The distance-minimizing data-driven method introduces a new computing paradigm and focuses on computational solid mechanics research. This method enables direct input of discrete material data sets (stress-strain pairs), bypassing the empirical constitutive modeling process and reducing modeling errors and uncertainties. To apply this method to boundary value problems, it is necessary to define a distance functional from the solution set to the material data set, seeking the functional extremum that satisfies the strain-displacement relationship and equilibrium equation from the material data set. In this study, we extend the method to structural dynamics, using the structural dynamic equilibrium equation as a constraint for the distance functional. We derive data-driven computing formulas, analyze the value of the constant matrix in the formula, and develop an algorithm for solving structural dynamic responses. The accuracy and efficiency of the proposed method are validated through linear and nonlinear dynamic response analyses of single-degree-of-freedom systems and multi-degree-of-freedom truss structures. Within this theory, the final value from the previous moment serves as the initial value for the current moment, facilitating faster numerical solutions and reducing computational time. Additionally, the material data set accommodates both linear and nonlinear material behaviors. It is also found that when the amount of material data exceeds 100, the amount of material data and excitation step minimally impact computational accuracy, with the signal-noise ratio (SNR) becoming the primary factor. Under the same conditions, the amount of material data and excitation step significantly affect computational efficiency, while the influence of SNR can be ignored. This study provides theoretical support for the development of data-driven dynamic solvers.

This paper derives the analytical solution for the buckling load of extension-twist multicoupled laminates. The optimization targets both the buckling load and coupling effect, with verification through simulations and experiments. Using the double trigonometric series method, the analytical solution for the buckling load of the extension-twist multicoupled laminate, simply supported on all four sides and subjected to in-plane compressive loads, is obtained. Based on this, a multi-objective optimization design model for the extension-twist multicoupled laminate is established, with the optimization objectives of maximal buckling load and coupling effect. The optimization is achieved using the sequential quadratic programming (SQP) algorithm, and the laminate with enhanced coupling effect and buckling load is designed. Based on the ply angle sequence of the optimal laminate, numerical simulations and robustness analyses confirm the buckling model. Compared to the simulation results, the analytical solution error for the buckling load of the laminate is within 5%, validating the theoretical framework. Experimental measurements using a multi-directional loading test machine reveal that the discrepancy between measured and theoretical buckling loads is within 3%, further verifying the theory's accuracy. This research provides valuable insights for improving the load-bearing capacity of structures such as wings and wind turbine blades.

Large-area and tunable strain gradients arise from inhomogeneous deformation in wrinkled thin films, making them promising for flexoelectric applications. Consequently, the structure and buckling modes of these films have garnered significant attention. In this paper, an electromechanical coupling model is developed to study the buckling behavior of thin-film-and-finite-thickness-substrate structures with flexoelectric effects. First, the influence of flexoelectric effects on the buckling evolution of thin-film-substrate structures is assessed using the minimum energy method. Two buckling modes, i.e., global buckling and local wrinkling, are distinguished by changing structural parameters and the flexoelectric coefficient. Results show that stronger flexoelectric effects lead to slenderer films and an increased likelihood of global buckling. Additionally, a stronger flexoelectric effect raises the critical strain required for buckling and significantly impacts local wrinkling mode. In local wrinkling, as the amplitude increases, the maximum strain in thin films decreases; sparser wrinkles with greater amplitude occur with a more pronounced flexoelectric effect. When the flexoelectric effect reaches a certain threshold, the buckling mode of the thin film shifts from local wrinkling to global buckling. The flexoelectric effect enhances structural stiffness and stretchability. Moreover, flexoelectric polarization can be continuously adjusted with compressive strain, highlighting its controllability in wrinkled thin films for generating and managing material polarity. These findings will aid in the design and application of micro and nanoscale electromechanical devices.

Sandstone is a typical discontinuous and heterogeneous material characterized by a significant presence of pores. Porosity is a crucial factor that influences the complex characteristics of sandstone, notably affecting its compressive strength and deformation parameters. It is of considerable theoretical significance and engineering value to investigate the impact of porosity on the fracture behavior of sandstone under compressive loading. In this paper, we apply both the Intermediately-Homogenized PeriDynamic (IH-PD) model and the Fully-Homogenized PeriDynamic (FH-PD) model to examine the fracture behavior of sandstone containing a single oval flaw subjected to uniaxial compression. The IH-PD model incorporates porosity as pre-existing PD damages, wherein mechanical bonds connected to PD nodes are randomly pre-broken to achieve the desired porosity. The IH-PD model considers the heterogeneous characteristics of sandstone without detailing the explicit geometry of the actual pores. Simulation results from the IH-PD model indicate that both pore size and particle size influence the fracture mode of sandstone under uniaxial compression. A comparative analysis of fracture modes and stress-strain curves from IH-PD simulations, FH-PD simulations, and experimental measurements confirms the accuracy and superiority of the IH-PD model in simulating compressive fracture behavior. The results indicate that only the IH-PD model, which accounts for the inherent heterogeneities of sandstone, can adequately reflect the variations in crack paths caused by changes in pore distribution. Moreover, the IH-PD model successfully reproduces tortuous crack paths, captures transverse cracks in sandstone under compression, and exhibits asymmetric fracture modes, which markedly differ from the FH-PD simulation outcomes. This work employs the IH-PD model to investigate the fracture behavior of sandstone containing a single oval flaw with varying porosity levels under uniaxial compression, elucidating the influence of porosity on the failure modes of sandstone. The findings underscore the significant impact of porosity on the paths, roughness, and tortuosity of cracks. As porosity increases, the cracks exhibit greater tortuosity and roughness, and the symmetry of fracture modes becomes more easily disrupted.

