期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 337, 期 -, 页码 549-597出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2018.03.045
关键词
Nonlinear continuum mechanics; Incompressible solids; Gibbs free energy; Variational multiscale method; Generalized-alpha method; Fluid-structure interaction
资金
- National Institutes of Health [1R01HL121754, 1R01HL123689]
- Burroughs Welcome Fund Career award at the Scientific Interface
- National Science Foundation (NSF) CAREER award [OCI-1150184]
- NSF [ACI-1053575]
We develop a unified continuum modeling framework using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the continuum body, which is well-behaved in both compressible and incompressible regimes. Our derivation also provides a rational justification of the isochoric-volumetric additive split of free energies in nonlinear elasticity. The variational multiscale analysis is performed for the continuum model to construct a foundation for numerical discretization. We first consider the continuum body instantiated as a hyperelastic material and develop a variational multiscale formulation for the hyper-elastodynamic problem. The generalized-a method is applied for temporal discretization. A segregated algorithm for the nonlinear solver, based on the original idea introduced in Scovazzi et al. (2016), is carefully analyzed. Second, we apply the new formulation to construct a novel unified formulation for fluid-solid coupled problems. The variational multiscale formulation is utilized for spatial discretization in both fluid and solid subdomains. The generalized-alpha method is applied for the whole continuum body, and optimal high-frequency dissipation is achieved in both fluid and solid subproblems. A new predictor multi-corrector algorithm is developed based on the segregated algorithm. The efficacy of the new formulations is examined in several benchmark problems. The results indicate that the proposed modeling and numerical methodologies constitute a promising technology for biomedical and engineering applications, particularly those necessitating incompressible models. (C) 2018 Elsevier B.V. All rights reserved.
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