# Nonlinear mechanics of accretion

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## Abstract

We formulate a geometric nonlinear theory of the mechanics of accretion. In this theory, the material manifold of an accreting body is represented by a time-dependent Riemannian manifold with a time-independent metric that at each point depends on the state of deformation at that point at its time of attachment to the body, and on the way the new material is added to the body. We study the incompatibilities induced by accretion through the analysis of the material metric and its curvature in relation to the foliated structure of the accreted body. Balance laws are discussed and the initial boundary value problem of accretion is formulated. The particular cases where the growth surface is either fixed or traction-free are studied and some analytical results are provided. We numerically solve several accretion problems and calculate the residual stresses in nonlinear elastic bodies induced from accretion.

## Keywords

Accretion Surface growth Nonlinear elasticity Residual stress Foliations Material metric## Mathematics Subject Classification

74B20 74A05 74A10 53Z05## Notes

### Acknowledgements

This research was partially supported by NSF—Grant Nos. CMMI 1130856 and ARO W911NF-16-1-0064.

## Supplementary material

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