UBC Theses and Dissertations
Eulerian formulation with Volume Of Solid (VOS) application to metal forming Al-Athel, Khaled S.
The volume of fluid (VOF) method has been used extensively in computational fluid dynamics (CFD) applications. The method is used to track the unconstrained flow of the fluid at the free surface in an Eulerian formulations framework. In this work we propose the use of the VOF method in nonlinear solid mechanics and metal forming applications, therefore the new method is called the Volume of Solid (VOS) method. The VOS method is to be used with Eulerian finite element (FE) formulations. In Eulerian formulation, the mesh is fixed in space and the material flows freely within the domain. This type of formulation overcomes many difficulties that are associated with other FE formulations such as mesh distortion and the need for re-meshing or a proper mesh motion scheme. The main drawback of the Eulerian formulation is the difficulty in tracking the unconstrained flow of the material at the free boundaries; therefore an additional scheme is needed to overcome this problem. The derivation of the VOS equations and its implementation in an Eulerian formulation along with applications in metal forming and metal cutting are the main goals of this research. In this work, we present the derivation of the Eulerian quasi-static and dynamic equilibrium equations. The complete development of the VOS method is presented for the commonly used uniform mesh using a piecewise linear interface construction method, and for a general case of a non-uniform mesh using a new filling pattern scheme. The formulation of the VOS method includes the calculation of the fractional volume value of the solid in each element and finding a directional vector to locate the interface of the free surface. The implementation of the VOS method is discussed by covering important topics that include the connectivity of the free surface interfaces in addition to introducing and modeling a new algorithm for the rigid-flexible contact problem. The formulation presented in this work is implemented in a VOS FE-code and used to simulate several metal forming and metal cutting applications. The VOS simulations are validated by comparing the results with other experimental and numerical work presented in the literature.
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