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

Research outputpeer-review

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.
Original languageEnglish
Title of host publicationInternational Conference on Mechanics - Eighth Polyakhov's Reading. AIP Confarence Proceedings
PublisherAmerican Institute of Physics
Volume1959
ISBN (Electronic)978-073541660-4
DOIs
Publication statusPublished - 2018

Cite this

Доманская, Т. О., Мальков, В. М., & Малькова, Ю. В. (2018). Bi-material plane with interface crack for the model of semi-linear material. In 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
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. Vol. 1959 American Institute of Physics, 2018.
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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.",
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Доманская, ТО, Мальков, ВМ & Малькова, ЮВ 2018, Bi-material plane with interface crack for the model of semi-linear material. in 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.

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

Research outputpeer-review

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