Deformation and Destruction of Materials and Structures Under Quasi-static and Impulse Loading

Dielectric elastomers are smart materials that are essential components in soft systems and structures. The core element of a dielectric elastomer is soft matter, which is mainly rubber-like and elastomeric. These soft materials show a nonlinear behaviour and have a nonlinear strain–stress curve. The best candidates for modelling the nonlinear behaviour of such materials are hyperelastic strain energy functions. Hyperelastic functions have been extensively used for modelling dielectric elastomer smart structures. This review paper introduces hyperelastic constitutive laws for modelling dielectric elastomers. For this purpose, first, a general scheme of hyperelastic models is expressed. Then, some well-known hyperelastic models are introduced. Finally, we review in detail the utilized hyperelastic models for different configurations of dielectric elastomers. Possible future works in this field are outlined eventually.

The article is devoted to the analysis of the behavior of various FCC metals under shock loading with irregularly shaped projectiles at speeds of 1.5–2.0 km/s.

The integro-differential approach, which is part of the universal method of solving boundary problems proposed by the authors, for the first time builds an exact solution of the boundary problem in a quarter plane for a system of Lame equations under the assumption of setting stress vectors at the boundary. The solution of a vector, two-component, boundary value problem is constructed decomposed by solutions of one-component boundary value problems. Previously, this boundary value problem was considered in a simpler formulation, assuming that displacement vectors were assigned at the boundary. It was suggested that the construction of a solution for the case of stresses is difficult. It is shown that the application of the integro-differential method practically does not complicate the solution of boundary problems with complicated boundary conditions. The research presented in the article is important in studying the behavior of solutions to boundary value problems of complex rheology described by systems of partial differential equations using decompositions by solutions of individual equations. It is proposed to develop this method for studying the behavior of multicomponent nanomaterials in order to build models of their self-organization and self-assembly. They can be used to study their physical and strength properties, as well as the possibility of controlling their parameters.

The paper presents the results of the development and testing of experimental schemes that allow us to study the characteristics of the interlayer strength of layered composite materials. The schemes are based on the technique of measuring bars. To determine the interlayer strength at separation, a modification of the Kolsky method for direct tension is used. A sample of a special shape is glued to adapters having threaded parts, by means of which the sample is installed in a split measuring bar. To determine the mechanical characteristics of composite materials during interlayer shear, three experimental schemes were proposed and tested: dynamic three-point bending of a short beam, dynamic compression of plate samples with incisions and dynamic extrusion of the middle part of the samples in the form of parallelepipeds. Loading of samples and registration of their deformation processes were carried out using the technique of measuring bars. A numerical simulation was carried out to check the dynamic equilibrium condition of the sample in an experiment on the dynamic bending of a short beam. The schemes were tested on samples of a layered composite material with a polymer matrix reinforced with carbon fabric. The results of a comparative analysis of the schemes for determining shear strength showed that the most preferable is the scheme of extrusion of the middle part of the parallelepiped, since, unlike the bending of the beam, it allows you to vary and control the loading conditions, and unlike the testing of incised samples, it is symmetrical, which eliminates the appearance of bending moments in the sample.

The article describes the constitutive model based on the applied inelasticity theory—one of the combined hardening flow theories. The authors identify the material functions closing the applied inelasticity theory and formulate the fundamental experiment. The life of structural materials in the case of non-isothermal cyclic loading is predicted by analyzing the durability of the air-cell diesel's edge and the uncooled conical nozzle tip in the case of thermal cycling. Life estimates based on the applied inelasticity theory are compared to experimental data and conservative life estimation methods. The authors also consider examples of estimating the life of a durable power generation system's structure. Loading modes resulting in considerable life reduction are described.

Experimental analysis of 12X18H10T stainless steel specimens subjected to strain-controlled cyclic loading that comprises sequential monotonic and cyclic loading under uniaxial tension-compression and standard temperature is used to identify some features and dissimilarities of isotropic and anisotropic hardening processes that occur during monotonic and cyclic loading. In order to describe these features in terms of the plasticity theory (the Bondar model), which can be classified as a combined-hardening flow theory, plastic-strain redirection criterion and the memory surface concept are introduced in the plastic-strain tensor space so as to separate monotonic and cyclic strain. Evolution equations for isotropic and anisotropic hardening processes are derived to describe the monotonic-to-cyclic and cyclic-to-monotonic evolutions in transients. The basic experiment used to determine the material functions consists of three stages: cyclic loading, monotonic loading, and subsequent cyclic loading until fracture. The results of the basic experiment are fundamental to the proposed method for identifying the material functions. Basic-experiment results and the identification method are used to identify the room-temperature material functions of 12X18H10T stainless steel. The paper compares the computational analysis and the experimental analysis of stainless steel subjected to a strain-controlled fatigue test (loading) in five stages: cyclic, monotonic, cyclic, monotonic, and cyclic loading until fracture. It further compares the computational and experimental kinetics of the stress-strain state throughout the deformation process. Changes in the amplitude and mean cycle stress during the cyclic stress stages are subsequently analyzed. These stages are characterized by hysteresis loop stabilization. Computational and experimental results fit reliably. The theory adequately describes the processes of how the kinetics, the amplitudes, and the mean cycle stress alter when subjecting a specimen to strain-controlled loading, which enables a more adequate description of stress-controlled loading, especially when loading is non-stationary and non-symmetric.

