A pseudoelastic response of hyperelastic composites reinforced with nonlinear elastic fibrous materials: Continuum modeling and analysis

Abstract

The present study aims to develop a continuum-based model to predict the pseudoelastic behavior of biological composites subjected to finite plane elastostatics. The proposed model incorporates a hyperelastic matrix material reinforced with nonlinear fibers, addressing challenges such as irreversible softening responses, large deformations, and nonlinear stress–strain responses. The kinematics of reinforcing fibers are formulated via the first and second gradient of continuum deformations and, more importantly, damage function and damage variables of Ogden–Roxburgh and Weibull type are integrated into the model to assimilate the various aspects of damage mechanisms present in soft tissues. Adopting the framework of variational principles and a virtual work statement, the Euler equation and admissible boundary conditions are obtained. The proposed model successfully predicts the Mullins effect observed in the human aorta and the Manduca muscle. Experimental validation with elastomeric composites demonstrates its utility to replicate softening and fiber damage phenomena, including deformation profiles. Further, the proposed molecular dynamics scheme offers an enhanced understanding of polymer chain entanglement processes, thereby facilitating the quantification of permanent damage in elastomeric composites. The obtained results may provide valuable insight toward understanding and modeling the mechanical behavior of soft biological tissues with practical implications for the design and analysis of biofabricated composites aimed at mimicking biological tissues.