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  • XII International Conference on Computational Plasticity: fundamentals and applications (COMPLAS 2013), Barcelona, 3-5 September, 2013
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  • XII International Conference on Computational Plasticity: fundamentals and applications (COMPLAS 2013), Barcelona, 3-5 September, 2013
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A bodner-partom visco-plastic dynamic sphere benchmark problem

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Cita com:
hdl:2117/182768

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Chabaud, Brandon M.
Brock, Jerry S.
Williams, Todd O.
Document typeConference report
Defense date2013
PublisherCIMNE
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
Developing benchmark analytic solutions for problems in solid and fluid mechanics is very important for the purpose of testing and verifying computational physics codes. Our primary objective in this research is to obtain a benchmark analytic solution to the equation of motion in radially symmetric spherical coordinates. An analytic solution for the dynamic response of a sphere composed of an isotropic visco-plastic material and subjected to spherically symmetric boundary conditions is developed and implemented. The radial displacement u is computed by solving the equation of motion, a linear second-order hyperbolic PDE. The plastic strains εp and εp are computed by solving two non-linear first-order ODEs in time. We obtain a solution for u in terms of the plastic strain components and boundary conditions in the form of an infinite series. Computationally, at each time step, we set up an iteration scheme to solve the PDE-ODE system. The linear momentum equation is solved using the plastic strains from the previous iteration, then the plastic strain equations are solved numerically using the new displacement. We demonstrate the accuracy and convergence of our benchmark solution under spatial mesh, time step, and eigenmode refinement.
URIhttp://hdl.handle.net/2117/182768
ISBN978-84-941531-5-0
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  • COMPLAS - XII International Conference on Computational Plasticity: fundamentals and applications (COMPLAS 2013), Barcelona, 3-5 September, 2013 [137]
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