Mechanics of Solids最新文献

The paper considers deformation of isotropic rectangular samples within the generalized plane stress state. Approximate models of different orders for elongated samples are constructed by representing the displacement field as an expansion in first- and second-order polynomials with unknown coefficient functions. The Kantorovich method within the Lagrange variational principle allows one to reduce the problem to a system of ordinary differential equations with constant coefficients and to form the corresponding boundary conditions. The models are verified by the finite element method (FEM) implemented in FlexPDE, the suitability of the obtained models is investigated depending on the relative thickness parameter of the rectangle. The inverse problem of reconstructing Poisson’s ratio and Young’s modulus from information on the displacement field on the lateral face is solved.

The article presents the results of an experimental study of complex elastoplastic deformation of L63 brass along two-link broken strain trajectories in the deviatoric strain space. The description of the experimental program, presentation and discussion of its results are carried out in the vector representation of stresses and strains using the terminology and approaches of A.A. Ilyushin’s theory of elastoplastic processes. The experiments were carried out in the mechanical testing laboratory of Tver State Technical University using the automated testing machine SN-EVM under combined loading of thin-walled tubular specimens with axial force and torque (P + M experiments). The loading process was assumed to be isothermal, and the strains were considered small. The material of the specimens was sufficiently isotropic initially, as confirmed by experiments under simple loading. The test programs were implemented in the deviatoric space of strains (rigid or kinematic loading). Two-link broken trajectories with the first link length of 3% and fracture angles of 90°, 135°, and 180° are investigated. Experimental diagrams characterizing the scalar and vector properties of the L63 brass material are presented. Approximations of deformation diagrams under simple and complex loading are proposed. The research results can be used in constructing mathematical models of plasticity theory.

A mechanical system consisting of a rigid body and a material point is considered. They interact with each other by means of internal forces whose physical nature is not defined. Both objects are affected by external forces specified as functions of time. The task is to construct a trajectory for a point mass such that the solid body, under the action of the force of interaction with this mass, changes its orientation in space according to a predetermined program. Based on the theorem on the change in the relative moment of momentum, a second-order vector differential equation, unresolved with respect to the highest derivative, is obtained that describes the system. A change of variables is found that allows replacing the original equation with a first-order vector differential equation resolved with respect to the derivative. All special cases arising from the use of the new equation are considered. The obtained relationships can be used to control spacecraft and robotic systems.

Algorithms for solving and calculation results for the problem of the movement of material in a rectangular pipe under the action of an increasing pressure drop in the frame of theory of finite elastic-viscoplastic strains are presented. The problem with specifying reversible and irreversible deformations by differential equations of their transfer is reduced to solving a system of differential equations with no-slip conditions on the pipe walls. An approximate solution of such a problem by the finite-difference method remains within the framework of the classical approach, without encountering additional difficulties. The elastic properties of an incompressible material are specified by a three-constant dependence of the elastic material on the invariants of the Almansi tensor, viscoplastic properties by flow theory with a generalized condition of maximum von Mises octahedral stresses for the case of taking into account the viscous resistance to plastic flow. The time and place of origin of viscoplastic flow, the patterns of movement of elastic-plastic boundaries, the elastic core, the evolution of stagnation zones in the corners of the pipe are calculated.

A fundamentally new method is proposed for assessing the plastic response of a material to dynamic loading during tests of cylindrical specimens impacted against a rigid barrier. Unlike the traditional Taylor test, this study considers a temporal yield criterion based on the concept of incubation time. This approach allows for a transition from averaged rate-based estimates to a more accurate and physically grounded description of material behavior over time. Impact tests of cylindrical specimens against a rigid anvil were conducted to determine the yield strength exhibited by the material at various impact velocities. The material behavior under high rate elastoplastic deformation was investigated. The impact-on-anvil test incorporates new dynamic characteristics of the material, which define the rate sensitivity of the yield strength based on the incubation time criterion. The test results are interpreted as a time-dependent yield strength, i.e., the threshold amplitude of the impact load as a function of its duration. It is shown how the parameters that enable prediction of the rate and temporal dependence of the yield strength under arbitrary impact-wave loading can be estimated from a single test.

