Quasi-static deformations of biological soft tissue

Quasi-static motions are motions for which inertial effects can be neglected, to the first order of approximation. It is crucial to be able to identify the quasi-static regime in order to efficiently formulate constitutive models from standard material characterization test data. A simple non-dimensionalization of the equations of motion for continuous bodies yields non-dimensional parameters which indicate the balance between inertial and material effects. It will be shown that these parameters depend on whether the characterization test is strain- or stress-controlled and on the constitutive model assumed. A rigorous definition of quasi-static behaviour for both strain- and stress-controlled experiments is obtained for elastic solids and a simple form of a viscoelastic solid. Adding a rate dependence to a constitutive model introduces internal time-scales and this complicates the identification of the quasi-static regime. This is especially relevant for biological soft tissue as this tissue is typically mod as being a non-linearly viscoelastic solid. The results obtained here are applied to some problems in cardiac mechanics and to data obtained from simple shear experiments on porcine brain tissue at high strain rates.