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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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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

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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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Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

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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...
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Three-Dimensional Analysis of Strain01:29

Three-Dimensional Analysis of Strain

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Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
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Hooke's Law01:26

Hooke's Law

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Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.
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Strain and Elastic Modulus01:15

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The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or geometry under tensile, volume (also known as bulk), or shear stress, respectively, and is a dimensionless quantity. The strain experienced by a body under tensile or compressive stress is called tensile or compressive strain, respectively. In contrast, the strain experienced under bulk stress and shear stress is known as volume and shear...
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Related Experiment Video

Updated: Oct 12, 2025

Applying Dynamic Strain on Thin Oxide Films Immobilized on a Pseudoelastic Nickel-Titanium Alloy
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Magnetoelastic thin films at large strains.

Elisa Davoli1, Martin Kružík2, Paolo Piovano3

  • 1Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria.

Continuum Mechanics and Thermodynamics
|November 22, 2021
PubMed
Summary

We developed a new model for thin magnetoelastic films using advanced mathematical techniques. This model accounts for both material deformation and magnetic field interactions in the film.

Keywords:
Eulerian–LagrangianFormulationsLarge-strain deformationsMagnetoelasticityThin-films

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Area of Science:

  • Continuum Mechanics
  • Magnetism
  • Materials Science

Background:

  • Magnetoelastic films are crucial in various technologies.
  • Existing models often simplify the complex interplay between elasticity and magnetism.
  • A rigorous derivation of a thin film model is needed.

Purpose of the Study:

  • To derive a reduced mathematical model for thin magnetoelastic films.
  • To incorporate both elastic deformation and magnetic phenomena.
  • To handle the complexities of three-dimensional deformations and Maxwell's equations.

Main Methods:

  • Utilizing Gamma-convergence techniques for model reduction.
  • Defining magnetization vectors on the deformed configuration.
  • Addressing the injectivity of deformations for planar domains.
  • Applying a rigorous treatment of Maxwell's system in the deformed film.

Main Results:

  • A novel limit model for thin magnetoelastic films is derived.
  • The model incorporates both Lagrangian and Eulerian terms due to coupled fields.
  • The mathematical framework addresses the challenges of deformed configurations.

Conclusions:

  • The derived model provides a more accurate description of thin magnetoelastic films.
  • This work offers a rigorous mathematical foundation for studying magnetoelastic phenomena in reduced dimensions.
  • The approach facilitates further theoretical and computational investigations.