Understanding the inelastic response of collagen fibrils: A viscoelastic-plastic constitutive model

Collagen fibrils, which are the lowest level fibrillar unit of organization of collagen, are thus of primary interest towards understanding the mechanical behavior of load-bearing soft tissues. The deformation of collagen fibrils shows unique mechanical features; namely, their high energy dissipation is even superior compared to most engineering materials. Additionally, there are indications that cyclic loading can fur-ther improve the toughness of collagen fibrils. Recent experiments from Liu at al. (2018) focused on the response of type I collagen fibrils to uniaxial cyclic loading, revealing some interesting results regarding their rate-dependent and inelastic response. In this work, we aim to develop a model that allows inter-preting the complex nonlinear and inelastic response of collagen fibrils under cyclic loading. We propose a constitutive model that accounts for viscoelastic deformations through a decoupled strain-energy den-sity function (into an elastic and a viscous parts), and for plastic deformations through plastic evolution laws. The stress-stretch response results obtained using this constitutive law showed good agreement with experimental data over complex loading paths. Ultimately we use the model to gain more insights on how cyclic loading and rate effects control the interplay between viscoelastic and plastic deformation in collagen fibrils, and to extrapolate the results from experimental data, analyzing how complex cyclic load influences energy dissipation and deformation mechanisms. Statement of significance In this work, we develop a viscoelastic-plastic constitutive model for collagen fibrils with the aim of an-alyzing the effects of inelasticity and energy dissipation in this material, and more specifically the com-petition between viscoelasticity and plasticity in the context of cyclic loading and overload. Experimen-tal and theoretical approaches so far have not fully clarified the interplay between viscous and plastic deformations during cyclic loading of collagen fibrils. Here, we aim to interpret the complex nonlinear response of collagen fibrils and, ultimately, suggest predictive capabilities that can inform tissue-level re-sponse and injury. To validate our model, we compare our results against the stress-stretch data obtained from experiments of cyclic loaded single fibrils performed by Liu et al. (2018).(c) 2022 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Automated summary

In this study, a viscoelastic-plastic constitutive model was developed to analyze the effects of inelasticity and energy dissipation in collagen fibrils, specifically in the context of cyclic loading and overload. The model was validated by comparing the stress-stretch data obtained from experiments with single fibrils subjected to cyclic loading conducted by Liu et al. (2018).