Nonlinear Viscoelastic Modeling of ACL Soft Tissue: A Weibull-Based Constitutive Approach

Anterior cruciate ligament (ACL) plays a vital role in the mechanical stability of the knee joint. The biomechanical behavior of ACL is primarily influenced by its hierarchical collagen structure and viscoelastic properties. This paper presents a nonlinear viscoelastic constitutive model to characterize creep and stress relaxation behaviors of ACL soft tissue. The model assumes collagen fibers as nonlinear elastic elements governed by the Weibull probability distribution, while the ground substance is modeled as a Maxwell-type viscoelastic network. The total stress response is derived by superposing the mechanical contributions of the collagen fibrils and the proteoglycan-rich matrix. Simulation results indicate that the model can replicate major viscoelastic phenomena such as stress relaxation, creep deformation, and hysteresis observed in experimental data. This approach provides an accurate representation of time-dependent mechanical responses of biological soft tissues and could aid in the design of biomimetic grafts or rehabilitation protocols following ACL injuries.

Keywords:

ACL , Viscoelasticity , Weibull distribution , Creep , Stress relaxation , Collagen fibers