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Plastic deformation represents a fundamental concept in materials science, which explains the irreversible change in the shape of a material when it experiences stress beyond its elastic capability. This phenomenon is important in structural engineering, especially in designing and analyzing cantilever beams—structures that are securely fixed at one end and bear loads at the opposite end. When these beams are subjected to loads within their elastic range, they will return to their...
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It is essential to understand how structural members behave under plastic deformation when the bending stress exceeds the material's yield strength. This state of deformation permanently alters the shape of the member, in contrast to the linear elastic behavior observed before yielding. The strain at any point in the member is expressed in terms of maximum strain. Notably, the neutral axis, which coincides with the centroid during elastic bending, shifts away from the centroid under plastic...
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In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
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Soft metamaterials with dynamic viscoelastic functionality tuned by pre-deformation.

William J Parnell1, Riccardo De Pascalis2

  • 11 School of Mathematics , University of Manchester , Oxford Road, Manchester M13 9PL , UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|March 19, 2019
PubMed
Summary
This summary is machine-generated.

Pre-stressing soft, inhomogeneous rods tunes their dynamic response, revealing a coupling between wave frequency and initial deformation. This behavior in viscoelastic metamaterials offers new possibilities for material design.

Keywords:
effective moduliincremental deformationsviscoelasticity

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Area of Science:

  • Continuum Mechanics
  • Materials Science
  • Acoustics

Background:

  • Soft, inhomogeneous materials exhibit viscoelasticity, leading to frequency-dependent properties.
  • These materials, including metamaterials and phononic crystals, display complex dynamic responses.
  • Understanding their behavior is crucial for advanced material applications.

Purpose of the Study:

  • To investigate how pre-stress influences the dynamic response of thin inhomogeneous rods.
  • To explore the relationship between initial large deformation and small amplitude wave propagation.
  • To analyze the effective loss and storage moduli in viscoelastic metamaterials.

Main Methods:

  • Theoretical analysis of quasi-linearly viscoelastic phases.
  • Homogenization techniques for long wavelengths.
  • Mathematical modeling of longitudinal wave propagation in pre-stressed rods.

Main Results:

  • Effective dynamic response of inhomogeneous rods is tunable by pre-stress.
  • A strong coupling is observed between wave frequency and initial large deformation.
  • The effective incremental response does not exhibit time-deformation separability.

Conclusions:

  • Pre-stress is a key parameter for controlling the dynamic behavior of soft metamaterials.
  • The findings challenge assumptions of time-deformation separability in effective responses.
  • This research contributes to understanding and designing advanced viscoelastic materials.