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We present a numerical algorithm for the determination of muscle response by the ÿnite element method. Hill's three-element model is used as a basis for our analysis. The model consists of one linear elastic element, coupled in parallel with one non-linear elastic element, and one non-linear contractile element connected in series. An activation function is deÿned for the model in order to describe a time-dependent character of the contractile element with respect to stimulation.Complex mechanical response of muscle, accounting for non-linear force-displacement relation and change of geometrical shape, is possible by the ÿnite element method. In an incremental-iterative scheme of calculation of equilibrium conÿgurations of a muscle, the key step is determination of stresses corresponding to a strain increment. We present here the stress calculation for Hill's model which is reduced to the solution of one non-linear equation with respect to the stretch increment of the serial elastic element. The muscle ÿbers can be arbitrarily oriented in space and we give a corresponding computational procedure of calculation of nodal forces and sti ness of ÿnite elements.The proposed computational scheme is built in our FE package PAK, so that real muscles of complex three-dimensional shapes can be modelled. In numerical examples we illustrate the main characteristic of the developed numerical model and the possibilities of solution of real problems in muscle functioning. ? 1998 John Wiley & Sons, Ltd.

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Complex behaviour of connective tissue can be modeled by a ®ber-®ber kinetics material model introduced in Mijailovic (1991), Mijailovic et al. (1993. The model is based on the hypothesis of sliding of elastic ®bers with Coulomb and viscous friction. The main characteristics of the model were veri®ed experimentally in Mijailovic (1991), and a numerical procedure for onedimensional tension was developed considering sliding as a contact problem between bodies. In this paper we propose a new and general numerical procedure for calculation of the stress-strain law of the ®ber-®ber kinetics model in case of Coulomb friction. Instead of using a contact algorithm (Mijailovic 1991), which is numerically inef®cient and never enough reliable, here the history of sliding along the sliding length is traced numerically through a number of segments along the ®ber. The algorithm is simple, ef®cient and reliable and provides solutions for arbitrary cyclic loading, including tension, shear, and tension and shear simultaneously, giving hysteresis loops typical for soft tissue response. The model is built in the ®nite element technique, providing the possibility of its application to general and real problems. Solved examples illustrate the main characteristics of the model and of the developed numerical method, as well as its applicability to practical problems. Accuracy of some results, for the simple case of uniaxial loading, is veri®ed by comparison with analytical solutions.