Air Blast Wave Research Articles

Histopathological and ultrastructural changes in the rats brain after air shock wave impact

The using of explosive substances and devices can lead to brain injuries, the diagnosis of which requires the determination of primary biomarkers. Therefore, the aim was to establish and study histopathological and ultrastructural changes in the rats brain after exposure to an air blast wave. The study was carried out on 18 male Wistar rats, which were randomly divided into two groups: sham (n=9) and experimental (n=9). The animals of the experimental group were anesthetized with halothane and gently fixed in a horizontal position on the abdomen with the front part of the rat's muzzle at a distance of 5 cm from the device opening and subjected to an excess pressure of 26-36 kPa. Animals of both groups were decapitated, brains were removed, fixed, histopathological and ultrastructural analyzes were conducted using standard methods. Intergroup differences were assessed by Mann-Whitney U-test. Light microscopy revealed primary lesions in the form of small focal, multifocal hemorrhages, cerebral vessel ruptures and microscopic ruptures of the brain substance. In almost all brain samples, there is a significant saturation of the venous vessels with the presence of erythrocyte stasis. Violation of the blood-brain barrier, the presence of edema of the perivascular space, and petechial hemorrhages in the neuropil were registered ultrastructurally. Based on the study results, a morphological algorithm for assessing primary histostructural intracranial brain injuries and their consequences after exposure to an air shock wave was proposed. The injuries were found to be caused by the direct traumatic effect of the air shock wave. In the acute post-traumatic period, histopathological and ultrastructural changes in the brain can manifest as changes in neurons and in the blood-brain barrier and be accompanied by perivascular multifocal small-focal hemorrhages, neuropil ruptures, edema of pericellular and perivascular spaces, which together can be considered as biomarkers of primary traumatic changes after exposure to an air shock wave.

High-precision measurement of refractive index in explosive-driven air blast waves for density and pressure determination

Air refractive index alteration is an important research technique used to examine blast density and pressure. However, precise time-course measurements of refractive index changes at a fixed point caused by air blast waves are challenging due to the necessity for high precision and noise immunity. This study proposes a dual-probe, dual-frequency fiber-optic displacement interferometer that achieves nanometer-level accuracy and can tolerate light intensity fluctuations and transmission-fiber interference. The specially designed sensor enables the measurement of refractive index at a fixed point resulting from explosive-driven air blast waves, further allowing for obtaining the pressure and density information.

Modeling of Non-Isothermal Viscoelastic-Viscoplastic Deformation of Bending Reinforced Plates

A model of non-isothermal viscoelastic-viscoplastic deformation of multidirectionally reinforced flexible plates has been developed. The viscoplastic deformation of isotropic materials of the composition is described by the relations of the flow theory with isotropic hardening, which take into account the dependences of the loading functions on temperature and strain rate intensity. The viscoelastic behavior of the composition components is described by the equations of the Maxwell–Boltzmann model. The weakened resistance of reinforced plates to transverse shifts is modeled by the Ambartsumian bending theory relations, and the geometric nonlinearity is modeled in the Karman approximation. The connection between the thermophysical and mechanical components of the problem of inelastic dynamic deformation of reinforced plates is taken into account. The temperature over the thickness of structures is approximated by a 7th order polynomial. The numerical solution of the formulated nonlinear two-dimensional problem is constructed using an explicit scheme of time steps. The viscoelastic-viscoplastic dynamic behavior of a relatively thin glass-plastic plate is studied with and without allowance for the thermal response in it. The structure is loaded transversely with an air blast wave. It is shown that the failure to take into account the thermal response in a fiberglass plate can significantly distort the calculated fields of residual deformations of the components of its composition, despite the fact that the maximum heating of such a structure does not exceed 10°C. Viscoelastic-plastic calculations, when the sensitivity of the composite materials to the rate of their deformation can be neglected, can reasonably be carried out without taking into account the thermal response of the composite plate, if there are no external heat sources of non-mechanical origin.

