A computationally efficient fibril-scale finite element model bridges molecular mechanisms and collagen fibril nonlinearity and failure.

Abstract

Collagen fibrils control the mechanical integrity of many load-bearing tissues, but experimentally isolating how cross-link class, density, and spatial organization regulate fibril nonlinearity and failure remains difficult. This limits mechanistic interpretation of aging- and diabetes-associated changes in collagenous tissue mechanics. Here we present a computationally efficient fibril-scale finite element (FE) framework for large-deformation tension of type I collagen fibrils. The model explicitly represents tropocollagen molecule (TCM) backbones, stochastic cross-link networks, and friction-mediated intermolecular sliding, with constitutive laws calibrated from molecular simulations. The framework enables length-converged ensemble simulations at experimentally relevant single-fibril scales. The model is benchmarked against two independent tensile datasets, reproducing the nonlinear response of human patellar tendon fibrils and capturing the leading stiffness and strength trends induced by methylglyoxal (MG)-treatment in rat Achilles tendon fibrils. Parametric studies show that cross-link density elevates the high-strain tangent modulus and ultimate tensile strength while leaving the low-strain modulus nearly unchanged. Enzymatic maturation has the largest effect at intermediate cross-link density, whereas non-enzymatic cross-links provide weaker stiffening and promote earlier microscopic rupture. At fixed mean density, spatial heterogeneity reduces fibril strength and localizes damage, with strength governed by the local minimum of the cross-link density profile. The model therefore provides a scale-bridging structure-property framework for testing how molecular cross-link changes alter fibril-scale mechanics and for supplying damage-aware inputs to higher-level models of collagenous tissues.