Chapter 7
Features of Subsonic Stage of Contact
Interaction of Viscoelastic Half-Plane
and Absolutely Rigid Striker
Leonid Igumnov, Ekaterina A. Korovaytseva, and Dmitrii V. Tarlakovskii
Abstract Plane non-stationary contact problem concerning interaction of
symmetric absolutely rigid striker and viscoelastic half-plane at subsonic stage of
interaction is considered. The striker motion is considered vertical. Free slipping is
taken as contact condition. For half-plane boundary-normal displacement determination, corresponding Green function is constructed. The resolving equation system is
formulated, including striker motion equation, relations for the force of contact interaction, the equation connecting half-plane boundary-normal displacement with the
striker displacement and integral relation connecting half-plane boundary-normal
displacement with contact stresses. For the obtained equation system, solution
difference scheme is constructed.
Keywords Viscoelastic half-plane · Non-stationary contact problem · Laplace
transform
7.1 Introduction
Only a limited amount of works is devoted to viscoelasticity dynamic contact problems solution in accessible literature, and only static or stationary dynamic processes
of contact interaction are considered. Indeed, in the work (Belokon’ and Shekhov
1979), contact problem concerning stamp stationary motion along viscoelastic bar is
solved. In the work (Grishin 1995), asymptotic solution concerning stationary motion
of a stamp with angles along a half-plane hereditary properties of which material
are described by a power law of nonlinear creep theory is obtained. In the work
(Galin 1980), analytical solutions of the problems concerning rigid stamp pressing
viscoelastic half plane, which properties are described by exponential creep kernel,
L. Igumnov · D. V. Tarlakovskii
Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny
Novgorod, Nizhny Novgorod, Russia
E. A. Korovaytseva · D. V. Tarlakovskii (B)
Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russia
e-mail: tdvhome@mail.ru
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_7
97
Features of Subsonic Stage of Contact
Interaction of Viscoelastic Half-Plane
and Absolutely Rigid Striker
Leonid Igumnov, Ekaterina A. Korovaytseva, and Dmitrii V. Tarlakovskii
Abstract Plane non-stationary contact problem concerning interaction of
symmetric absolutely rigid striker and viscoelastic half-plane at subsonic stage of
interaction is considered. The striker motion is considered vertical. Free slipping is
taken as contact condition. For half-plane boundary-normal displacement determination, corresponding Green function is constructed. The resolving equation system is
formulated, including striker motion equation, relations for the force of contact interaction, the equation connecting half-plane boundary-normal displacement with the
striker displacement and integral relation connecting half-plane boundary-normal
displacement with contact stresses. For the obtained equation system, solution
difference scheme is constructed.
Keywords Viscoelastic half-plane · Non-stationary contact problem · Laplace
transform
7.1 Introduction
Only a limited amount of works is devoted to viscoelasticity dynamic contact problems solution in accessible literature, and only static or stationary dynamic processes
of contact interaction are considered. Indeed, in the work (Belokon’ and Shekhov
1979), contact problem concerning stamp stationary motion along viscoelastic bar is
solved. In the work (Grishin 1995), asymptotic solution concerning stationary motion
of a stamp with angles along a half-plane hereditary properties of which material
are described by a power law of nonlinear creep theory is obtained. In the work
(Galin 1980), analytical solutions of the problems concerning rigid stamp pressing
viscoelastic half plane, which properties are described by exponential creep kernel,
L. Igumnov · D. V. Tarlakovskii
Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny
Novgorod, Nizhny Novgorod, Russia
E. A. Korovaytseva · D. V. Tarlakovskii (B)
Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russia
e-mail: tdvhome@mail.ru
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_7
97