68
V. L. Kotov et al.
evaluating resistance to high-velocity penetration of rigid strikers into low-strength
soil media.
Keywords Expansion of a spherical cavity · Analytical solution · Elasticity ·
Plasticity · Mohr-Coulomb-Tresca’s plasticity condition
5.1 Introduction
A special role in the high-velocity impact theory is given to determine parameters of
contact interaction of bodies. Practice shows (Ben-Dor et al. 2005; Veldanov et al.
2011; Omidvar et al. 2012, 2014, 2015) that a good approximation of the pressure on
the contact surface of a rigid striker with a resisting medium is a solution of the spherical or cylindrical cavity expansion problem. To determine stress and rate fields in the
plastic deformation region adjoining the cavity, an effective algorithm of numerical
analysis was developed (Forrestal and Longcope 1982; Forrestal and Luk 1992), that
makes it possible to obtain a solution of the problem with an accuracy sufficient for its
practical application. Numerical analyses of the spherical cavity expansion problem
and their application to evaluating contact stresses and forces resisting penetration
of rigid bodies into soil, concrete, and metal are given in (Forrestal and Longcope
1982; Forrestal and Luk 1992; Shi et al. 2014, 2015; Kong et al. 2017; Sun et al.
2017; Kotov 2008, 2019). Papers (Kotov et al. 2011; Linnik et al. 2012) present an
analytical solution of the above problem, based on the assumption of incompressibility of the medium behind the shockwave front. Dynamic compressibility of a
medium is characterized by a shock adiabat, and shear resistance is defined by the
Mohr-Coulomb plasticity condition. Based on the proposed analytical solution, a
methodology for evaluating forces resisting penetration of a rigid body into soft soil
was developed (Kotov et al. 2013). Relations for the maximal value of the force
resisting penetration of a rigid sphere and a conic-nosed striker into dry and watersaturated sands were derived (Bragov et al. 2018). Comparison of the analytical,
numerical, and experimental results of determining resistance to penetration testifies
to their good qualitative and quantitative agreement in the impact velocity range of
50–400 m/s.
On contact interactions via generalized continua framework, one can read in
(dell’Isola et al. 2012, 2016). More information about analysis of saturated soil and
porous media can be found in (dell’Isola and Hutter 1998, 1999; dell’Isola et al. 2000).
Some of these works shares the same framework of generalized continua (Abali et al.
2017; Auffray et al. 2013; Alibert et al. 2003; dell’Isola et al. 2015, 2017; Rahali et al.
2015), nowadays, widely used on designing new artificial microstructured composites whose name is metamaterials (Barchiesi et al. 2018; Del Vescovo and Giorgio
2014; dell’Isola et al. 2019; Placidi et al. 2016, 2017).
Nevertheless, analytical solutions of this problem or approximations of the results
of numerical solutions are still of interest to numerous applications of impact
V. L. Kotov et al.
evaluating resistance to high-velocity penetration of rigid strikers into low-strength
soil media.
Keywords Expansion of a spherical cavity · Analytical solution · Elasticity ·
Plasticity · Mohr-Coulomb-Tresca’s plasticity condition
5.1 Introduction
A special role in the high-velocity impact theory is given to determine parameters of
contact interaction of bodies. Practice shows (Ben-Dor et al. 2005; Veldanov et al.
2011; Omidvar et al. 2012, 2014, 2015) that a good approximation of the pressure on
the contact surface of a rigid striker with a resisting medium is a solution of the spherical or cylindrical cavity expansion problem. To determine stress and rate fields in the
plastic deformation region adjoining the cavity, an effective algorithm of numerical
analysis was developed (Forrestal and Longcope 1982; Forrestal and Luk 1992), that
makes it possible to obtain a solution of the problem with an accuracy sufficient for its
practical application. Numerical analyses of the spherical cavity expansion problem
and their application to evaluating contact stresses and forces resisting penetration
of rigid bodies into soil, concrete, and metal are given in (Forrestal and Longcope
1982; Forrestal and Luk 1992; Shi et al. 2014, 2015; Kong et al. 2017; Sun et al.
2017; Kotov 2008, 2019). Papers (Kotov et al. 2011; Linnik et al. 2012) present an
analytical solution of the above problem, based on the assumption of incompressibility of the medium behind the shockwave front. Dynamic compressibility of a
medium is characterized by a shock adiabat, and shear resistance is defined by the
Mohr-Coulomb plasticity condition. Based on the proposed analytical solution, a
methodology for evaluating forces resisting penetration of a rigid body into soft soil
was developed (Kotov et al. 2013). Relations for the maximal value of the force
resisting penetration of a rigid sphere and a conic-nosed striker into dry and watersaturated sands were derived (Bragov et al. 2018). Comparison of the analytical,
numerical, and experimental results of determining resistance to penetration testifies
to their good qualitative and quantitative agreement in the impact velocity range of
50–400 m/s.
On contact interactions via generalized continua framework, one can read in
(dell’Isola et al. 2012, 2016). More information about analysis of saturated soil and
porous media can be found in (dell’Isola and Hutter 1998, 1999; dell’Isola et al. 2000).
Some of these works shares the same framework of generalized continua (Abali et al.
2017; Auffray et al. 2013; Alibert et al. 2003; dell’Isola et al. 2015, 2017; Rahali et al.
2015), nowadays, widely used on designing new artificial microstructured composites whose name is metamaterials (Barchiesi et al. 2018; Del Vescovo and Giorgio
2014; dell’Isola et al. 2019; Placidi et al. 2016, 2017).
Nevertheless, analytical solutions of this problem or approximations of the results
of numerical solutions are still of interest to numerous applications of impact