Numerical simulation of some biomechanical problems. (English) Zbl 1008.92007
Summary: The paper is concerned with the numerical solution of nonlinear conservation laws, and biomechanical models of spine and of loaded wrist are formulated and analysed. The models are based on a contact problem in nonlinear elastic rheology. The stress-strain relation is derived from a positive definite strain energy density function. For weak solutions of the problem, a variational inequality approach is used. Then the secant modules method and finite element method are applied. First, the model of the weight bearing wrist, and secondly the model of the Chance’s fracture of lumbar spine are discussed.
MSC:
| 92C10 | Biomechanics |
| 65C60 | Computational problems in statistics (MSC2010) |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
nonlinear elasticity; contact problems; variational inequality; finite element method; wrist; spine; fracturesReferences:
| [1] | Belytschko, T.; Kulak, R. F.; Schultz, A. B.; Galante, J. O., Finite element stress analysis of an intervertebral disc, J. Biomech., 7, 277 (1974) |
| [5] | Kulak, R. F.; Belytschko, T.; Schultz, A. B., Non-linear behaviour of the human intervertebral disc under axial load, J. Biomech., 9, 377 (1976) |
| [7] | Nečas, J.; Hlaváček, I., Solution of Signorini’s contact problem in the deformation theory of plasticity by secant modules method, Appl. Math., 28, 3, 199-214 (1983) · Zbl 0512.73097 |
| [9] | Nedoma, J.; Bartoš, M.; Kestřánek, Z.; Kestřánek, Z.; Stehlík, J., Numerical Methods for Constrained Optimization in 2D and 3D Biomechanics, Num. Linear Algebra Appl., 6, 557-586 (1999) · Zbl 1010.74070 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
