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Related Concept Videos

Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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Bending of Members Made of Several Materials01:11

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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Generalized Hooke's Law01:22

Generalized Hooke's Law

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The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
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Shearing Stress01:18

Shearing Stress

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Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
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Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

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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...
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Updated: Mar 23, 2026

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
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Adjoint multi-start-based estimation of cardiac hyperelastic material parameters using shear data.

Gabriel Balaban1,2, Martin S Alnæs3, Joakim Sundnes3,4

  • 1Simula Research Laboratory, P.O. Box 134, 1325, Lysaker, Norway. gabrib@simula.no.

Biomechanics and Modeling in Mechanobiology
|March 24, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient adjoint method for estimating parameters in cardiac tissue models, improving accuracy and reducing computational cost for hyperelastic material analysis. The approach enhances the optimization process for complex biomechanical data.

Keywords:
Adjoint equationCardiac mechanicsHyperelasticityMulti-start optimizationParameter estimation

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Area of Science:

  • Biomechanics
  • Computational mechanics
  • Biomaterials science

Background:

  • Cardiac muscle exhibits complex hyperelastic, nonlinear, and anisotropic stress responses during relaxation.
  • Parameter estimation for these models is challenging due to a large number of parameters.
  • Traditional gradient calculation via finite differences is computationally expensive and prone to error.

Purpose of the Study:

  • To develop an efficient gradient calculation method for parameter estimation in cardiac tissue models.
  • To address the dependency on initial guesses in gradient-based optimization algorithms.
  • To provide accurate material parameter estimates for cardiac tissue using experimental data.

Main Methods:

  • Implementation of an automatically derived adjoint equation for gradient computation.
  • Application of the adjoint framework to a least squares fitting problem using simple shear test data.
  • Utilizing a multi-start procedure to overcome initial guess dependency in optimization.
  • Employing finite element models for parameter estimation.

Main Results:

  • The adjoint method significantly improves the efficiency of gradient calculation compared to finite differences.
  • The multi-start procedure effectively mitigates the sensitivity to initial parameter guesses.
  • Accurate material parameters for the Holzapfel and Ogden strain energy laws were obtained.

Conclusions:

  • The adjoint equation approach offers a computationally efficient and accurate method for parameter identification in cardiac biomechanics.
  • This framework facilitates better understanding and modeling of cardiac muscle tissue behavior.
  • The study provides valuable material parameter data for cardiac tissue modeling and simulation.