This paper addresses the problem of altering the natural vibration frequencies of an elastic body with embedded piezoelectric elements by applying an electric potential to them. Presented mathematical formulation of the problem based on the principle of virtual displacements for a piecewise-homogeneous electroelastic body. Finite deformations are represented as the sum of linear and nonlinear parts, which are linearized with respect to a state featuring a small deviation from the initial equilibrium position caused by the reverse piezoelectric effect. Provided experimental and numerical results validate the reliability of the numerical algorithm based on the finite element method. Using a plate with an embedded piezoelectric element as an example, presented numerical results demonstrate the influence of various parameters on the change in natural vibration frequencies: the stiffness characteristics of the elastic body; the dimensions, location, and number of piezoelectric actuators; the area ratio of the piezoelectric element to the elastic body; and the magnitude and sign of the electric potential.

This paper considers the natural finite-dimensional (12-dimension) subalgebra of the symmetry algebra associated with the symmetry group of three-dimensional hyperbolic equations of the spatial problem of perfect plasticity, proposed in 1959 by D.D. Ivlev for the states corresponding to an edge of the Coulomb–Tresca prism, represented in the isostatic coordinate net. An algorithm is given for developing the optimal system of one-dimensional subalgebras of this natural finite-dimensional subalgebra of the symmetry algebra, comprising one three-parameter element, 12 two-parameter elements, 66 one-parameter elements, and 108 individual elements (total 187 elements). It was previously demonstrated that the symmetry algebra of the plane problem equations has mathematical dimension 7; the optimal system of one-dimensional subalgebras consists of 1 two-parameter, 11 one-parameter, and 20 individual infinitesimal generators (total 32 elements). The symmetry algebra of the axisymmetric problem equations has dimension 5; the optimal system of one-dimensional subalgebras consists of 1 one-parameter and 22 individual infinitesimal generators (total 23 elements).

This paper investigates the mechanical resistance to shear deformation of flat multilayer panels with thin coatings made of carbon fiber reinforced plastics and honeycomb filling made of fiberglass tape. The effective shear moduli and ultimate strength of panels are determined during shear tests of rectangular specimens at different heights of the honeycomb filler. It is shown that the effective shear moduli along and across the gluing planes of the tape in the honeycomb cells exhibit statistically significant difference and decrease with the filling height. By contrast, the effective shear strengths in the above directions show statistically insignificant difference and do not correlate with the height of the honeycomb filling. Numerical analysis of the finite element models of the specimens yields underestimated calculated values of the effective shear moduli. The factors leading to this effect are investigated numerically based on the models of representative specimen cells.

An review of the temperature dependences of the elasticity characteristics of cubic crystals of simple substances is presented. It is shown that the general trend is a decrease in elastic moduli E, G, and B with temperature due to the weakening of interatomic bonds caused by thermal expansion of the crystal lattice. However, there are also anomalous dependencies, such as an increase in the shear modulus G with temperature, observed for BCC crystals of vanadium V, niobium Nb, tantalum Ta, and FCC crystals of palladium Pd, platinum Pt. A common feature for the cubic crystals considered, except for BCC chromium Cr, is an increase in Poisson’s ratio ν with temperature. The factor of elastic anisotropy A also shows a general upward trend, but for some crystals, BCC V, Nb, Ta, and FCC Al, local minima are observed, and for BCC Cr and FCC Pd, maxima are observed.

The paper presents fundamental principles of the mathematical theory of plasticity for spatial states, corresponding to an edge of the Coulomb–Tresca prism, when the flow of a body is governed by generalized associated flow rule. A detailed analysis is provided for the relations resulting from the generalized flow rule for an isotropic body, associated with the Tresca yield condition, and restricting the freedom of plastic flow to the minimum extent for the specified states. It has been shown that the spatial relations of plasticity theory formulated by A.Yu. Ishlinskii in 1946 follow from the generalized version of the flow theory. It has been established that the constitutive relations of Ishlinskii for the states on the edge of the Coulomb–Tresca prism express the commutativity of the stress and plastic strain increment tensors. An additional tensor symmetry relation is obtained by applying this commutativity relation.