### Abstract

Here, we use the theory of surface elasticity to extend the morphological instability analysis of stressed solids developed in the works of Asaro, Tiller, Grinfeld, Srolovitz and many others. Within the framework of Gurtin-Murdoch model, the surface phase is assumed to be a negligibly thin layer with the elastic properties which differ from those of the bulk material. We consider the mass transport mechanism driven by the variation of surface and bulk energy along undulated surface of stressed solid. The linearized surface evolution equation is derived in the case of plane strain conditions and describes the amplitude change of surface perturbations with time. A parametric analysis of this equation leads to the definition of critical conditions which depend on undulation wavelength, residual surface stress, applied loading, surface and bulk elastic constants and predict the surface morphological stability.

Original language | English |
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Pages (from-to) | 070016-1-070016-5 |

Journal | AIP Conference Proceedings |

Volume | 1959 |

DOIs | |

Publication status | Published - 2 May 2018 |

Event | International Scientific Conference on Mechanics: 8th Polyakhov's Reading - Saint Petersburg Duration: 29 Jan 2018 → 2 Feb 2018 |

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### Scopus subject areas

- Mathematics(all)

### Cite this

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*AIP Conference Proceedings*, vol. 1959, pp. 070016-1-070016-5. https://doi.org/10.1063/1.5034691

**Stability analysis of nanoscale surface patterns in stressed solids.** / Kostyrko, Sergey A.; Shuvalov, Gleb M.

Research output

TY - JOUR

T1 - Stability analysis of nanoscale surface patterns in stressed solids

AU - Kostyrko, Sergey A.

AU - Shuvalov, Gleb M.

PY - 2018/5/2

Y1 - 2018/5/2

N2 - Here, we use the theory of surface elasticity to extend the morphological instability analysis of stressed solids developed in the works of Asaro, Tiller, Grinfeld, Srolovitz and many others. Within the framework of Gurtin-Murdoch model, the surface phase is assumed to be a negligibly thin layer with the elastic properties which differ from those of the bulk material. We consider the mass transport mechanism driven by the variation of surface and bulk energy along undulated surface of stressed solid. The linearized surface evolution equation is derived in the case of plane strain conditions and describes the amplitude change of surface perturbations with time. A parametric analysis of this equation leads to the definition of critical conditions which depend on undulation wavelength, residual surface stress, applied loading, surface and bulk elastic constants and predict the surface morphological stability.

AB - Here, we use the theory of surface elasticity to extend the morphological instability analysis of stressed solids developed in the works of Asaro, Tiller, Grinfeld, Srolovitz and many others. Within the framework of Gurtin-Murdoch model, the surface phase is assumed to be a negligibly thin layer with the elastic properties which differ from those of the bulk material. We consider the mass transport mechanism driven by the variation of surface and bulk energy along undulated surface of stressed solid. The linearized surface evolution equation is derived in the case of plane strain conditions and describes the amplitude change of surface perturbations with time. A parametric analysis of this equation leads to the definition of critical conditions which depend on undulation wavelength, residual surface stress, applied loading, surface and bulk elastic constants and predict the surface morphological stability.

UR - http://www.scopus.com/inward/record.url?scp=85047223982&partnerID=8YFLogxK

U2 - 10.1063/1.5034691

DO - 10.1063/1.5034691

M3 - Article

AN - SCOPUS:85047223982

VL - 1959

SP - 070016-1-070016-5

JO - AIP Conference Proceedings

JF - AIP Conference Proceedings

SN - 0094-243X

ER -