### Abstract

Original language | English |
---|---|

Title of host publication | International Conference on Mechanics - Eighth Polyakhov's Reading. AIP Confarence Proceedings |

Publisher | American Institute of Physics |

Volume | 1959 |

ISBN (Electronic) | 978-073541660-4 |

DOIs | |

Publication status | Published - 2018 |

### Cite this

*International Conference on Mechanics - Eighth Polyakhov's Reading. AIP Confarence Proceedings*(Vol. 1959). [070009] American Institute of Physics. https://doi.org/10.1063/1.5034684

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*International Conference on Mechanics - Eighth Polyakhov's Reading. AIP Confarence Proceedings.*vol. 1959, 070009, American Institute of Physics. https://doi.org/10.1063/1.5034684

**Bi-material plane with interface crack for the model of semi-linear material.** / Доманская, Татьяна Олеговна; Мальков, Вениамин Михайлович; Малькова, Юлия Вениаминовна.

Research output › › peer-review

TY - CHAP

T1 - Bi-material plane with interface crack for the model of semi-linear material

AU - Доманская, Татьяна Олеговна

AU - Мальков, Вениамин Михайлович

AU - Малькова, Юлия Вениаминовна

PY - 2018

Y1 - 2018

N2 - The singular plane problems of nonlinear elasticity (plane strain and plane stress) are considered for bi-material infinite plane with interface crack. The plane is formed of two half-planes. Mechanical properties of half-planes are described by the model of semi-linear material. Using model of this harmonic material has allowed to apply the theory of complex functions and to obtain exact analytical global solutions of some nonlinear problems. Among them the problem of bi-material plane with the stresses and strains jumps at an interface is considered. As an application of the problem of jumps, the problem of interface crack is solved. The values of nominal (Piola) and Cauchy stresses and displacements are founded. Based on the global solutions the asymptotic expansions are constructed for stresses and displacements in a vicinity of crack tip. As an example the case of a free crack in bi-material plane subjected to constant stresses at infinity is studied. As a special case, the analytical solution of the problem of a crack in a homogeneous plane is obtained from the problem for bi-material plane with interface crack.

AB - The singular plane problems of nonlinear elasticity (plane strain and plane stress) are considered for bi-material infinite plane with interface crack. The plane is formed of two half-planes. Mechanical properties of half-planes are described by the model of semi-linear material. Using model of this harmonic material has allowed to apply the theory of complex functions and to obtain exact analytical global solutions of some nonlinear problems. Among them the problem of bi-material plane with the stresses and strains jumps at an interface is considered. As an application of the problem of jumps, the problem of interface crack is solved. The values of nominal (Piola) and Cauchy stresses and displacements are founded. Based on the global solutions the asymptotic expansions are constructed for stresses and displacements in a vicinity of crack tip. As an example the case of a free crack in bi-material plane subjected to constant stresses at infinity is studied. As a special case, the analytical solution of the problem of a crack in a homogeneous plane is obtained from the problem for bi-material plane with interface crack.

U2 - 10.1063/1.5034684

DO - 10.1063/1.5034684

M3 - Article in an anthology

VL - 1959

BT - International Conference on Mechanics - Eighth Polyakhov's Reading. AIP Confarence Proceedings

PB - American Institute of Physics

ER -