A Finite Element Approach for Skeletal Muscle using a Distributed Moment Model of Contraction

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Abstract
The present paper describes a geometrically and physically nonlinear continuum model to study the mechanical behaviour of passive and active skeletal muscle. The contraction is described with a Huxley type model. A Distributed Moments approach is used to convert the Huxley partial differential equation in a set of ordinary differential equations. An isoparametric brick element is developed to solve the field equations numerically. Special arrangements are made to deal with the combination of highly nonlinear effects and the nearly incompressible behaviour of the muscle. For this a Natural Penalty Method (NPM) and an Enhanced Stiffness Method (ESM) are tested. Finally an example of an analysis of a contracting tibialis anterior muscle of a rat is given. The DM-method proved to be an efficient tool in the numerical solution process. The ESM showed the best performance in describing the incompressible behaviour.