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

Jia Lu

doi:10.1007/s10659-025-10134-8

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

Journal article

Peer reviewed

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

Jia Lu

Journal of elasticity, Vol.157(2), 43

05/2025

DOI: 10.1007/s10659-025-10134-8

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Abstract

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.

Biomechanics

Engineering

Materials Science

Classical and Continuum Physics

Classical Mechanics

general

Mathematical Applications in the Physical Sciences

Theoretical and Applied Mechanics

Details

Title: Subtitle: Analytical Structural Constitutive Models for Collagenous Soft Tissue: Treatment of Waviness Integrals
Creators: Jia Lu - Department of Mechanical Engineering, The University of Iowa
Resource Type: Journal article
Publication Details: Journal of elasticity, Vol.157(2), 43
Publisher: Springer Nature
DOI: 10.1007/s10659-025-10134-8
ISSN: 0374-3535
eISSN: 1573-2681
Grant note: P116S210005 / U.S. Department of Eduction
Language: English
Date published: 05/2025
Academic Unit: Mechanical Engineering
Record Identifier: 9984822961802771

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