MODELING OF MUSCLE BEHAVIOR BY THE FINITE-ELEMENT METHOD USING HILL 3-ELEMENT MODEL

We present a numerical algorithm for the determination of muscle respo nse by the finite element method. Hill's three-element model is used a s a basis for our analysis. The model consists of one linear elastic e lement, coupled in parallel with one non-linear elastic element, and o ne non-linear contractile element connected in series. An activation f unction is defined for the model in order to describe a time-dependent character of the contractile element with respect to stimulation. Com plex mechanical response of muscle, accounting for non-linear force-di splacement relation and change of geometrical shape, is possible by th e finite element method. In an incremental-iterative scheme of calcula tion of equilibrium configurations of a muscle, the key step is determ ination of stresses corresponding to a strain increment. We present he re the stress calculation for Hill's model which is reduced to the sol ution of one non-linear equation with respect to the stretch increment of the serial elastic element. The muscle fibers can be arbitrarily o riented in space and we give a corresponding computational procedure o f calculation of nodal forces and stiffness of finite elements. The pr oposed computational scheme is built in our FE package PAK, so that re al muscles of complex three-dimensional shapes can be modelled. In num erical examples we illustrate the main characteristic of the developed numerical model and the possibilities of solution of real problems in muscle functioning. (C) 1998 John Wiley & Sons, Ltd.