Modeling of Dynamic Thermo-Elastic-Viscous-Plastic Deformation of Flexible Shallow Reinforced Shells

A mathematical model of non-isothermal elastic-viscous-plastic deformation of flexible shallow shells with multidirectional reinforcement structures has been developed. Wave processes and weak resistance to transverse shear in curved panels are modeled in terms of Ambartsumian’s bending theory. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The composition components are assumed to be isotropic materials, and their plasticity is described by the flow theory with a loading function depending on the strain rate and temperature. The connectedness of the thermomechanical problem under dynamic loading of composite shallow shells is taken into account. In the transverse direction of constructions, the temperature is approximated by a 7th order polynomial. The formulated two-dimensional nonlinear initial-boundary value problem is solved using an explicit numerical scheme of time steps. The thermo-elastic-visco-plastic and thermo-elastic-plastic behavior of fiberglass and metal-composite shallow shells orthogonally reinforced in two tangential directions, loaded in the transverse direction by an air blast wave, has been studied. It is shown that flexible curved fiberglass panels at certain points can additionally heat up by 14…27°C, and similar metal-composite conctructions – by 70°С or more. In this case, peak temperature values are kept at short-term intervals – on the order of fractions of 1 ms. It is shown that, unlike flexible plates, similar shallow shells (with the same reinforcement structure and the same characteristic dimensions) under dynamic loading in the transverse direction must be calculated not only taking into account the dependence of the plastic properties of the composition components on their strain rate, but also taking into account thermal response in such thin-walled constructions. A more intense inelastic deformation of curved composite panels is observed when they are loaded from the side of the convex front surface.

Blasting-induced seismic impact on protected objects on ground surface at Zapolyarny Mine of Medvezhyi Ruchei LLC

In open-pit mineral mining with drilling and blasting, a significant part of buildings and structures, as a rule, suffer from the blasting-induced seismic impact. Some production facilities under consideration, due to their long service life, have defects, which makes them less resistant to the blasting-induced seismic impact. In such cases, assessment of the blasting-induced seismic impact requires experimental investigation to be performed. The main and common characteristic in the assessment of the seismic impact induced by the air blast wave that can cause damage to natural and engineering structures is the peak particle velocities measured in the area of these structures. The approach proposed by M.A. Sadovsky was applied to determining PPV due to the blasting-induced seismic impact. The scope of this work included the research of seismic wave propagation from explosions in an open pit at Zapolyarny Mine of Medvezhyi Ruchei LLC. ZETLAB seismographs were used to study the effect of the seismic explosion waves on the protected facilities. The research was performed for the upper rock mass strata composed of basalts. The tests were carried out to determine physical and mechanical properties of basalts. The measurement profiles of blasting-induced seismic waves were oriented in the northern, western and northwestern directions. As a result of the measurements and experimental data processing using the regression analysis in the range of reduced distances from 11 m/kg1/3 up to 1100 m/kg1/3, the relation of the reduced distance and PPV was obtained. The relation makes it possible to determine the permissible weight of a single charge to ensure safety of the protected structures.

