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A model of macroscale deformation and microvibration in skeletal muscle tissue. (English) Zbl 1168.92008
Summary: This paper deals with modeling the passive behavior of skeletal muscle tissues including certain microvibrations at the cell level. Our approach combines a continuum mechanics model with large deformations and incompressibility at the macroscale with chains of coupled nonlinear oscillators. The model verifies that an externally applied vibration at the appropriate frequency is able to synchronize microvibrations in skeletal muscle cells. From the numerical analysis point of view, one faces a partial differential-algebraic equation (PDAE) that after semi-discretization in space by finite elements possesses an index up to three, depending on certain physical parameters. In this context, the consequences for the time integration as well as possible remedies are discussed.
MSC:
92C10Biomechanics
74A99Generalities, axiomatics, foundations of continuum mechanics of solids
74C05Small-strain, rate-independent theories
65L05Initial value problems for ODE (numerical methods)
65M12Stability and convergence of numerical methods (IVP of PDE)
65M20Method of lines (IVP of PDE)