Hill, D. J. and Pullin, D. and Ortiz, M. and Meiron, D. (2010) An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids. Journal of Computational Physics, 229 (24). pp. 9053-9072. ISSN 0021-9991 http://resolver.caltech.edu/CaltechAUTHORS:20110302-102610242
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We present a finite-difference based solver for hyper-elastic and viscoplastic systems using a hybrid of the weighted essentially non-oscillatory (WENO) schemes combined with explicit centered difference to solve the equations of motion expressed in an Eulerian formulation. By construction our approach minimizes both numerical dissipation errors and the creation of curl-constraint violating errors away from discontinuities while avoiding the calculation of hyperbolic characteristics often needed in general finite-volume schemes. As a result of the latter feature, the formulation allows for a wide range of constitutive relations and only an upper-bound on the speed of sound at each time is required to ensure a stable timestep is chosen. Several one- and two-dimensional examples are presented using a range of constitutive laws with and without additional plastic modeling. In addition we extend the reflection technique combined with ghost-cells to enforce fixed boundaries with a zero tangential stress condition (i.e. free-slip).
|Additional Information:||© 2010 Elsevier Inc. Received 26 February 2010; revised 23 July 2010; accepted 16 August 2010. Available online 27 August 2010.|
|Subject Keywords:||Hyper-elasticity; Plasticity; Finite-difference; WENO; Eulerian|
|Official Citation:||D.J. Hill, D. Pullin, M. Ortiz, D. Meiron, An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids, Journal of Computational Physics, Volume 229, Issue 24, 10 December 2010, Pages 9053-9072, ISSN 0021-9991, DOI: 10.1016/j.jcp.2010.08.020. (http://www.sciencedirect.com/science/article/B6WHY-50W8126-2/2/bfb364b791b104effbb4afe5c944a30f)|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||03 Mar 2011 16:14|
|Last Modified:||11 May 2012 20:03|
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