The purpose of this research is to construct a constitutive equation for unstimulated (passive) and tetanized skeletal muscle tissue. Results of experimental tests and anatomical studies provided the_foundation for the development of the model. The anterior gracilis muscle was removed from the thigh of the Sprague-Dawley rat and placed in an oxygenated physiological salt solution at 25°C. Three kinds of mechanical tests were conducted on the passive muscle:​ stress relaxation tests using prescribed input strains and strain rates, loading and unloading tests at various strain rates, and sinusoidal tests, c0nducted at predetermined peak amplitudes and frequencies of oscillation. Tetanic stimuli generated force response curves and established the active mathematical model. SelectedImuscles were stained to determine musc1e composition.

A model for the muscle was generated by the arrangement of three anatomic components:​ a connective tissue sheath composed of collagenous fibers was in parallel with muscle cells and both were in series with collagenous tendon ends. The quasi-linear viscoelastic expression developed previously for collagenous tissue was utilized to develop the functional form of the constitutive equation for both the tendon ends and connective tissue sheath. Experimental stress relaxation tests were conducted on the muscle to determine the material parameters for the collagenous components in the model and to deduce the behavior of the muscle cells. The constitutive equations for the tissue components were mathematically combined to compute the stresses in the composite tissue and the computer was used to simplify the calculations. The resulting composite constitutive equation was then used to predict the results of constant strain—rate loading, constant strain-rate loading and unloading and sinusoidal input deformation tests. Good agreement was found between theory and the passive experimental tests for peak strain levels below 40-45% and for strain rates less than 50%lmin (20-30 rad./min. in the sinusoidal tests). The mathematical expression for the tetanic force-muscle length curves was generated from empirical tests on the tetanized gracilis muscle and agreement between the resulting tetanic stress-passive strain curves was observed for strains below 50%.