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

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике

Выдержка

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.
Язык оригиналаанглийский
Название основной публикацииInternational Conference on Mechanics - Eighth Polyakhov's Reading. AIP Confarence Proceedings
ИздательAmerican Institute of Physics
Том1959
ISBN (электронное издание)978-073541660-4
DOI
СостояниеОпубликовано - 2018

Цитировать

Доманская, Т. О., Мальков, В. М., & Малькова, Ю. В. (2018). Bi-material plane with interface crack for the model of semi-linear material. В International Conference on Mechanics - Eighth Polyakhov's Reading. AIP Confarence Proceedings (Том 1959). [070009] American Institute of Physics. https://doi.org/10.1063/1.5034684
Доманская, Татьяна Олеговна ; Мальков, Вениамин Михайлович ; Малькова, Юлия Вениаминовна. / Bi-material plane with interface crack for the model of semi-linear material. International Conference on Mechanics - Eighth Polyakhov's Reading. AIP Confarence Proceedings. Том 1959 American Institute of Physics, 2018.
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title = "Bi-material plane with interface crack for the model of semi-linear material",
abstract = "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.",
author = "Доманская, {Татьяна Олеговна} and Мальков, {Вениамин Михайлович} and Малькова, {Юлия Вениаминовна}",
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Доманская, ТО, Мальков, ВМ & Малькова, ЮВ 2018, Bi-material plane with interface crack for the model of semi-linear material. в International Conference on Mechanics - Eighth Polyakhov's Reading. AIP Confarence Proceedings. том. 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.

International Conference on Mechanics - Eighth Polyakhov's Reading. AIP Confarence Proceedings. Том 1959 American Institute of Physics, 2018. 070009.

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике

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.

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M3 - Article in an anthology

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

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Доманская ТО, Мальков ВМ, Малькова ЮВ. Bi-material plane with interface crack for the model of semi-linear material. В International Conference on Mechanics - Eighth Polyakhov's Reading. AIP Confarence Proceedings. Том 1959. American Institute of Physics. 2018. 070009 https://doi.org/10.1063/1.5034684