L. A. Igumnov

High-rate deformation and fracture of steel 09G2S

The results of experimental and theoretical studies of steel 09G2S deformation and fracture laws in a wide range of strain rates and temperature variations are given. The dynamic deformation curves and the ultimate characteristics of plasticity in high-rate strain were determined by the Kolsky method in compression, extension, and shear tests. The elastoplastic properties and spall strength were studied by using the gaseous gun of calibre 57 mm and the interferometer VISAR according to the plane-wave experiment technique. The data obtained by the Kolsky method were used to determine the parameters of the Johnson-Cook model which, in the framework of the theory of flow, describes how the yield surface radius depends on the strain, strain rate, and temperature.

Multiscale Simulation of Porous Quasi-Brittle Ceramics Fracture

Multiscale computer simulation approach has been applied to research mechanisms of failure in ceramic nanostructured ceramics under dynamic loading. The obtained experimental and theoretical data indicate quasi-brittle fracture of nanostructured ZrB2 ceramics under dynamic compression and tension. Damage nucleation and accumulation in quasi brittle nanostructured ceramics were simulated under impact loadings. Fracture of nanostructured ultra-high temperature ceramics under pulse and shock-wave loadings is provided by fast processes of intercrystalline brittle fracture and relatively slow processes of quasi-brittle failure via growth and coalescence of opened microcracks. For nanostructures ZrB2 ceramics with porosity of 7 %, the compressive strength at strain rate of 1800 s-1 is equal to 2440±50 MPa, the tensile strength at strain rate of 300 s-1 is equal to 155±20 MPa.

Numerical-analytic investigation of the dynamics of viscoelastic and porous elastic bodies

This paper presents the results of mathematical and discrete modeling of linear dynamics problems for three-dimensional viscoelastic and porous elastic bodies. The employed methods and approaches are based on formulating boundary integral equations solved using boundary elements. The model of a standard viscoelastic body is employed as the viscoelastic model. The properties of porous elastic materials are described using the full Biot model with four basic functions. Examples of numerical solutions of the problems are compared with known results of solutions.

Boundary Element Method in Three Dimensional Transient Poroviscoelastic Problems

The present paper is dedicated to dynamic behavior of poroelastic and poroviscoelastic solids. Poroviscoelastic formulation is based on Biot’s theory of poroelasticity in combination with elastic-viscoelastic correspondence principle. The correspondence principle is applied to describe viscoelastic properties of a skeleton of the porous material. Classical models of viscoelasticity are employed such as Kelvin-Voigt model standard linear solid model and model with weakly singular kernel. The problem is treated in Laplace domain. Direct boundary integral equation system is used to perform a solution. Mixed boundary element discretization is introduced to obtain discrete analogues. Time-step method based on Runge-Kutte nodes of numerical inversion of Laplace transform is applied to perform solution in time domain. A problem of Heaviside-type vertical load acting on a slab bonded on a poroviscoelastic halfspace and a problem of poroviscoelastic cube with cavity subjected to a normal internal pressure are considered. The comparison of dynamic responses when poroviscoelastic material is described by different viscoelactic models is presented. Viscosity parameter influence on dynamic responses of displacements and pore pressure is studied. Surface waves on poroviscoelastic halfspace are modelled with the help of boundary element method.

Dynamic deformation of soft soil media: Experimental studies and mathematical modeling

A complex experimental-theoretical approach to studying the problem of high-rate strain of soft soil media is presented. This approach combines the following contemporary methods of dynamical tests: the modified Hopkinson-Kolsky method applied tomedium specimens contained in holders and the method of plane wave shock experiments. The following dynamic characteristics of sand soils are obtained: shock adiabatic curves, bulk compressibility curves, and shear resistance curves. The obtained experimental data are used to study the high-rate strain process in the system of a split pressure bar, and the constitutive relations of Grigoryan’s mathematical model of soft soil medium are verified by comparing the results of computational and natural test experiments of impact and penetration.

Numerically Analytical Modeling the Dynamics of a Prismatic Body of Two- and Three-Component Materials

Wave propagation in fully and partially saturated porous media is studied, using the example of the problem of two-component and three-component media having, respectively, four and five base functions for describing the wave process. The arising system of partial differential equations and the boundary conditions are written in terms of Laplace transforms for a time variable. To construct the original of the analytical solution, a stepped method of numerically inverting Laplace transform is used. Computations were done for various values of the saturation coefficients. To solve the problem of the effect of an axial force in the form of Heaviside function in time upon the end of a prismatic poroelastic cantilever beam in 3-D formulation, the boundary-element method is used. Boundary integral equations of the direct approach are written in explicit time. The boundary-element model is constructed using a time-step procedure . Along boundary elements, correlated approximation is applied. Discrete analogues are obtained by applying the collocation method to a regularized boundary integral equation. A specific feature of a wave process in saturated porous media is the presence of three types of waves: in contrast with the elastic case, there appears a slow wave, which can considerably change the wave picture. To demonstrate the effect of a slow wave arising, variation of the permeability coefficient is used. The appearance of the slow wave effect is observed on the pore pressure curves: for the pore pressure of a liquid filling two peaks of the amplitude are observed.

A Three-Dimensional Boundary Element Approach for Transient Anisotropic Viscoelastic Problems

This paper presents a three-dimensional direct boundary element approach for solving transient problems of linear anisotropic elasticity and viscoelasticity. In order to take advantage of the correspondence principle between viscoelasticity and elasticity the formulation is given in the Laplace domain. Anisotropic viscoelastic fundamental solutions are obtained using the correspondence principle and anisotropic elastic Green’s functions. The standard linear solid model is used to represent the mechanical behavior of viscoelastic material. Solution in time domain is calculated via numerical inversion by modified Durbin’s method. Numerical example is provided to validate the proposed boundary element formulation.

One-Dimensional Wave Propagation in a Three Phase Poroelastic Column

In the present paper, the solution of a finite one-dimensional column with Neumann and Dirichlet boundary conditions are deduced based on the theory of mixture. The solution is obtained in the Laplace domain and the time-step method is chosen to obtain the time domain solution. The material data of Massillion sandstone are used for calculations. The column response to the dynamic loading is examined in terms of displacement, pore water pressure, and pore air pressure.

Experimental study and mathematical modeling of the behavior of St.3, 20Kh13, and 08Kh18N10T steels in wide ranges of strain rates and temperatures

Results of an experimental study of the behavior of St.3, 20Kh13, and 08Kh18N10T steels under static and dynamic loading are reported. The influence of the strain rate and temperature on characteristics of strength and plasticity is studied. Based on the data obtained, the parameters of the Johnson–Cook model are determined. This model is used in commercial software to describe the yield surface radius as a function of loading parameters. The adequacy of the identified model is verified in a series of special test experiments.

Impact Compressibility of a Poly(ethylene glycol)Based Nanocomposite Fluid

The behavior of a poly(ethylene glycol)-based nanocomposite shear thickening fluid (STF) under impact loading conditions has been experimentally studied using the Kolsky method and related techniques. The dependence of the pressure in the STF on the volume strain magnitude has been determined. It is established that the radial and axial components of the stress tensor almost coincide, which shows that the material behaves like an incompressible liquid. The character of the stress-strain curves (hysteresis) indicates that the STF is characterized by some energy dissipation in the load-unload cycle.