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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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A Magneto-Viscoelasticity Problem with Aging.

Sandra Carillo1,2, Claudio Giorgi3

  • 1Dipartimento Scienze di Base e Applicate per l'Ingegneria, SAPIENZA Università di Roma, 00161 Roma, Italy.

Materials (Basel, Switzerland)
|November 11, 2022
PubMed
Summary

This study introduces a new model for magneto-viscoelastic materials, combining aging and magnetic field effects. We prove existence and uniqueness for this coupled system, advancing the study of materials with memory.

Keywords:
aging materials with memoryintegro-differential evolution equationmagneto-mechanic interactionsmagneto-viscoelasticity

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Area of Science:

  • Continuum Mechanics
  • Materials Science
  • Magnetism

Background:

  • Viscoelastic materials exhibit time-dependent mechanical behavior, often modeled using integral equations.
  • Aging in materials introduces time-dependent changes in properties, distinct from memory effects.
  • Magneto-viscoelasticity explores the interplay between mechanical deformation and magnetic fields.

Purpose of the Study:

  • To develop and analyze a one-dimensional magneto-viscoelastic model incorporating material aging.
  • To investigate the coupling of viscoelasticity, aging, and external magnetic field effects.
  • To establish theoretical foundations for materials exhibiting combined viscoelastic, aging, and magnetic properties.

Main Methods:

  • A non-linear partial differential equation (PDE) for magnetic field influence (Landau-Lifshitz model).
  • A linear integro-differential equation for viscoelastic behavior with time-dependent relaxation functions.
  • Mathematical analysis to prove existence and uniqueness of solutions under specific regularity conditions.

Main Results:

  • A novel mathematical model for magneto-viscoelasticity with aging is formulated.
  • The model couples non-linear magnetic effects with time-dependent viscoelasticity and aging.
  • Existence and uniqueness of a solution are demonstrated for the proposed model.

Conclusions:

  • The study provides a theoretical framework for understanding magneto-viscoelastic materials with aging.
  • This research bridges the gap in modeling materials with combined viscoelastic, aging, and magnetic phenomena.
  • The findings offer new insights into the behavior of advanced materials under coupled physical influences.