Velocity‐based formulations for standard and quasi‐incompressible hypoelastic‐plastic solids |
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| Authors: | Alessandro Franci Eugenio Oñate Josep Maria Carbonell |
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| Affiliation: | 1. Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Campus Norte UPC, Barcelona, Spain;2. Universitat Politècnica de Catalunya (UPC), 08034 Barcelona, Spain |
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| Abstract: | We present three velocity‐based updated Lagrangian formulations for standard and quasi‐incompressible hypoelastic‐plastic solids. Three low‐order finite elements are derived and tested for non‐linear solid mechanics problems. The so‐called V‐element is based on a standard velocity approach, while a mixed velocity–pressure formulation is used for the VP and the VPS elements. The two‐field problem is solved via a two‐step Gauss–Seidel partitioned iterative scheme. First, the momentum equations are solved in terms of velocity increments, as for the V‐element. Then, the constitutive relation for the pressure is solved using the updated velocities obtained at the previous step. For the VPS‐element, the formulation is stabilized using the finite calculus method in order to solve problems involving quasi‐incompressible materials. All the solid elements are validated by solving two‐dimensional and three‐dimensional benchmark problems in statics as in dynamics. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | finite element methods Lagrangian non‐linear dynamics hypoelastic solids |
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