A continuum model for the mechanics of viscoelastic fiber composite

초록

A refined continuum model describing the mechanics of viscoelastic fiber composites subjected to finite plane deformations is presented. Emphasis is placed on the integration of nonlinear viscoelastic responses of soft biological tissues composed of collagen fibers and surrounding matrix proteins. The nonlinear elastic response of the matrix phase is characterized via the Mooney–Rivlin strain energy potential and the viscous dissipation inherent to soft tissues is modeled using a Prony series within an integral-type viscoelastic framework. The proposed approach systematically incorporates strain-gradient fields into the model of continuum deformations to explicitly account for microstructural effects, including the flexural resistance of the reinforcing collagen fibers critical to maintaining overall tissue stability. The associated Euler equilibrium equations are formulated via variational principles, leading to a system of nonlinear differential equations, the solutions of which are obtained using a custom-built finite element scheme. Validated against experimental data, the proposed model closely assimilates the nonlinear stress relaxation and strain-rate sensitivity of representative biological tissues such as human skeletal muscle and arteries, thereby establishing a robust theoretical and computational framework for design and analysis of soft tissues and clinical surgical planning. © 2026

키워드