Reference map technique for finite-strain elasticity and fluid-solid interaction

• Main Authors: Rycroft, Chris H. (Author), Nave, Jean-Christophe (Author), Kamrin, Kenneth N (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mechanical Engineering (Contributor)
• Format: Article
• Language: English
• Published: Elsevier, 2016-11-22T15:59:59Z.
• Subjects: Article
• Online Access: Get fulltext

The reference map, defined as the inverse motion function, is utilized in an Eulerian-frame representation of continuum solid mechanics, leading to a simple, explicit finite-difference method for solids undergoing finite deformations. We investigate the accuracy and applicability of the technique for a range of finite-strain elasticity laws under various geometries and loadings. Capacity to model dynamic, static, and quasi-static conditions is shown. Specifications of the approach are demonstrated for handling irregularly shaped and/or moving boundaries, as well as shock solutions. The technique is also integrated within a fluid-solid framework using a level-set to discern phases and using a standard explicit fluid solver for the fluid phases. We employ a sharp-interface method to institute the interfacial conditions, and the resulting scheme is shown to efficiently capture fluid-solid interaction solutions in several examples.
United States. Dept. of Energy. Office of Science (Computational and Technology Research, contract number DE-AC02-05CH11231)
National Science Foundation (U.S.) (Grant DMS-0813648)
National Science Foundation (U.S.) (Mathematical Sciences Postdoctoral Research Fellowship)
Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Program))