Chapter 4
Finite Element Method Study
of the Protection Damping Elements
Dynamic Deformation
Anastasia V. Demareva, Aleksandr I. Kibets, Maria V. Skobeeva,
Oleg G. Savichin, and Aleksandr F. Lyakhov
Abstract The problem of dynamic deformation of structures damping elements
made of metal hollow spheres (MHS) filler is considered. MHS filler is a porous
material obtained by joining homogeneous metal hollow spheres. The MHS filler is
modeled by a continually homogeneous, orthotropic, physically nonlinear medium.
The solution of the determining equation system is based on the finite element
method moment scheme and the explicit finite-difference time integration “cross”
type scheme. The problem of stability loss and supercritical behavior of a titanium spherical shell under compression loading between two non-deformable plates
approaching with a constant velocity is considered. According to the problem numerical solution results, the dependence of the contact force on the plates movement was
built, on the basis of which the deformation diagram and the parameters of the MHS
filler mathematical model of the were determined. The problem of plate falling on
a spherical shells’ set located on a fixed base is solved using the obtained data. As
it is shown by the calculation results analysis, the developed computational model
allows to determine with acceptable accuracy the integral deformation parameters
of the MHS filler (contact forces, displacements, displacement velocities) and to
evaluate its damping properties.
Keywords Damper · Porous filler · Impact · Finite element method
4.1 Introduction
Porous metals are so-called functional materials, which are used because of their
special properties, among which can be noted the low density and the ability to
effectively absorb impact energy (Thornton and Magee 1975; Davies and Zhen 1983;
Baumeister and Banhart 1998; Gibson and Ashby 1997; Banhart 2001; Ramchandra
et al. 2003). This combination of characteristics is due to the fact that porous metals
A. V. Demareva · A. I. Kibets (B) · M. V. Skobeeva · O. G. Savichin · A. F. Lyakhov
Research Institute for Mechanics, National Research Lobachevsky State University of Niznhy
Novgorod, Gagarin ave., 23, 603950 Nizhny Novgorod, Russia
e-mail: kibec@mech.unn.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_4
57
Finite Element Method Study
of the Protection Damping Elements
Dynamic Deformation
Anastasia V. Demareva, Aleksandr I. Kibets, Maria V. Skobeeva,
Oleg G. Savichin, and Aleksandr F. Lyakhov
Abstract The problem of dynamic deformation of structures damping elements
made of metal hollow spheres (MHS) filler is considered. MHS filler is a porous
material obtained by joining homogeneous metal hollow spheres. The MHS filler is
modeled by a continually homogeneous, orthotropic, physically nonlinear medium.
The solution of the determining equation system is based on the finite element
method moment scheme and the explicit finite-difference time integration “cross”
type scheme. The problem of stability loss and supercritical behavior of a titanium spherical shell under compression loading between two non-deformable plates
approaching with a constant velocity is considered. According to the problem numerical solution results, the dependence of the contact force on the plates movement was
built, on the basis of which the deformation diagram and the parameters of the MHS
filler mathematical model of the were determined. The problem of plate falling on
a spherical shells’ set located on a fixed base is solved using the obtained data. As
it is shown by the calculation results analysis, the developed computational model
allows to determine with acceptable accuracy the integral deformation parameters
of the MHS filler (contact forces, displacements, displacement velocities) and to
evaluate its damping properties.
Keywords Damper · Porous filler · Impact · Finite element method
4.1 Introduction
Porous metals are so-called functional materials, which are used because of their
special properties, among which can be noted the low density and the ability to
effectively absorb impact energy (Thornton and Magee 1975; Davies and Zhen 1983;
Baumeister and Banhart 1998; Gibson and Ashby 1997; Banhart 2001; Ramchandra
et al. 2003). This combination of characteristics is due to the fact that porous metals
A. V. Demareva · A. I. Kibets (B) · M. V. Skobeeva · O. G. Savichin · A. F. Lyakhov
Research Institute for Mechanics, National Research Lobachevsky State University of Niznhy
Novgorod, Gagarin ave., 23, 603950 Nizhny Novgorod, Russia
e-mail: kibec@mech.unn.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_4
57