Traditional methods for analyzing the P-Δ effect in tall structures often fail to adequately account for time-varying axial forces, which can lead to an underestimation of its impact on structural safety. This paper introduces a high-order accurate analysis method based on the weak-form quadrature element method (QEM). We develop Hermite-type quadrature element models for both distributed and concentrated mass structures. The proposed method is capable of addressing dynamic P-Δ effects caused by arbitrary axial loads without iterative computations, yielding precise solutions. Its efficacy and accuracy are validated through comparative analysis involving three distinct case studies. Numerical results confirm that the proposed approach delivers highly accurate P-Δ effect analyses, achieving exceptional precision in dynamic response with a single quadrature element, even in complex structural systems. Overall, this method offers a novel and efficient solution for detailed analysis of P-Δ effects in tall structures.

This study presents a two-dimensional (2D) bond-based peridynamics (BBPD) model based on the incompressible neo-Hookean (NH) constitutive model for simulating the tensile large deformation and failure behavior of incompressible hyperelastic membranes. First, the force density vector and micropotential function of the PD bond are derived by equating the strain energy density of the 2D BBPD model with that of the NH hyperelastic constitutive model. The model parameters are found to be related to the ratio of principal stretches in the neighborhood of the PD bond. Then a bond-associated horizon is introduced, and principal stretches are calculated based on the calculation of the deformation gradient within this horizon. A 2D BBPD model for NH hyperelastic materials is thus established. To validate the model, the nominal stress-stretch curves for a square hyperelastic membrane under uniaxial tension and biaxial tension with different biaxial tension speed ratios are calculated using the proposed BBPD model, and compared with theoretical curves. The deformation and load-displacement curves of a hyperelastic membrane with a central circular hole under uniaxial and biaxial tensile loads are also calculated and compared with finite element method (FEM) predictions. Finally, the deformation and failure processes of the hyperelastic membrane with a central circular hole under different tensile loads are calculated, and the influences of loading conditions on the mechanical properties and failure behavior of the NH hyperelastic membrane are analyzed based on the evolution analysis of strain energy density and damage of material points at the crack tip. It is found that the proposed BBPD model achieves less than 10% error in calculations. The failure load of the hyperelastic membrane with a central circular hole decreases while the failure displacement increases with rising biaxial tension speed ratios. Crack bifurcation occurs in the hyperelastic membrane with a central circular hole, with the bifurcation angle increasing alongside the biaxial tension speed ratio.

Materials with negative Poisson's ratios, as typical mechanical metamaterials, exhibit indentation resistance when impacted, significantly enhancing their impact resistance while remaining lightweight and capable of high energy absorption. Previous research primarily focused on the mechanical properties of honeycomb structures under forward impacts, with limited studies on the dynamic response of multi-cell structures with negative Poisson's ratios—particularly those made of double material cells—under inclined loads. However, structural failures from inclined load impacts are unavoidable in engineering practice. This study integrates gradient design in multicellular structures with inclined load impacts to analyze energy absorption and crushing deformation modes of structures. We propose a gradient bimaterial negative Poisson's ratio honeycomb structure featuring a curved edge concave bimaterial cell. By changing the materials of the transverse and longitudinal curved bars, we design four types of material gradient honeycomb structures: positive gradient, negative gradient, symmetrical positive gradient, and symmetrical negative gradient. Using numerical methods, we examine the dynamic behavior of each gradient structure under in-plane oblique impact loading. It is found that the honeycomb structure with a negative gradient bimaterial arrangement performs best in energy absorption during oblique impacts. We detail the deformation mode, nominal stress-strain curve, and energy absorption of the negative gradient structure at different impact velocities and impact oblique angles. Results indicate that both impact velocity and impact oblique angle significantly affect energy absorption. Regardless of speed, the smaller the impact oblique angle, the better the energy absorption of the honeycomb structure, meaning crashworthiness decreases as the impact oblique angle increases.

