Accretion-ablation mechanics

Satya Prakash Pradhan

doi:10.1098/rsta.2022.0373

2023-11-06

Satya Prakash Pradhan

Arash Yavari *

DOI：10.1098/rsta.2022.0373

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摘要

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In this paper, we formulate a geometric nonlinear theory of the mechanics of accreting-ablating bodies. This is a generalization of the theory of accretion mechanics of Sozio & Yavari (Sozio & Yavari 2019 J. Nonlinear Sci.29, 1813-1863 (doi:10.1007/s00332-019-09531-w)). More specifically, we are interested in large deformation analysis of bodies that undergo a continuous and simultaneous accretion and ablation on their boundaries while under external loads. In this formulation, the natural configuration of an accreting-ablating body is a time-dependent Riemannian 3-manifold with a metric that is an unknown a priori and is determined after solving the accretion-ablation initial-boundary-value problem. In addition to the time of attachment map, we introduce a time of detachment map that along with the time of attachment map, and the accretion and ablation velocities, describes the time-dependent reference configuration of the body. The kinematics, material manifold, material metric, constitutive equations and the balance laws are discussed in detail. As a concrete example and application of the geometric theory, we analyse a thick hollow circular cylinder made of an arbitrary incompressible isotropic material that is under a finite time-dependent extension while undergoing continuous ablation on its inner cylinder boundary and accretion on its outer cylinder boundary. The state of deformation and stress during the accretion-ablation process, and the residual stretch and stress after the completion of the accretion-ablation process, are computed. This article is part of the theme issue 'Foundational issues, analysis and geometry in continuum mechanics'.

Keyword:

accretion

ablation

surface growth

nonlinear elasticity

residual stress

geometric mechanics