Fiber Plasticity and Localization in Soft Composites

This work presents a modeling effort to capture global instability events, such as kink-band formation, during non-monotonic loading conditions of soft composites driven by fiber plasticity. Biological fiber-reinforced composites such as tendon, undergo cyclic loading and exhibit a complex damage responsefrom damage initiation in the form of kink band formation, fiber/matrix debonding, fiber rupture and to ultimate failure and collagen fibril plasticity is known to play a crucial role in that damage cascade. In engineered fiber-reinforced soft composites, it is important to investigate the effects of fiber plasticity to optimize the strength and toughness of these materials. Localized deformation patterns of the kink-band type have been observed in biological composite materials such as mamalian tendon tissue, with uni-directional collagen-fibril reinforcement when subjected to tensile fatigue loading . In the relevant literature, the formation of these kinks is not well understood, and they are only treated as a precursor to material failure. In parallel, apart from the finite elastic strains that are apparent in these materials, there is evidence of plastic deformation mechanisms present in collagen fibrils when loaded in uniaxial tension. From a modeling perspective, loss of ellipticity of the governing equations of equilibrium, allows the prediction of emergence of macroscopic localization fronts. Loss of ellipticity of both phenomenological and micro-mechanical models has been extensively analyzed to investigate localized deformation patters in several classes of materials, including fiber-reinforced composites with hyperelastic or elastoplastic constituents. Most of these studies, however, focus on monotonic loading conditions involving compressive or tensile stresses along the fiber direction. In this work, we focus in the emergence of localization in fiber-reinforced soft composites with elastoplastic fibers and elastic matrix under non-monotonic loading conditions. This study brings new insight to damage initiation of biological fibrous tissues and engineered soft composites. To this end, a finite-strain model of a two-phase material following the Voigt assumption is developed. The material model for the matrix is considered hyperelastic and nearly incompressible with no dissipation mechanism. The fiber model is elasto-plastic with a single slip plane along the direction of the fibers. This allows us to capture the effects of fiber plasticity in the composite and then the model is used to track the emergence of discontinuity fronts in the context of loss of ellipticity. We examine the emergence of discontinuity fronts in the composite as a continuum, and in the fiber phase during loading and unloading. It is confirmed that upon initial tensile loading in the direction of the fibers, and plastic deformation of the fibers, the fiber material can exhibit macroscopic localization during unloading. Contrary to past studies, loss of ellipticity in this case can occur as the composite is still under tensile loading; it is noteworthy that while the fiber stretch is tensile at loss of ellipticity, the elastic fiber stretch is contractile.