The paper presents the results of an experimental study, as well as numerical modeling of deformation and fracture of pine beams under dynamic loading. Experiments are carried out on an installation implementing a dynamic three-point bending scheme. To create a load and register the forces acting on the beams during loading, the technique of measuring bars is used. Deflections are calculated according to the Kolsky formulas based on data from measuring bars, as well as by direct measurement using the digital image correlation method based on high-speed video recording. A procedure for determining the ultimate strain of pine in perpendicular to the fiber direction is proposed according to experiments on three-point bending of beams. Modeling of dynamic three-point bending of beams in LS-DYNA is carried out. To describe the behavior of pine, the MAT_WOOD material model is used. The use in the model of the value of ultimate strain determined during the experimental study allowed us to obtain a good coincidence of the crack formation time in full-scale and numerical experiments.

An experimental study of the dynamic properties of three types of fiber-reinforced concrete under dynamic uniaxial compression relative to the original fine-grained concrete was carried out. Three types of fiber-reinforced concrete were produced: with polymer fiber, steel fiber, and with a combination of two types of fiber. Static and dynamic tests were carried out. Dynamic compression tests were carried out using the Kolsky method at strain rates from 10² to 10³ s⁻¹. The tests were carried out using a FASTCAM Mini UX100 high-speed camera. The paper presents the compositions of the studied materials, test parameters, as well as a comparative analysis of the data obtained. The introduction of a reinforcing fiber into the original fine-grained concrete increased the dynamic strength of the material. The highest strength under dynamic uniaxial compression was shown by fiber-reinforced concrete with steel fiber. The dependences obtained demonstrate that the maximum breaking stresses achieved in the experiments grow linearly with an increase in the strain rate, as do the corresponding limiting strains. The time before the onset of fracture decreases with increasing strain rate according to a power law.

We consider the unsteady problem of elastic diffusion deformations of a rectangular orthotropic plate considering the diffusion fluxes relaxation. External perturbations lay in the plate plane and allow us to use a two-dimensional elastic diffusion model for continuum as a mathematical model. The solution is convolutions of Green’s functions with functions defining the boundary perturbations. Green’s functions finding method is based on the Laplace transform and double trigonometric Fourier series. We are using residues and tables of operational calculus for transition to the originals of Green’s functions. The interaction effects of mechanical and diffusion fields for a three-component material are calculated using the example of a rectangular plate under tensile forces. We have also investigated the influence of relaxation processes on mass transfer kinetics. Calculation results are in analytical and graphical forms.

The research is aimed at selecting an adequate design model of the structure in the tasks of assessing the strength of underground pipelines adjacent to the structure. In a series of computational experiments, the influence of the structure on the soil base under static and dynamic influences was studied. To analyze the influence of the structure’s detail on the seismic response and dynamic deformation of the foundation, three design models of a structure are considered. Invariants of the calculation experiments were the mass and the center of mass of the structure, the shape of the footprint and the overall dimensions of structures, the dynamic influence, and the elastic constants for all materials. It is established that the simplest model of a structure—a homogeneous array—shows the greatest differences in the static effect on the soil base during settlement and the dynamic effect from compression and shear waves. It is shown, some degree of detail of the structure should be considered when calculating seismic impacts of underground pipelines adjacent to the structure.

The initial and boundary value problem describing the nonstationary dynamics of a homogeneous thin anisotropic elastic moment shell is constructed. The model takes into account the material anisotropy, free rotation, independent normal unit vector rotation, and its transverse normal strain. The functional and the physical law for the shell are constructed using the Hamilton functional, physical relations for a three-dimensional body described by the Cosserat model, the hypothesis of direct normal for the displacement field, and an analogous supposition for the rotation vector. The boundary value problem for the elastic moment shell is obtained as a necessary condition for an extremum of this functional. Various versions of natural boundary conditions are considered. It is pointed out that transition to an isotropic material only simplifies the physical relations without reducing the number of unknowns. The latter can be realized only at the expense of introducing some additional hypotheses concerning the displacement and rotation fields or considering special geometries of the middle surface.

This paper is devoted to the study of adhesive force influence on transient deformation of a membrane interacted with rigid indenter. The research is carried out by splitting the process of interaction into two phases. The phases are analyzed sequentially. The first phase of interaction includes time period without mechanical contact. After the mechanical contact takes place, the second phase begins: it includes the influence of contact pressure as adhesive forces. In this study, we considered both phases of transient interaction for an infinite membrane with a rigid indenter accounting for adhesive forces. The original numerical–analytical algorithm for determining the contact stresses under the indenter is proposed. The graphical results for the first phase of interaction are shown.

