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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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Implicit constitutive relations for nonlinear magnetoelastic bodies.

R Bustamante1, K R Rajagopal2

  • 1Departamento de Ingeniería Mecánica , Universidad de Chile , Beaucheff 850, Santiago Centro, Santiago, Chile.

Proceedings. Mathematical, Physical, and Engineering Sciences
|March 21, 2015
PubMed
Summary

This study introduces new implicit constitutive relations for magnetoelastic bodies, enabling accurate modeling of materials responding to magnetic fields. These advanced models overcome limitations of classical theories for large deformations and small strains.

Keywords:
ferromagnetic materialsmagneto-active rubbernonlinear elasticity

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Area of Science:

  • Solid Mechanics
  • Continuum Mechanics
  • Materials Science

Background:

  • Implicit constitutive relations have advanced elasticity theory.
  • Previous work extended these models to electroelastic bodies.
  • Classical models inadequately describe magnetoelastic phenomena.

Purpose of the Study:

  • To develop implicit constitutive relations for magnetoelastic bodies.
  • To model materials responding to magnetic stimuli beyond classical limitations.
  • To provide a rational framework for magnetoelastic behavior.

Main Methods:

  • Development of implicit constitutive relations for large deformations.
  • Linearization of models for small displacement gradients.
  • Application to boundary value problems.

Main Results:

  • Successful development of implicit constitutive relations for magnetoelasticity.
  • Linearized model explains phenomena classical models cannot.
  • Solutions provided for slab and cylinder boundary value problems.

Conclusions:

  • The developed implicit constitutive relations offer a superior framework for magnetoelasticity.
  • The models accurately describe complex magnetoelastic phenomena.
  • This work advances the understanding and application of magnetoelastic materials.