On nonlinear strain vectors and tensors in continuum theories of mechanics
A non-linear mathematical model of hyperbolic thermoelastic continuum with fine microstructure is proposed. The model is described in terms of 4-covariant field theoretical formalism. Fine microstructure is represented by d-tensors, playing role of extra field variables. A Lagrangian density for hyperb...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2014-03-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20720/16980 |
| _version_ | 1818025011637649408 |
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| author | Vladimir A Kovalev Yuriy N Radayev |
| author_facet | Vladimir A Kovalev Yuriy N Radayev |
| author_sort | Vladimir A Kovalev |
| collection | DOAJ |
| description | A non-linear mathematical model of hyperbolic thermoelastic continuum with fine microstructure is proposed. The model is described in terms of 4-covariant field theoretical formalism. Fine microstructure is represented by d-tensors, playing role of extra field variables. A Lagrangian density for hyperbolic thermoelastic continuum with fine microstructure is given and the corresponding least action principle is formulated. 4-covariant field equations of hyperbolic thermoelasticity are obtained. Constitutive equations of microstructural hyperbolic thermoelasticity are discussed. Virtual microstructural inertia is added to the considered action density. It is also concerned to the thermal inertia. Variational symmetries of the thermoelastic action are used to formulate covariant conservation laws in a plane space-time. For micropolar type II thermoelastic Lagrangians following the usual procedure independent rotationally invariant functional arguments are obtained. Objective forms of the Lagrangians satisfying the frame indifference principle are given. Those are derived by using extra strain vectors and tensors. |
| first_indexed | 2024-12-10T04:09:20Z |
| format | Article |
| id | doaj.art-4a42fdea92374c5da3d0ef9d4ce20ffc |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-10T04:09:20Z |
| publishDate | 2014-03-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-4a42fdea92374c5da3d0ef9d4ce20ffc2022-12-22T02:02:47ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812014-03-01181668510.14498/vsgtu131018138On nonlinear strain vectors and tensors in continuum theories of mechanicsVladimir A Kovalev0Yuriy N Radayev1Moscow City Government University of ManagementA. Ishlinsky Institite for Problems in Mechanics, Russian Academy of SciencesA non-linear mathematical model of hyperbolic thermoelastic continuum with fine microstructure is proposed. The model is described in terms of 4-covariant field theoretical formalism. Fine microstructure is represented by d-tensors, playing role of extra field variables. A Lagrangian density for hyperbolic thermoelastic continuum with fine microstructure is given and the corresponding least action principle is formulated. 4-covariant field equations of hyperbolic thermoelasticity are obtained. Constitutive equations of microstructural hyperbolic thermoelasticity are discussed. Virtual microstructural inertia is added to the considered action density. It is also concerned to the thermal inertia. Variational symmetries of the thermoelastic action are used to formulate covariant conservation laws in a plane space-time. For micropolar type II thermoelastic Lagrangians following the usual procedure independent rotationally invariant functional arguments are obtained. Objective forms of the Lagrangians satisfying the frame indifference principle are given. Those are derived by using extra strain vectors and tensors.https://journals.eco-vector.com/1991-8615/article/viewFile/20720/16980thermoelasticitymicrostructurefieldextra fieldactioncovarianceconservation lawd-tensor4-currentenergy-momentum tensorkinematic constraintlagrange multiplierrotationframe indifference principleextrastrain tensor |
| spellingShingle | Vladimir A Kovalev Yuriy N Radayev On nonlinear strain vectors and tensors in continuum theories of mechanics Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki thermoelasticity microstructure field extra field action covariance conservation law d-tensor 4-current energy-momentum tensor kinematic constraint lagrange multiplier rotation frame indifference principle extrastrain tensor |
| title | On nonlinear strain vectors and tensors in continuum theories of mechanics |
| title_full | On nonlinear strain vectors and tensors in continuum theories of mechanics |
| title_fullStr | On nonlinear strain vectors and tensors in continuum theories of mechanics |
| title_full_unstemmed | On nonlinear strain vectors and tensors in continuum theories of mechanics |
| title_short | On nonlinear strain vectors and tensors in continuum theories of mechanics |
| title_sort | on nonlinear strain vectors and tensors in continuum theories of mechanics |
| topic | thermoelasticity microstructure field extra field action covariance conservation law d-tensor 4-current energy-momentum tensor kinematic constraint lagrange multiplier rotation frame indifference principle extrastrain tensor |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20720/16980 |
| work_keys_str_mv | AT vladimirakovalev onnonlinearstrainvectorsandtensorsincontinuumtheoriesofmechanics AT yuriynradayev onnonlinearstrainvectorsandtensorsincontinuumtheoriesofmechanics |