Abstract
In this chapter two velocity-based finite element formulations for compressible materials are presented, namely the Velocity (V) and the mixed Velocity–Pressure (VP) formulations. For both schemes the linear momentum equations are solved iteratively for the velocity increments. The linearization of the governing equations is performed without specifying any constitutive law. The aim of this chapter is to maintain as much as possible the generality of the algorithms, leaving the formulations open to different material models. It will be shown that the only requirement demanded to the constitutive laws is that the rate of stress must be linearly related with the rate of deformation.
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Franci, A. (2017). Velocity-Based Formulations for Compressible Materials. In: Unified Lagrangian Formulation for Fluid and Solid Mechanics, Fluid-Structure Interaction and Coupled Thermal Problems Using the PFEM. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-45662-1_2
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DOI: https://doi.org/10.1007/978-3-319-45662-1_2
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