Dynamical properties of the growing continuum using multiple-scale method

Abstract

The theory of growth and remodeling is applied to the 1D continuum. This can be mentioned e.g. as a model of the muscle fibre or piezo-electric stack. Hyperelastic material described by free energy potential suggested by Fung is used whereas the change of stiffness is taken into account. Corresponding equations define the dynamical system with two degrees of freedom. Its stability and the properties of bifurcations are studied using multiple-scale method. There are shown the conditions under which the degenerated Hopf's bifurcation is occuring.

Keywords

• Muscle fibre
• Growth
• Multiple scale method
• Hopf's bifurcation