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Dissipation potentials from elastic collapse.

Joe Goddard1, Ken Kamrin2

  • 1Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|July 12, 2019
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Summary
This summary is machine-generated.

This study generalizes Maxwell's formula to derive dissipation potentials from elastic potentials in systems with failure and recovery. It links continuum-level responses to microscopic transitions, explaining viscous and plastic behaviors.

Keywords:
dissipative systemselastic failureenergy landscapenonlinear Onsager symmetry

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Area of Science:

  • Continuum mechanics
  • Materials science
  • Nonlinear dynamics

Background:

  • Generalizes Maxwell's classical formula for dissipative systems.
  • Draws parallels between elastic potential in failure/recovery systems and dissipation potentials.
  • Connects continuum-level responses to microscopic transitions over multi-well potentials.

Purpose of the Study:

  • To derive dissipation potentials from elastic potentials in dissipative systems.
  • To explain the transition from viscous to plastic response based on microscopic transitions.
  • To demonstrate the emergence of the Reiner-Rivlin fluid from nonlinear isotropic elasticity.

Main Methods:

  • Generalization of Maxwell's formula.
  • Analysis of elastic potential in systems with continual failure and recovery.
  • Modeling microscopic transitions over multi-well potential energy landscapes.
  • Investigation of discrete and continuum mechanical analogues.

Main Results:

  • Dissipation potentials are derived from elastic potentials.
  • Stored elastic energy transitions to dissipated elastic energy.
  • Nonlinear viscous response becomes plastic for specific time scales.
  • The Reiner-Rivlin fluid is shown to arise from nonlinear isotropic elasticity.

Conclusions:

  • The framework provides a unified approach to understanding dissipative phenomena.
  • Microscopic transitions are key to explaining macroscopic material behavior.
  • Potential extensions to other dissipative processes are discussed.