Role of Microstructure in the Mechanics of Soft Matter

Abstract

Materials which exhibit non-linear mechanical behaviors under large deformations are generally classified as “soft matter”. Elastomers represent an important class of soft materials which have wide commercial applications and isotropic non-linear behavior. In contrast, biological materials have anisotropic responses due to their heterogeneous and composite architectures. The underlying microstructure determines the arterial macroscopic behavior and is represented through constitutive models to describe the stress-strain relationships. Mechanical characterization and development of constitutive models that describe these non-linear and anisotropic properties are essential to our understanding of the structure-property relationships in these materials. In this study, we use two model systems to link the local microstructure to the overall macroscopic behaviors of soft matter. First, we delineate the roles of individual network topological factors in determining the overall macroscopic behavior of isotropic silicone elastomers using specimens fabricated with differential amounts of crosslinking. We performed mechanical experiments, within a theoretically motivated continuum mechanical framework, using a custom made planar biaxial testing instrument. These experiments demonstrate the contributions of physical entanglements and chemical crosslinks to the overall mechanical properties of silicone elastomers. Further, we show that the slip-link form of strain energy function is better suited to describe the material properties in the low to moderate regions of the stress-strain behavior. However, this model does not predict the stiffening response of elastomers at higher deformations, which is better captured using the Arruda-Boyce form of strain energy function. To explore the effects of individual topological factors on the overall network properties, we performed swelling experiments of silicone specimens in xylene and quantified variations in the polymer-solvent interaction parameter, χ, given by the Frenkel-Flory-Rehner (FFR) model. Further, we characterized the viscoelastic properties using dynamic mechanical analysis. Our results show that χ is not a constant, as assumed in the FFR model, but bears a linear relation to the equilibrium polymer volume fraction. To characterize the contribution of trapped entanglements to the overall mechanical behaviors, we use scaling laws in polymer physics and investigate the dependence of equilibrium volume fraction and experimentally obtained elastic moduli. Further, dynamic mechanical analysis demonstrated an increase in complex modulus with increase in the cross linking density. Finally, we examined variations in the uniaxial and the dynamical mechanical properties of silicone elastomers with storage time. Our results show that the time dependent increase in the modulus correlated with the formation of slip-links in the samples aged for a significantly long time in air. Together, these comprehensive studies show the importance of individual network features which affect the overall macroscopic properties of elastomers. Second, we use a multilayered and composite arterial model system to explore the passive material properties of arteries due to anisotropic layouts of extracellular matrix proteins, collagen and elastin. We characterized the mechanical properties of diseased human ascending thoracic aortic dissected (TAD) tissues, obtained from consenting patients undergoing emergency surgical repair to replace the diseased region, using multiple biaxial tests. We fit these results to micro structurally motivated Holzapfel-Gasser-Ogden model which is frequently used in the arterial mechanics literature. Our results show a higher stiffness for TAD tissues as compared to control aorta, without the presence of atherosclerotic plaques or other arterial disease. To study the directional variation in the mechanical properties of TAD tissues, we compared the stiffness in circumferential longitudinal directions at high and low stress region of equibiaxial experimental data. We observed no differences in the stiffness of TAD tissues in the circumferential and longitudinal directions. Further, we do not see any directional variations in the ultimate tensile stress, maximum extensibility, and modulus calculated in the low stretch region of uniaxial stress-strain response in TAD tissues. Histological analysis of TAD tissues showed a decrease in elastin content and an increase in collagen content as compared to control tissues. Higher TAD tissue stiffness also correlated with reduced elastin content in the arterial walls. To investigate the strain rate dependence of measured mechanical properties we use high testing rates of 1mm/sec to show that the TAD tissues have higher stiffness in the circumferential direction as compared to longitudinal direction. Finally, we used peel experiments to quantify the rupture potential of aortic dissected tissues. Our results show that TAD tissues have reduced delamination strength between layers as compared to control aortic tissues. To the best of our knowledge, no previous study has reported the mechanical property of human TAD tissues and these are the only biomechanical results on TAD tissues reported in specimens from South Asian patients. We hope that such studies will be useful for researchers who rely on microstructure based constitutive models to accurately describe the mechanical environment of cells which are important in the remodeling of tissues and in numerical models to assess mechanical criteria which may lead to the growth or dissection of arterial tissues.