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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.

Members Made of Elastoplastic Material

Members Made of Elastoplastic Material

The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...

Deformation of Member under Multiple Loadings

Deformation of Member under Multiple Loadings

When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...

Residual Stresses in Bending

Residual Stresses in Bending

In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...

Bending of Curved Members - Strain Analysis

Bending of Curved Members - Strain Analysis

The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
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Bending of Members Made of Several Materials

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In analyzing a structural member composed of two different materials with identical cross-sectional areas, it is crucial to understand how their distinct elastic properties affect the member's response under load. The analysis involves assessing stress and strain distributions using the transformed section concept, which accounts for variations in material properties.
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Related Experiment Video

Updated: Jul 3, 2026

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Published on: April 11, 2018

On modelling nonlinear viscoelastic effects in ligaments.

E Peña¹, J A Peña, M Doblaré

¹Group of Structural Mechanics and Materials Modeling, Aragón Institute of Engineering Research, University of Zaragoza, Maria de Luna 7, 50018 Zaragoza, Spain. fany@unizar.es

Journal of Biomechanics

|August 2, 2008

Summary

This summary is machine-generated.

Human ligament stress relaxation is strain-dependent, requiring new biomechanics models. This study presents a nonlinear viscoelastic model accurately predicting ligament behavior under finite deformation.

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Last Updated: Jul 3, 2026

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

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Published on: April 11, 2018

Treatment of Ligament Constructs with Exercise-conditioned Serum: A Translational Tissue Engineering Model

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Investigating Stress-relaxation and Failure Responses in the Trachea

Investigating Stress-relaxation and Failure Responses in the Trachea

Published on: October 18, 2022

Area of Science:

Biomechanics
Biomaterials Science
Tissue Engineering

Background:

Standard quasilinear viscoelasticity theory inadequately describes human ligament behavior.
Ligamentous materials exhibit strain-dependent stress relaxation, a nonlinear phenomenon.
Finite deformation analysis is crucial for accurate tissue biomechanics.

Purpose of the Study:

To characterize and demonstrate the significance of nonlinear stress-relaxation in ligaments under finite deformation.
To develop and validate a modified viscoelastic model accounting for strain dependency.
To investigate the distinct viscoelastic properties of ligament matrix and fibers.

Main Methods:

Developed a structural model based on local additive stress tensor decomposition.
Generalized Kelvin-Voigt nonlinear viscous models with a specific free energy density function.
Fitted model parameters to experimental data from human medial collateral ligament specimens.
Validated the model against multi-axial loading scenarios and finite deformations.

Main Results:

The nonlinear, strain-dependent stress relaxation of ligaments was accurately characterized.
The developed model successfully predicted strain-dependent relaxation and strain-rate dependent behavior.
Distinct viscoelastic properties of matrix and fibers were considered, highlighting their importance.
Model validation confirmed accurate predictions under various loading conditions.

Conclusions:

A novel nonlinear viscoelastic model accurately captures human ligament behavior under finite deformation.
Strain dependency is a critical factor in ligament stress relaxation, necessitating advanced modeling.
The model provides a more realistic framework for understanding ligament biomechanics and injury mechanisms.