through 3D numerical simulation

In polymer extrusion shape of the extrudate depend largely on the process parameters such as die shape, extrusion speed and temperature. Especially for complex profiles, it is impossible to predict this dependence a priori. By performing 3D finite element analyses more insight can be obtained in how the process parameters influence the final shape. In the present study it is assumed that the polymer is a liquid of which the elastic response can be neglected. This assumption, together with a steady state approach and the low Reynolds numbers that characterize extrusion, justifies the modeling of polymer extrusion as a Stokes flow. This Stokes flow can be discretized in an Eulerian framework using the MINI-element. The resulting system of equations can subsequently be solved using an iterative solver. However, the accuracy of the solution is influenced considerably by the manner in which the shape of the extruded profile is meshed. The shape of the extrudate is not known a priori. As a result it is not possible to have the mesh of the domain coincide with the actual shape of the profile before hand. It is therefore necessary to solve a free boundary problem for that portion of the profile that has exited the die to determine the real shape of the profile. Then the mesh of the domain has to be adopted to coincide with the real shape. Results of numerical experiments will be presented which indicate that the solution of the velocity field changes considerably if the shape of the domain is updated to comply with the real shape of the polymer extrudate. Due to the steady state assumption the shape of the free surface can be computed exactly for the given velocity profile in one step. This makes it possible to determine the shape of the profile at little extra cost

Modeling friction near sharp edges using a Eulerian reference frame: appliction to aluminium extrusion

When using a Eulerian finite element approach to model the material deformation that occurs in e.g. forming processes, the accurate capturing of friction is of crucial importance to the quality of the computational results. For the algorithm that incorporates the frictional phenomena into the system of equations, the direction of the contact surface normal in a node is an essential parameter. However, this normal is not uniquely defined in the nodes of a curved, discretized surface. Therefore, a substitute normal has to be reconstructed. The commonly used (averaging) methods to determine the normal are either mesh or geometry dependent which renders poor results on coarse meshes. Therefore, a new method is presented that reconstructs the direction of the normal from the flow field near the node. Comparing the flow fields on a coarse mesh with those obtained on a very fine mesh reveals that a more accurate solution field is obtained using the method introduced here