On the example of a plane problem of the mechanics of a beam with finite length fastening areas located on one of the front-face surfaces, it is shown that in the study of deformation processes with additional account of the fixed area compliance requires the introduction of the concept of the stress–strain state type transformation at the transition across the boundary from an unfastened to a fastened section. Appropriate mathematical models are also required to describe such a phenomenon. Within the framework of the classical Kirchhoff–Love model it is impossible to take into account the presence of such fixed sections. At the same time, within the framework of the simplest S.P. Timoshenko shear model, this transformation is possible if the section is fixed only on one of the front-face surfaces. The kinematic and force conditions for coupling of fastened and unfastened beam sections have been formulated. Based on the derived relations, an exact analytical solution to the problem of static bending of a cantilevered beam under the action of a constant surface load has been found. This solution is in good agreement with the results obtained by modeling of a beam using rectangular finite elements in a plane stress state, as well as using the ANSYS software package based on the equations of a plane problem of elasticity theory. An exact analytical solution has been obtained for the problem of transverse bending vibrations of a flat beam with two cantilevered parts and a finite length section between them under vibration loading by a transverse force acting on one of the unfastened section.

In the problems of damping vibration, the question often arises on the practical implementation of damping actuators. The damping efficiency is considered for a console beam described by a linear viscosity Bernoulli–Euler model. The article presents the methods of damping transverse vibrations implemented by a dynamic damper from a piezoelectric layer distributed symmetrically along the axis of symmetry of the beam. Piezoelectric layers with a triangular and rectangular shape of electrode plates are considered, which affect the nature of mechanical stresses upon application of electrical voltage. The electrode plates are thin layers made of nickel or silver several microns thick and located normal to the polarization axis, that is, along the length of the piezoceramic plate. The control of the piezoelectric layers is realized by changing the potential difference between the electrode plates, while the piezoelectric material uncoated by the electrode plate on both sides is useless to use as an active material. In turn, mathematical models of the effect of piezoelectric elements on the cantilever beam are derived from the Hamilton principle. The Pareto-efficiency of quenching by piezoelectric plates with different electrode shapes is evaluated relative to two criteria: the level of control voltage and the maximum deflection of the beam. Also, for a more general analysis, the quenching efficiency is also given for a beam with a piezoelectric plate applied along the entire length and an electrode layer. In addition to Pareto sets, efficiency is also considered in a more applied and particular example—time history. It is worth noting that the synthesis of Pareto-optimal controls is based on the Germeier convolution, and the search for optimal feedback is based on the application of the theory of linear matrix inequalities and effective algorithms for solving them.

In this paper, the dynamic response of a poroelastic material to an impulse load has been analytically investigated. The poroelastic material is represented by a three-phase elastically deformable partially saturated porous medium, one phase is a deformable solid skeleton, and the other two are fluid and gas that fill the pore space. The mathematical formulation is a system of equations including the laws of conservation of mass for fluid phases and a solid frame, an equilibrium equation for a three-phase continuum, a constitutive relation for a three-phase medium, a relation for determining the stress tensor, and Darcy’s law of filtration. The solution of the equations of motion of a one-dimensional poroelastic medium is written in terms of the variables of the displacement of a solid skeleton, and the pore pressure of fluid and gas in the Laplace domain. The time domain solution is calculated using the numerical inversion stepped method of the Laplace transform. The effect of material parameters on the dynamic response is analyzed in a series of numerical experiments. The results of this study may help to gain better insight into one-dimensional wave propagation in unsaturated soils.

A non-stationary dynamic problem of linear viscoelasticity for a piecewise homogeneous body is considered for the case when the disturbed domain is finite. The interrelation between such a problem and the spectral problem of piecewise homogeneous body free oscillations is established. The structure of the eigenvalues set of the spectral problem is investigated. A method of searching for eigenvalues near the limit points of the spectral set is proposed. The integral Laplace transform in time is applied to the non-stationary dynamic problem for a linear viscoelastic piecewise homogeneous structure. For the case when each of the hereditary kernels is a finite sum of exponentials, the solution in the originals is presented as a series of residues at the points of the spectrum. Thus, the constructing of the non-stationary solution is reduced to the search for the elements of the spectral set. As an example, the solution to the plane axisymmetric problem of transient longitudinal waves’ propagation in a cross-section of a hollow infinitely long cylinder consisting of two coaxial elastic layers and a viscoelastic layer between them is constructed and discussed. As a result, it becomes possible to investigate and to reveal the influence of the piecewise inhomogeneity on the non-stationary waves’ propagation in a cylinder with viscoelastic and elastic layers.

A study of the mechanical properties of a thin titanium nitride (TiN) film deposited using the magnetron sputtering on a silicon surface has been carried out. The values of indentation hardness and reduced Young’s modulus were evaluated using nanoindentation in a course of a series of experiments with increasing indentation load. The microgeometrical characteristics of the film surface (average roughness, maximum roughness height) were determined from the results of atomic force microscopy. The chemical composition and thickness of the film were estimated using scanning electron microscopy.