Self-sustained motion has proven to be an effective approach for tackling complex problems and addressing various challenges across a variety of disciplines, such as bionics, soft robotics, and engineering, owing to its efficiency, resourcefulness, and flexibility. However, traditional single-mode self-sustained systems are often limited to specific tasks and lack adaptability to environmental changes. This study addresses these limitations by developing a multi-modal self-sustained system using circular silicone oil paper. It demonstrates that hot steam drives the silicone oil paper to achieve self-sustained motion, thereby constructing a self-sustained system. In this system, the circular silicone oil paper placed on a steam-supported surface continuously oscillates and tumbles under the influence of hot steam. The study analyzes the mechanisms behind these motions and establishes a geometric model for the self-sustained behavior of the circular silicone oil paper. Computational programming examines how the oscillation frequency and amplitude of the circular silicone oil paper relate to steam temperature and structural dimensions. Critical conditions for motion pattern transitions and phase diagrams are identified, with experimental studies validating theoretical predictions. The research findings reveal that by adjusting structural size and steam temperature, the circular silicone oil paper can freely switch among three modes: stationary, self-sustained oscillation, and self-sustained tumbling. The frequency and amplitude of self-sustained oscillation increase with higher steam temperatures, larger outer diameters, and an increased inner-to-outer diameter ratio. The multi-modal self-sustained system developed in this study can better adapt to diverse tasks and environments while reducing costs and energy consumption. Therefore, it holds significant potential for applications in fields such as autonomous robotics, medical devices, waste heat recovery, and thermo-mechanical conversion.

Metal structures are widely used in modern industrial fields, but their manufacturing and service processes often produce composite defects that affect the mechanical properties and service life. Defects can appear both on the surface and beneath the structure, making it challenging for a single nondestructive testing (NDT) method to address all issues. Furthermore, using multiple NDT methods can result in low efficiency and high costs. To address this, a novel electromagnetic-acoustic integrated testing method, called PECT-EMAT, has been developed in this study, with its detection capability evaluated based on the theory of probability of detection (POD). Firstly, we established a simulation method and experimental system for PECT-EMAT to test aluminum alloy specimens with both surface cracks and bottom thinning defects, and explored a signal separation method using spectrum analysis. Next, we built a POD model based on statistical methods and created a signal database for composite defects. Finally, we conducted a statistical analysis of this database to determine the minimum detectable size of the PECT-EMAT hybrid testing method. The research findings indicate that: (1) For metal structures with both surface cracks and bottom thinning defects, the proposed PECT-EMAT method can effectively identify composite defects through signal separation. (2) The PECT signals and EMAT signals separated from the original detection signals exhibit distinct characteristics for detecting surface cracks and bottom thinning defects, respectively, leading to the establishment of a signal features' database for composite defects. (3) POD analysis reveals that the minimum detectable lengths for surface cracks are 2.72 mm in simulation and 2.12 mm in experiments, while for bottom thinning defects, they are 4.13 mm and 1.92 mm, respectively. This study provides a theoretical foundation for the adoption of the PECT-EMAT hybrid testing method and offers a reliable technical means for detecting complex defects in engineering structures.

Under mechanical loading, metallic materials can fail in various ways, including yielding, fracture, buckling, wear, fatigue, and so on, with fracture being particularly destructive. Ductile fracture, characterized by dimples on the fracture surface, is commonly observed in pure metals and alloys. From the microscopic point of view, the ductile fracture of metals and alloys is closely associated with the nucleation, propagation, and coalescence of voids, influenced by factors such as stress state, void size, void volume fraction, void shape, and temperature. Micromechanics-based models developed for ductile damage considering the void evolution, such as the Gurson model and its extensions, usually presume spherical voids, but creating models that consider realistic void shapes and their evolution presents significant challenges. Moreover, conducting mechanical analyses of ductile failure across specimen and component scales requires addressing cross-scale issues. This study first constructed representative volume element models incorporating isolated voids of different initial shapes. Finite element simulations were carried out based on the representative volume elements by adopting a J2 plasticity model for the matrix, systematically analyzing how initial void shape affects stress-strain responses and ductile damage under triaxial tensile and shear loading conditions. A neural network-based surrogate model was trained with the numerical data generated by the simulations to approximate stress-strain responses and damage evolution. This model effectively predicted how initial void shape influences ductile damage. Subsequently, a user-defined material subroutine was developed and integrated into a commercial finite element code to simulate the impact of initial void shapes on the ductile failure process in notched specimens. Results indicated that a reduced aspect ratio for the voids decreased the damage rate, leading to delayed softening at the specimen level. This work demonstrates the potential of using surrogate models to predict ductile damage involving complex microstructural features.