## Abstract

Abstract—: The paper considers a sequence of solutions to the one-dimensional problem of irreversible deformation of a functionally graded material under conditions of uneven thermal expansion. Numerical solutions are obtained for the problems of heating an elastoplastic sphere, the material constants of which are linear functions of the radius, and exact solutions, in which the material constants are approximated by piecewise constant functions. It is shown that the deformation of a functionally graded elastoplastic material, in which the material constants are specified by piecewise-constant distributions, can be qualitatively described by numerical solutions, in which the material constants are continuous approximations of the corresponding piecewise-constant functions. The obtained numerical and analytical solutions of boundary value problems are graphically analyzed.

Original language | English |
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Pages (from-to) | 800-807 |

Number of pages | 8 |

Journal | Mechanics of Solids |

Volume | 55 |

Issue number | 6 |

DOIs | |

Publication status | Published - Nov 2020 |

Externally published | Yes |

## Keywords

- deformation
- plasticity
- residual stress
- temperature stress
- thermoelasticity

## ASJC Scopus subject areas

- Mechanics of Materials
- General Physics and Astronomy