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Accretion-ablation mechanics.

Satya Prakash Pradhan1, Arash Yavari1,2

  • 1School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|November 5, 2023
PubMed
Summary
This summary is machine-generated.

This study develops a geometric nonlinear theory for accreting-ablating bodies, analyzing large deformations with simultaneous mass gain and loss. It models these bodies as time-dependent Riemannian manifolds, providing a framework for complex mechanical behaviors.

Keywords:
ablationaccretiongeometric mechanicsnonlinear elasticityresidual stresssurface growth

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Area of Science:

  • Continuum Mechanics
  • Nonlinear Dynamics
  • Geometric Mechanics

Background:

  • Existing theories of accretion mechanics lack comprehensive analysis of simultaneous accretion and ablation.
  • Large deformation analysis is crucial for understanding bodies with changing boundaries under load.

Purpose of the Study:

  • To formulate a generalized geometric nonlinear theory for accreting-ablating bodies.
  • To analyze the mechanics of bodies undergoing simultaneous accretion and ablation with large deformations.
  • To provide a framework for understanding the time-dependent reference configuration of such bodies.

Main Methods:

  • Formulation of a geometric nonlinear theory using time-dependent Riemannian manifolds.
  • Introduction of time of attachment and detachment maps to describe the body's evolving configuration.
  • Application of the theory to a thick hollow circular cylinder undergoing accretion and ablation.

Main Results:

  • The natural configuration is a time-dependent Riemannian manifold with an evolving metric.
  • Accretion and ablation velocities, along with attachment/detachment maps, define the time-dependent reference configuration.
  • Calculated deformation and stress states during and after the accretion-ablation process for a hollow cylinder.

Conclusions:

  • The developed geometric theory provides a robust framework for analyzing accreting-ablating bodies with large deformations.
  • The model accurately captures the complex interplay of accretion, ablation, and external loading.
  • This work advances the understanding of foundational issues in continuum mechanics related to evolving bodies.