Spreading Effect of Enhanced Blast in Explosives and Propellants

We performed tests on one of our propellants to determine its TNT equivalence. In such tests we detonate a charge of explosive at one end of a propellant cylindrical sample. We use two types of diagnostics: 1) to determine the propellant energy release rate, we wrap it with a thin aluminum shell, and measure the radial velocity of the shell along the propellant sample with velocity interferometers (PDV); and 2) we use commercial blast gauges at a distance of about 10m from the test sample, to determine the blast effect of the propellant (after deducting the blast effect of the driving explosive). We expected the two types of diagnostics to agree with one another, but this has not been the case. From the velocity gauges we see that only the part of the propellant which is near the explosive has fully reacted, and that the extent of this part depends on the size and configuration of the driving explosive. But from the blast diagnostics it seems, that as if the whole propellant has reacted. We’ve seen some sporadic indications in the literature to such an enhanced blast effect from propellants [1-5]. We refer here to such an enhanced blast effect as a spreading effect. We claim, that when a reacting propellant (or explosive) is spread out in space (without changing its total energy release upon reacting), the blast effect at a given distance is enhanced substantially compared to the same energy yield without spreading. In our tests, the relative amount of reacted propellant decreases substantially with distance from the initiating explosive, but because it does not react in a continuous fashion, there is a spreading effect, that enhances the level of air blast substantially. To demonstrate the action of the spreading effect, we make 1D simulations of outgoing detonations of an HB (H=HMX, B=Binder) explosive in spherical symmetry. For different runs we dilute the explosive with the binder to various extents, from W=1 (pure explosive) to W=0.01 (1% explosive). For each such formulation we compute the detonation parameters using our in-house chemical equilibrium code (not presented here). For each formulation we adjust the explosive radius so that the total detonation energy stays the same. For all runs we monitor the rigid boundary reflected pressure (pr) of the created blast wave in air, at a radial distance of 12m. We get that as W decreases below 0.5, the total amount of HMX decreases below 6% of the amount for pure HMX, but pr increases by about 12% relative to that of pure HMX. We attribute this enhanced blast effect to the spreading of the explosive, while keeping the amount of energy released unchanged (spreading effect).

Blast suppression with water barriers

The article presents the results of numerical simulation of an explosive of interaction between air blast wave and water barrier. To find the best spape of relaxation material and to evaluate the suppression degree resulted from the interaction of the blast wave with protective liquid barriers, calculations for various shapes and sizes of water barriers were provided. Keywords: high explosive blast, blast protection, shock-wave structures, relaxation media, water barrier

MODELING OF THERMO-ELASTIC-VISCO-PLASTIC DEFORMATION OF SHALLOW METAL-COMPOSITE SHELLS USING THE REFINED THEORY OF BENDING

The dynamic problem of thermo-elastic-viscous-plastic deformation of shallow composite shells is formulated using the refined theory of bending. In this case, tangential displacements along the thickness of constructions are approximated by polynomials of the third and higher orders, and the deflection does not depend on the transverse coordinate. Normal transverse stresses in the composition have a linear distribution over the thickness. The temperature over the thickness of the curved panels is approximated by a 7th order polynomial. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The constructions are multidirectionally reinforced with continuous fibres. The composition materials are isotropic; their plastic deformation is described by the flow theory with isotropic hardening, and the loading function depends on temperature and strain rate. The numerical solution of the coupled nonlinear two-dimensional initial-boundary value problem is obtained using an explicit scheme. Elastic-viscous-plastic, thermo-elastic-plastic and thermo-elastic-viscous-plastic response of a metal-composite cylindrical shallow shell of a rectangular shape with an orthogonal 2D-reinforcement structure has been studied. The construction is frontally loaded with an air blast wave. It has been demonstrated that curved metal-composite panels under such loading must be calculated, taking into account the temperature response that occurs in them and the sensitivity of the plastic properties of the composite materials to the rate of their deformation. In this case, it is necessary to apply the refined theory of bending of shallow shells, and not its simplest version, the Ambartsumian theory. A more intense thermomechanical response of a curved panel is observed when it is dynamically loaded from the convex front surface. In this case, at individual points of the construction, the temperature can briefly increase by 200 °C. It has been found that under dynamic loading of shallow shells from the side of any face-surface, they snapping towards the concavity of thin-walled structures.

