Thermomechanical Hysteresis of Biological and Synthetic Hydrogels : Theory, Characterisation, and Development of a Novel Deformation Calorimeter

The nucleus pulposus of the intervertebral disc is a gelatinous viscous hydrogel that has an essential role in the mechanics of the intervertebral disc joint. The viscoelastic properties of the nucleus pulposus significantly change in the course of time and particularly at the outset of disc degeneration. Viscoelasticity is the result of entropy production and may be characterized by hysteresis when the tissue undergoes cyclic mechanical loading. "Nature never undertakes any change unless her interests are served by an increase in entropy" once commented Max Planck. In the context of mechanobiology, we present an original concept wich is referred to the hysteresis theory and states that for a given range of frequency and biological tissue, the maximum mechanotransduction signal coincides with maximum hysteresis. If verified, this statement would introduce a relevant variable in the study of pathophysiological conditions such as degeneration of the nucleus pulposus and serve as a reliable variable to define optimized mechanical load settings for the culture of tissue engineered materials. This doctoral work deals with the proposition of this theory and defines the experimental and theoretical framework to verify this hypothesis in following studies. Hysteresis is not specific to a single process, but is the result of many internal processes that can happen simultaneously. Deformation may imply entropic and/or elastic changes in the tissue which from a phenomenolgical point of view is equivalent, and yet are fundamentally different in nature. Deformation may also be accompanied by reversible and irreversible processes that result in mechanical hysteresis. A clear knowledge on the thermomechanical processes involved during the deformation of biological tissues enables the experimenter to overcome perhaps too restrictive assumptions and may lead to new insights. In this work, we provide a prototype of a deformation calorimeter that is specifically designed for biological hydrogel tissues, thereby refocusing the theory of biological materials on solid experimental thermodynamic grounds. This prototype produced satisfactory results with a measurement precision of 3% and a characteristic time constant of 40 seconds. The thermal stability of the deformation calorimeter was, however, not suficient to experimentally investigate the thermomechanical properties of very soft tissue (kPa scale) such as the nucleus pulposus, but acceptable for stiffer materials ranging in the MPa scale. In conjunction, a theoretical framework is proposed to recover the information that is hidden in hysteresis. Based on continuum mechanics and, in particular, mixture and normal dissipation theories, the governing nonlinear heat equation for thermomechanical porous materials was derived. This equation is general and valid for finite perturbations in temperature and deformations. A particular model for hydrogels was also proposed. Finally, hysteresis and damping properties of the