Inspired by the layered structure of human vertebrae and spider webs, a thin-walled bionic gradient layered bellows (TBLB) was proposed by integrating layered design and gradient-designed filling structures into traditional bellow configurations. This structure enhances energy absorption while effectively reducing the initial peak crushing force (IPCF). A combined experimental and numerical simulation approach was employed to comparatively analyze the energy absorption performance of 0-2 Layer TBLB and traditional multicellular tube (TMT) under axial loading. Results demonstrate that increasing the layered number stabilizes deformation and strengthens energy absorption. Specifically, the specific energy absorption (SEA) of 1-Layer and 2-Layer TBLB significantly improved by 108 and 154%, respectively, compared to 0-Layer TBLB. While 2-Layer TBLB exhibited comparable energy absorption to TMT, its IPCF was 44.1% lower than that of TMT. Additionally, positive-gradient bellow structures outperformed negative-gradient counterparts in energy absorption capability. The effects of multi-layered corrugated cores with different cross-sections and impact velocity (V) on TBLB’s energy absorption were further investigated. Hexagonal multi-layered corrugated cores demonstrated superior energy absorption to circular counterparts, achieving 10% higher SEA and 36.2% improvement in compression force efficiency (CFE). Moreover, the SEA of TBLB increased with rising V, indicating that higher V enhances the energy absorption advantages of TBLB. These findings highlight the critical role of layered design, gradient configuration, and cross-sectional geometry in optimizing crashworthiness performance.

Aiming at the problem of flutter and instability of supersonic panel. the nonlinear dynamic control equation of pre-stretched porous panel is established based on Von Kármán thin plate large deflection theory and first-order piston aerodynamic load model. The dynamic model incorporates pre-stretching effects in functionally graded porous panels. Considering three different pore distribution modes. The Galerkin method transforms the governing equations into nonlinear systems through chordwise integration. Stability criteria are derived via Routh-Hurwitz analysis and Hopf bifurcation theory. Closed-form solutions for critical frequency and flutter velocity are obtained. Numerical validation is performed using fourth-order Runge-Kutta integration. Results demonstrate superior performance in symmetric distribution cases: It demonstrates the best flutter resistance, followed by asymmetric and then uniform distributions. The application of merely $$0.02\% $$ pre-stretching strain results in significant improvements in both critical flutter velocity and flutter frequency; when compared to the non-pre-stretched condition, the pre-stretched configuration delays the system critical point occurrence, effectively reducing flutter incidence. The pre-stretching-porosity coupling control methodology proposed in this study, establishes a new theoretical paradigm for panel design: prioritizing symmetric porosity distribution with optimal pre-stretching strain, can effectively suppress flutter while enhancing stability performance.

In this analysis, we have examined the acoustic wave propagation in a layer of piezoelectric material sandwiched between two n-type halfspaces of semiconductor material. The equations describing the motion, Gauss law for piezoelectric and the electron diffusion equation for semiconductor together with the interfacial boundary conditions for the two materials forms the mathematical model of the problem. The characteristic equation describing the wave propagation for symmetric and asymmetric modes was obtained after obtaining the analytical expressions for different field quantities governing the wave motion in compact form. With the irreducible Cardano method, the complex characteristic equation was solved numerically using functional iteration method. The simulation of the results was done by employing MATLAB software for the following heterostructures: (i) Si-PZT-Si (ii) Ge-PZT-Ge to obtain the dispersion curve for phase velocity, attenuation of waves and specific loss factor of energy dissipation in the material for both symmetric as well as asymmetric modes of propagation. The characteristics of considered layered structures are significantly influenced by properties of the inserted layer. The study of acoustic waves in piezoelectric layer sandwiched in semiconductor half-spaces is very important to understand the effect of material constituents on the propagating waves which modifies the characteristics of these waves. These studies are helpful in fabrication of acoustic wave devices such as sensors, actuators, transducers etc.

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.

This paper presents an energy-based approach for predicting elastoplastic fracture, formulated through the concept of a critical strain energy threshold. The method combines a newly introduced energy fracture criterion with a modified relaxation model of plasticity belonging to the structural-temporal class of theories. This combination enables the accurate description of materials exhibiting complex deformation behavior, including non-monotonic stress–strain curves and the yield point phenomenon, which are particularly relevant for metallic materials deformed at relatively low strain rates. A key advantage of the approach lies in its compactness and physical interpretability: the model parameters are directly related to the material’s initial defect structure and remain independent of the loading history. This allows for predictive capability across different grain sizes and material states without introducing damage accumulation functions or additional fitting parameters. The model is validated against experimental data for magnesium alloys Mg–0.3Ca (wt %) and Mg–1.0Al–1.0Ca–0.4Mn (wt %) with varying grain sizes. The predicted deformation curves (up to fracture) show good agreement with the experiments, even under conditions of developed plastic deformation. In one case, a single critical energy value proved sufficient, while in the other, a Hall–Petch-type grain size dependence was incorporated. The proposed framework shows strong potential for extension to more complex loading paths and other classes of metallic alloys.