Empirical Attenuation Law for Air Blast Waves Due to the Detonation of Explosives Outdoors

The detonation of explosives in the open air was studied, analyzing different amounts of explosives detonated at different distances, monitoring the overpressure or air blast wave generated with the aim of determining a model, which allows to establish safety zones. A series of tests measuring the air wave with different loads and sensors placed at various distances from the origin of the explosion were carried out. The work was focused on designing full-scale trials that allowed to develop a predictive empirical method based on the calculation model of the equivalent mass of TNT. A total of 18 different gelatinous dynamite charges, placing the sensor at six different distances from the origin of the explosion, produced a total of 90 tests measuring the air wave produced by the detonation of gelatinous dynamite. Later, the outdoor detonation of 10 TNT explosive charges was analyzed to extend the model and improve its scope. With all this, it has been possible to develop a predictive model that allows assessing the overpressure generated by the detonation of a TNT-equivalent explosive charge. The results are useful to predict the air blast wave in common open-air blasts, such as those carried out with shaped charges to demolish metallic structures. On the other hand, the results are also useful to determine the air blast wave overpressure in the case of large explosive charges detonated in the open air, such as accidental explosive detonation or terrorist bombs. It is important to point out the relevance of the results achieved after the detonation of large explosive charges (more than 80 kg) simulating a type of bomb frequently used by terrorists. Reproducing the explosion on a real scale, the results are fully representative of the overpressure produced by an explosion of these characteristics without the need of extrapolating the results of tests with small loads. In addition, the detonation was carried out with TNT, which can serve as a standard to compare with any other type of explosive.

Progressive collapse of Murrah Federal Building: Revisited

As a typical incident of progressive collapse of RC structures caused by the terroristic vehicular bomb attack, the large-scale collapse of Murrah Federal Building (MFB) in 1995 has been attracting extensive attentions. The alternate path method and the direct simulation method are commonly adopted to evaluate the progressive collapse resistance of buildings. However, the simultaneous damage of the structural members adjacent to the removed column and the instantaneous interactions between the blast wave and the structures are neglected. This paper aims to revisit the progressive collapse of MFB through the high-fidelity numerical simulations. Firstly, the hybrid finite element model of MFB was established including both the near-range refined model and far-range simplified model. Secondly, based on the explicit dynamic finite element program LS-DYNA, the Arbitrary Lagrangian-Eulerian (ALE) method and Fluid-Structure Interaction (FSI) algorithms were adopted to simulate the ignition of explosive, propagation of air blast wave and its interactions with the building structures, which was validated based on an external explosion test on RC frame structure. Furthermore, the collapse of MFB was predicted and compared with the on-site photographs in terms of the collapse scopes of entire building and the damage of local structural members. Finally, three seismic resistant design schemes of MFB were proposed, and the corresponding progressive collapse resistance of which was further evaluated. It derives that, (i) the numerical simulation combining the hybrid modelling and ALE approaches can well reproduce the collapse process of MFB; (ii) the progressive collapse of MFB is mainly caused by the insufficiency of flexural bearing capacity of the transfer girder due to the failure of three supporting ground columns, rather than the rotation of the transfer girder; (iii) the three improved schemes can partially prevent the shear failure of the ground columns and mitigate the collapse scopes of MFB by 25%–50%, while the progressive collapse still occurs due to the shear failure of transfer girder; (iv) transfer girder is not recommended for blast-resistant buildings due to its low redundancy.

The Refined Model of the Elastic-Plastic Dynamic Behavior of Reinforced Curved Panels Sensitive to Strain Rate

