Analytical Structural Constitutive Models for Collagenous Soft Tissue: Treatment of Waviness Integrals

• Published in: Journal of elasticity Vol. 157; no. 2
• Main Author: Lu, Jia
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.05.2025; Springer Nature B.V
• Subjects: Biomechanics; Classical and Continuum Physics; Classical Mechanics; Constitutive equations; Constitutive models; Constitutive relationships; Distribution functions; Engineering; Indicators; Materials Science; Mathematical Applications in the Physical Sciences; Mathematical models; Numerical integration; Probability distribution functions; Response functions; Salience; Soft tissues; Statistical analysis; Theoretical and Applied Mechanics; Waviness; Structural constitutive model; Collagenous tissue; 74B20; 74L15; 74M25; Waviness; 74A20; Recruitment
• ISSN: 0374-3535; 1573-2681
• DOI: 10.1007/s10659-025-10134-8

This article presents two structural constitutive models for collagenous tissues. A salient feature of these models is that they are represented analytically by probability distribution functions that are directly available in standard scientific computing packages. No numerical integration is needed at the user’s end. The models are apt for describing the realistic behavior of collagenous tissues. Most notably, they are able to generate response curves whose slopes are sigmoid. The models can delineate, analytically, the transition from the initial quasi-exponential response to the subsequent non-exponential phase characterized by a sigmoid slope. The constitutive equations have an additive structure, and this structure is leveraged to develop response functions relative to a pre-deformed configuration. The models are evaluated against experimental and simulated response data. Spot-on fits are achieved in all cases. The predictive capability is assessed in the context of biaxial response by fitting a subset of loading paths and predicting the responses of unfitted paths. The models provide indicators of waviness exposure, and these indicators can be used to estimate the trustworthiness of the parameters obtained from regression.