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Related Concept Videos

Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
If...
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

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...
Strain-Energy Density01:20

Strain-Energy Density

Understanding the strain energy density in materials under axial load is crucial for evaluating their mechanical behavior and durability. When a rod is subjected to such a load, it elongates and stores energy, known as strain energy, as potential energy within the material. This energy is measured in terms of energy per unit volume.
In the elastic region of a material, the relationship between the stress and the strain is linear and follows Hooke's Law. The strain energy density in this region...
Strain Energy01:13

Strain Energy

Strain energy is a fundamental concept in the field of materials science and structural engineering, describing the energy absorbed by a material or structure when it is deformed under load.
Consider a rod that is fixed at one end and subjected to an axial force at the free end. This axial force induces stress within the rod, leading to its elongation. As the axial force increases, so does the elongation of the rod, illustrating a direct relationship between the force applied and the resulting...
Shearing Strain01:20

Shearing Strain

The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

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.

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Magnetic Resonance Derived Myocardial Strain Assessment Using Feature Tracking
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Published on: February 12, 2011

Physical invariant strain energy function for passive myocardium.

M H B M Shariff1

  • 1Department of Applied Mathematics and Science, Khalifa University of Science, Technology and Research, Sharjah, UAE. shariff@kustar.ac.ae

Biomechanics and Modeling in Mechanobiology
|April 25, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a new orthotropic constitutive equation for incompressible solids using a principal axis technique. This invariant equation simplifies material characterization and accurately models passive myocardium behavior.

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Area of Science:

  • Solid Mechanics
  • Continuum Mechanics
  • Materials Science

Background:

  • Principal axis formulations are common in isotropic elasticity but less so for anisotropic problems.
  • Developing accurate constitutive models for anisotropic materials is crucial for understanding their mechanical behavior.

Purpose of the Study:

  • To develop a physical invariant orthotropic constitutive equation for incompressible solids using a principal axis technique.
  • To introduce a strain energy function with physically interpretable invariants for material characterization.
  • To propose and validate a specific constitutive model for passive myocardium.

Main Methods:

  • Application of a principal axis technique to develop an orthotropic constitutive equation.
  • Formulation of a strain energy function dependent on six physically interpretable invariants.
  • Development of a specific constitutive model for passive myocardium.

Main Results:

  • A one-variable (general) function-based invariant orthotropic constitutive equation for incompressible solids was developed.
  • The strain energy function incorporates six invariants with clear physical interpretations, aiding experimental characterization.
  • The proposed model for passive myocardium shows good agreement with existing simple shear and biaxial experimental data.

Conclusions:

  • The developed constitutive equation offers a simplified yet comprehensive approach to modeling anisotropic incompressible solids.
  • The physical invariants facilitate experimental determination of material-specific constitutive equations.
  • The passive myocardium model demonstrates the utility and accuracy of the proposed framework for biological tissues.