The initial-boundary value problem of dynamic elastic-viscoplastic deformation of flexible curved panels (shallow shells) with plane -cross and spatial reinforcement structures is formulated. The inelastic behavior of the materials of the composition components is described by the constitutive equations of the theory of plastic flow with isotropic hardening, and their sensitivity to strain rate is taken into account. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The used kinematic and dynamic two-dimensional relations and the corresponding boundary conditions make it possible to describe, with varying degrees of accuracy, the mechanical bending behavior of shallow composite shells. This takes into account the possible weak resistance of such reinforced panels to transverse shears. In the first approximation, the used two-dimensional equations, the initial and boundary conditions degenerate into the relations of the traditional non-classical Ambartsumyan theory. For the numerical integration of the formulated nonlinear dynamic problem, an algorithm of time steps is applied, based on the use of an explicit scheme of the cross type. The elastoplastic and elastic-viscoplastic behavior of the reinforced cylindrical shallow shells under transverse dynamic loads generated by an air blast wave is investigated. Metal-composite and fiberglass thin-walled constructions are considered. It is shown that the refusal to take into account the dependence of the plastic properties of the components of the composition on the rate of their deformation does not allow adequately describing the inelastic dynamic behavior of both metal-composite and fiberglass shallow shells. It is shown that in the calculations of even relatively thin reinforced cylindrical panels (with a relative thickness of 1/50), the use of the Ambartsumyan theory leads to completely unacceptable results in comparison with the refined bending theory. It has been demonstrated that even for relatively thin curved fiberglass panels, replacing the traditional flat -cross reinforcement structure with a spatial structure with obliquely laid fiber families can significantly reduce not only the intensity of deformations in the binder, but also the maximum deflection values in modulus. For metal-composite shallow shells with a weakly expressed anisotropy of the composition, the positive effect of the indicated replacement of reinforcement structures is practically not manifested.

Effect of ambient pressure on propagation characteristics and laws of air blast waves

It is important to study the effect of ambient pressure on air blasts, and the explosion process of TNT explosives was calculated by using the AutoDyn-2D software in this paper. Moreover, the explosion parameters under different ambient pressure conditions were predicted, and the propagation characteristics and laws of the air blast waves were obtained. The results showed that the overpressure of the incident wave, reflected wave, and Mach wave was positively related to the ambient pressure. High ambient pressure resulted in a decrease in the barotropic time and velocity of the incident wave, but its impulse increased. The wavefront of the Mach wave propagated in a curved form, and the pressure distribution on the Mach stem was not uniform. The height of the triple points was inversely proportional to the increase in the ambient pressure, and this trend was significant with the increase in the distance.

A new blast wave scaling

A new scaling is developed for both air and underwater blast waves based on dimensional analysis. The new length, time, velocity, and pressure scales are based on three control parameters: the energy release of the explosive $$E_{_\mathrm {HE}}$$ , the density of the undisturbed ambient medium $$\rho _{_0}$$ , and the speed of sound in the undisturbed ambient medium $$C_{_0}$$ . The shock wave propagation is divided into two regimes based on its decay characteristics, and the resulting control parameters are different in each regime. For strong shocks with Mach numbers $$M_{_\mathrm {SW}} \gtrsim 5$$ , the increase in the shock wave radius R with time t is approximated by a power law with an exponent of 2/5 as previously described by G. I. Taylor. Shock propagation in this regime is shown to not be a function of the ambient medium sound speed, but only the ambient medium density, explosive energy release, and time. For weak shock waves with Mach numbers $$M_{_\mathrm {SW}} \lesssim 5$$ , the shock wave radius increase with time can be approximated by a linear function plus a logarithmic-type correction which decays to a sound wave at sufficiently long time. Shock propagation in this regime is scaled according to the medium’s ambient density, sound speed, explosive energy release, and time. The new scaling is compared to, and agrees well with, published experimental data for air and underwater blasts, from milligram explosions to nuclear blasts. The new scaling improves upon traditional Hopkinson and Sachs scaling by relating shock propagation in liquid and gas environments, allowing them to be scaled to a single functional relationship. The functional scaling relationships developed here are dimensionless.

Issues of Data Acquisition and Interpretation of Paraseismic Measuring Signals Triggered by the Detonation of Explosive Charges

The paper tackles the issues of data acquisition during the measuring of vibrations caused by the detonation of explosive charges in various types of works (blasting in mines, demolition works, tunneling). Depending on the placement of an explosive charge (a charge detonated on the surface or a charge placed in a hole), it triggers side effects in the form of mechanical vibrations, which are propagated in the environment and may pose a hazard to buildings. In the case of propagation in the air, there is an acoustic wave and an airblast wave. For the assessment analysis on the impact of vibrations on buildings, a ground-propagated signal is used, while what is propagated by air is a disturbance. Selected examples in the paper demonstrate how an acoustic wave and an airblast wave interferes with the signal recorded by geophones. Afterwards, the paper presents the results of the tests conducted at a training area, during which various masses of explosive charges placed in different ways were detonated. The examples demonstrate that this interference may lead to the misinterpretation of recorded measurements. This paper is the first of two papers that will present the results of research into this matter and the suggested resolutions in order to eliminate this interference.

