A Model for Nonlinear Viscoelastic Mechanical Responses of Collagenous Soft Tissues
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A Model for Nonlinear Viscoelastic Mechanical Responses of Collagenous Soft Tissues Michelle L. Oyen Center for Applied Biomechanics, Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22902 ABSTRACT: Experimental observations of the time-dependent mechanical responses of collagenous tissues have demonstrated behavior that deviates from standard treatments of linear or quasilinear viscoelasticity. In particular, time-dependent deformation can be strongly coupled to strain level, and strain-rate independence can be observed under monotonic loading, even for a tissue with dramatic stress relaxation. It was postulated that this nonlinearity is fundamentally associated with gradual recruitment of individual collagen fibrils during applied mechanical loading. Based on previously observed experimental results for the time-dependent response of collagenous soft tissues, a model is developed to describe the mechanical behavior of these tissues under uniaxial loading. Tissue stresses, under applied strain-controlled loading, are assumed to be a sum of elastic and viscoelastic stress contributions. The relative contributions of elastic and viscoelastic stresses is assumed to vary with strain level, leading to strain- and timedependent mechanical behavior. The model formulation is examined under conditions of monotonic loading at varying constant strain rates and stress-relaxation at different applied strain levels. The model is compared with experimental data for a membranous biological soft tissue, the amniotic sac, and is found to agree well with experimental results. The limiting behavior of the novel model, at large strains relative to the collagen recruitment, is consistent with the quasilinear viscoelastic approach. INTRODUCTION: Many collagenous soft tissues perform important mechanical functions in vivo, including skin, arteries, tendons, and the chorioamnion membranes (“amniotic sac”) [1-3]. Because of the clinical importance of these tissues, much attention has been given to their mechanical behavior in vitro, particularly in laboratory mechanical testing conditions [1-3]. Two characteristic features of the mechanical behavior of collagenous soft tissues have been examined: the nonlinear nature of the stress-strain response and the relatively large contribution of timedependence to the overall mechanical response [1,2]. Many existing microstructurally-based models for soft tissue mechanical response have examined the stress-strain nonlinearity of soft tissues within the context of uncrimping and sequential recruitment of collagen fibrils [4-7]. Soft biological tissues are frequently considered as a two phase fiber-reinforced composite material, in which the stiff collagen fibers are contained within a ground substance primarily composed of proteoglycans and water [4]. Differences between tissue types (tendon versus articular cartilage) are primarily characterized by different component volume fractions and different fiber arrangements and orientations. Thes
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