This paper deals with modeling the passivebehavior of skeletal muscle tissue includingcertain microvibrations at the cell level. Our approach combines a continuum mechanics model with large deformation and incompressibility at the macroscale with chains of coupled nonlinear oscillators.The model verifies that an externally appliedvibration at the appropriate frequency is able to synchronize microvibrations in skeletal muscle cells.From the numerical analysis point of view, one faces here a partial differential-algebraic equation (PDAE) that after semi-discretization in space by finite elements possessesan index up to three, depending on certain physicalparameters. In this context, the consequences forthe time integration as well as possible remedies are discussed.