Modeling the propagation of air blast waves in mine workings

The article presents a physical and mathematical model of the propagation of air shock waves in the network of coal mine workings after an instant explosion of the methane-air mixture in a given area. An approach to the implementation of a method for solving problems on the propagation of air shock waves in a branched network of mine workings is presented, taking into account arbitrary angles of their conjugation. The results of calculating the propagation of air shock waves in the model networks of mine workings are presented.

Approach to substantiation of rational decisions on protection of fuel and energy complex objects to the impact of emergency explosions

The article presents in a formalized form the formulation of the problem of finding rational values of the parameters of the basic elements that make up the object of protection and external protection systems of the object (fuel and energy complex) from the impact of an air blast wave. A scientific and methodological apparatus for solving the problem of increasing the security of objects to the impact of an air blast wave in the conditions of restrictions on the parameters of the protection system and resources for the implementation of these measures is formulated. The proposed methodology is based on the security indicator, which makes it possible to interconnect both the intrinsic characteristics of the object and the most probable parameters of the damaging air blast waves. The solution to the optimization problem of delivering the values of the security indicator to the maximum is carried out using the gradient method. The rational parameters of the protection system obtained on the basis of the described approach will make it possible to plan measures to protect the objects of the fuel and energy complex against the impact of emergency explosions in conditions of restrictions on the cost of their implementation.

Reliability of building structures in case of an air blast wave

The analysis shows that the parameters of the air shock wave vary significantly and have a pronounced random nature. In general, in structural analysis, design parameters of the shock wave are random functions or random variables; therefore, the reaction parameters of the system under consideration will also be random. Then, fulfillment of certain conditions (for example, strength) is only possible with a certain probability, and the reliability of the system under consideration can be estimated using methods of building structures reliability, methods of mathematical statistics and probability theory. As a result, a probabilistic model of an air shock wave has been developed and the reliability of a free-standing wall has been estimated for random exposure parameters, as well as for random strength characteristics of materials. Based on the calculation results, it was concluded that the calculation of reliability using methods of mathematical and statistical probability theory makes it possible to bring the strength analysis of building structures closer to actual operating conditions.

Dynamic Response Analysis of Large Arch-Roof Oil Tank Subjected to the Coupling Impact of Two-Source Blast Waves Based on Finite Element Method

Research on failure law of target oil storage tank subjected to the coupling impact of multiple blast waves is one of the theoretical bases for domino effect accident prevention and control of chemical industrial parks. Taking the coupling impact of two-source blast waves as an example, the propagation law of blast waves in air and the distribution law of peak overpressure on the surface of tank wall are analyzed, and the dynamic response laws of displacement, stress, strain and energy for a 5000 m3 atmospheric steel arch-roof oil tank are studied by using ANSYS/LS-DYNA. The results are compared with those subjected to single blast wave and show that the maximum overpressure peak value is formed near the ground in 0° direction on the surface of tank wall, which is 79.6% larger than that subjected to single blast wave. The peak values of displacement, stress and strain for the tank wall subjected to the coupling impact of two-source blast waves are 114.9%, 39.6%, 134.9% larger than those subjected to single blast wave, respectively. The failure mode of arch-roof tank subjected to two-source blast waves is to form multiple concave plastic deformation zones on the explosion face, which extend to the surrounding area and produce plastic hinge lines and form irreversible residual deformation and cracking finally. The analysis results can provide reference for explosion-resistant design of tank structure and reasonable layout of tank area scene.