We derive the time fractional heat conduction equation (FHCE) for a functionally graded elliptical annulus plate using non-Fourier heat conduction principles that account for memory effects rather than instantaneous responses, influenced by a moving laser heat source. Thermal conductivity, heat capacity, and density are presumed to vary axially and depend on temperature. The upper and lower plates are at zero, while Biot criteria and the Kirpichev reference number for convection energy transfer boundaries regulate the geometrically curved areas. Kirchhoff’s variable transformation linearises the FHCE governing the given conditions. The heat equation is resolved through the application of the Laplace transform, modified Mathieu transform, and Taylor series, followed by their inversions. The inverse of Kirchhoff’s Laplace domain transformation establishes the temperature distribution. Numerical analyses of titanium carbide and nickel properties yielded graphs depicting temperature, motion, and stress variations during laser pulse duration and velocity.

Currently, there are two theories of metal plasticity in solid mechanics: the classical mathematical theory of plasticity [1, 2] and the physical and mathematical theory of plasticity [3]. Both theories are used to solve applied problems of plasticity, in particular, in the development and improvement of technological processes of metal pressure treatment [5–7]. This paper examines the relationship between the above-mentioned theories. Based on the analysis of the initial postulates and principles, the disadvantages and advantages of the theories for solving problems of theoretical design of technological processes of metal pressure treatment are identified. The analysis allows us to assert that the physical and mathematical theory of plasticity is a more general theory, which includes the mathematical theory of plasticity as a special case and which does not have the disadvantages of the latter. It follows from this that the physical and mathematical theory of metal plasticity is an important scientific achievement in solid mechanics.

The Johnson-Cook constitutive model is extensively utilized in numerical simulations of high-velocity impact and penetration scenarios, with its primary material parameters (A, B, n, C, and m) directly governing the material’s flow stress. However, material parameters obtained exclusively through dynamic and static experiments generally prove inadequate for direct application in penetration analysis, necessitating further calibration for penetration studies. To investigate the influence of penetrator core material parameters on computational outcomes—particularly maximum penetration depth—during high-velocity penetration of semi-infinite metallic targets by long-rod projectiles, numerical simulations employing an experimentally validated ANSYS/LS-DYNA model were conducted. These simulations examined 93W alloy penetrator cores with varied material parameters impacting Rolled Homogeneous Armor steel at identical velocities. Results demonstrate that the initial yield strength (parameter A) constitutes the predominant factor influencing penetration depth; within the investigated range (500–2500 MPa), increasing A enhances penetration performance by 15.23%, while penetration depth sensitivity to the remaining parameters (B, n, C, m) remains below 5% across ranges typically covered by most materials.

The article is devoted to elastic-plastic torsion of a multilayered rod under torque. It is assumed that the rod consists of several layers. Each layer has its own elastic properties, but the plastic properties of both layers are the same. For simplicity, a three-layer rod is considered. The contact boundaries of the layers are located along the x-axis. The lateral boundary of the rod is free of stresses, the displacements and stresses are continuous at the interlayer boundaries. The stress tensor components at a point are calculated, using the contour integrals obtained from the conservation laws calculated on the edge of the cross section. Then, the second invariant of the stress tensor is compared with the yield strength. At the points where the yield strength is reached, the plastic state occurs, and the remaining parts are elastic. This lets us construct a boundary between the plastic and elastic regions. This method provides a way to calculate the elastic-plastic boundaries for the standard rolled profiles of rods. This issue will be considered in future studies. It should be noted that previously, using the conservation laws, the main boundary value problems were solved for the plastic two-dimensional medium, elastic-plastic torsion of isotropic rods and elastic media for finite-sized bodies.

In order to clarify the influence of interfacial bonding properties on the anti-penetration performance of UHMWPE rigid target plates, this study was carried out using a combination of experiments and numerical simulations. In the experiments, 1.1 g wedge-shaped broken pieces were used to conduct multiple penetration tests on UHMWPE laminated target plates with two different adhesives, and the internal damage morphology after penetration was observed by CT scanning technology. In the numerical analysis, a finite element model corresponding to the experimental conditions is established based on LS-DYNA, and different interfacial bond strengths are simulated by changing the bond coefficients, so as to obtain the penetration process, ballistic limit velocity and energy absorption characteristics of the target plate. The results show that the interfacial bonding strength has a significant effect on the anti-invasive performance of the target plate, which shows a trend of increasing and then decreasing. When the bonding coefficient is in the moderate range, the target plate has the highest ballistic limit velocity, the optimal energy absorption efficiency, and the interfacial damage extension is more homogeneous; while too low or too high bonding strength will reduce the anti-penetration capability of the target plate, too low bonding leads to serious delamination damage, and too high bonding leads to local load concentration and accelerated failure. The results of the study can provide an effective reference basis for the structural design and interface optimization of UHMWPE rigid target plates.