МОДЕЛИРОВАНИЕ УПРУГОВЯЗКОПЛАСТИЧЕСКОГО ПОВЕДЕНИЯ АРМИРОВАННЫХ ПЛАСТИН В РАМКАХ УТОЧНЕННОЙ ТЕОРИИ ИЗГИБА

The dynamic problem of elastic-viscoplastic deformation of flexible plates with spatial reinforcement structures is formulated. The plastic behavior of the components of the composition is described by equations of flow theory with isotropic hardening, taking into account the sensitivity of these materials to the rate of their deformation. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The relations used, with varying degrees of accuracy, describe the mechanical state of the bent plates and allow for the possible weakened resistance of the reinforced constructions to transverse shears. In a first approximation, the equations used, the boundary and initial conditions are reduced to the equalities of the widely used non-classical Reddy theory. To solve the stated nonlinear initial-boundary-value problem, a step-by-step algorithm is used, based on the use of an explicit numerical of the “cross” type scheme. The elastic-viscoplastic dynamic behavior of rectangular composite plates of different relative thicknesses under the action of a load corresponding to excess pressure in an air blast wave is investigated. Fiberglass-plastic and metal composite structures are considered. It is shown that for composite plates with a relative thickness of the order of 0.1, the calculation by the Reddy theory underestimates the maximum values of the strain intensity of the components of the composition by more than 12% compared with the calculation by the refined theory. A fairly simple Reddy theory is quite acceptable for calculating relatively thin plates. It is shown that for fiberglass-plastic plates with a relative thickness of the order of 0.1, replacing the traditional plane-cross reinforcement structure with the spatial structure of the reinforcement reduces the maximum deflection by more than 20%, and the greatest value of the strain intensity of the components of the composition is reduced by 10-20% or more. For metal-composite plates of any thickness and for fiberglass-plastic plates having a small relative thickness, the positive effect of from such a replacement of the reinforcement structures is practically not observed.

Modeling of non-isothermic viscoelastic-plastic behavior of flexible reinforced plates

Based on a step-by-step procedure over time, a numerical-analytical model of the nonisothermal viscoelastic-plastic behavior of crisscrossed-reinforced material is constructed. The components of the composition are isotropic; their viscoelastic deformation is described by the Maxwell - Boltzmann model of the body, and instantaneous inelastic behavior is described by the relations of the theory of elastoplastic deformation with isotropic hardening. In this case, the temperature dependence of the loading function and material constants is taken into account. The conditions of the viscoelastic deformation, the beginning of unloading, neutral and active viscoelastic-plastic loading of the thermosensitive materials of the composition are formulated. Relationship between the mechanical and thermophysical characteristics of the composite material is taken into account. The structural relationships of the thermophysical component of the problem are presented. The developed mathematical model is focused on the use of explicit schemes for the numerical integration of viscoelastic-plastic and thermophysical problems. The initial-boundary problem of nonisothermal viscoelastic-plastic bending deformation of fibrous plates is formulated. The poor resistance of such thin-walled constructions to transverse shear is described in the framework of Ambardzumyan's theory. The geometric nonlinearity of the problem is taken into account in the Karman approximation. In the transverse direction, the temperature is approximated by a second-order polynomial. To reduce the three-dimensional heat conduction problem to two-dimensional relations, the method of additional boundary conditions is used. The dynamic bending of a flat-crisscrossed-reinforced fiberglass plate under the influence of an air blast wave is investigated. It is shown that in the absence of external thermal heating in the process of oscillations, this structure heats by only 2-3ºС. In such cases, the calculation can reasonably be carried out without taking into account the temperature effect. In the presence of intense thermal loading of the structure, the heat sensitivity of the materials of the composition must be taken into account. It has been demonstrated that in the presence of a temperature field inhomogeneous over the thickness of the plate, the shape and magnitude of the residual deflection significantly depend on which face surface an external dynamic load is applied to.