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Quick Search     Adv Search 2026 Vol. 47, No. 2 Published: 2026-04-28 141 A Review of Improved Methods in Classical Constitutive Models for Polymers under Impact Loading Polymer materials have gained widespread application in aerospace, transportation, and industrial processing due to their excellent wear resistance, efficient energy absorption capabilities, and outstanding impact resistance. In these application scenarios, the mechanical behavior of these materials exhibits complex rate sensitivity and temperature dependence, especially under extreme high-speed impact loading. These nonlinear responses are critical factors for structural integrity. This poses significant challenges for constitutive modeling. In classical physical models, researchers mainly improve the performance of the models by modifying rubber elasticity models, optimizing thermally activated flow rules, or introducing network branching structures. However, these improvements rely on many undetermined coefficients, which makes specific parameter calibration quite difficult in practical engineering. As for classical phenomenological models, the model performance is mainly improved by modifying the hardening term and introducing new branches. Essentially, these methods enhance the model's ability to describe mechanical behavior by assigning it more undetermined coefficients, but this also leads to problems such as difficulties in parameter calibration. Machine learning methods provide a new research direction for constitutive modeling. These methods are superior to classical models in terms of prediction accuracy and generalization ability, and can significantly reduce experimental costs. Purely data-driven machine learning models rely entirely on data to capture the mechanical response of materials, and face problems such as large data requirements, possible violation of physical laws, and overfitting or underfitting. Therefore, scholars have proposed hybrid models that combine traditional constitutive theory with machine learning algorithms to overcome these limitations. Among them, physics-informed neural networks (PINNs) have shown particularly broad application prospects due to their unique ability to learn physical laws, and have become a current research hotspot. In summary, this review systematically elucidates the evolution and optimization strategies of polymer constitutive models, providing a theoretical foundation for developing next-generation models with both physical consistency and high predictive accuracy. 2026 Vol. 47 (2): 141-160 [Abstract] ( 6 ) HTML (1 KB)  PDF   (0 KB)  ( 2 ) 161 Research on deformation and damage in notched S38C axles by synergetic application of acoustic emission and digital image correlation techniques UUnderstanding and precise characterization of the deformation and damage mechanisms involved in materials is essential to predict various structures’ performance, which requires big data on deformation and failure. However, the conventional mechanical tests and techniques may become inadequate to obtain the enough information reflecting deformation and damage in the structures’ interior, and fail to meet the demands of high-throughput characterization made by modern material genome engineering and data-driven industries. Herein we attempt to solve the issue by synergistic application of acoustic emission (AE) and digital image correlation (DIC) during mechanical tests. The AE technique is capable of detecting the real-time events of plastic deformation and damage interior of the specimens while the DIC helps to obtain deformation on the surfaces. As an example, deformation and damage in notched samples of S38C axles under tensile loading, widely used in express trains, has been studied. By analyzing the scaling laws between energy and duration of the acoustic emission events as well as the surface displacement field produced by DIC, we have found that plastic deformation in S38C axles is carried by dislocation glide and failure initiates through formation of surface cracks. Based on the dislocation dominated mechanism, we have further proposed the median frequency, the accumulative AE energy and AE entropy to characterize the plastic properties. Moreover, we have also proposed a model to simulate the whole deformation and failure process in the notched samples of S38C axles by phase field modeling coupled with mechanism-based crystal plasticity. The simulated force-displacement curve, distribution of strain field and damage evolution agree qualitatively with the experimental results. It is expected that the results obtained may help to understand the deformation and damage mechanisms in S38C axles. By the synergistic application of AE and DIC as well as the phase field model, efficient and precise characterization of the mechanical properties including elastic, plastic and fracture parameters can be achieved. 2026 Vol. 47 (2): 161-170 [Abstract] ( 8 ) HTML (1 KB)  PDF   (0 KB)  ( 2 ) 171 A novel spatial multiple-solution search method driven by sparse strain data for deformation reconstruction based on inverse finite element method The inverse finite element method (iFEM), employed as a shape reconstruction technique within the aerospace field, has attracted substantial attention due to its capacity for accurately reconstructing structural deformation from sparse measured strain via the adjustment of weighting coefficients. However, engineering application constraints that lead to sparse strain data acquisition, the iFEM approach, even with adjusted weights, exhibits limitations in accurately reconstructing deformations, thereby restricting its practical applicability. Consequently, a novel iFEM deformation reconstruction methodology has been developed. This method is characterized by a rigorous theoretical framework, a straightforward implementation process, and broad applicability, facilitating an exhaustive multi-solution search within the deformation space under sparse strain input. The methodology begins with the theoretical derivation of the iFEM solution error equation, accounting for sparse strain input. Upon judicious error truncation, a matrix mapping relationship is established between the iFEM-reconstructed deformation field and the true deformation field under sparse strain conditions. The incorporation of physically plausible deformation assumptions, alongside a virtual deformation field function approach, enables a multi-solution search within the reconstructed deformation space, guided by sparse data. A deformation reconstruction case has been investigated for a cantilevered aluminum alloy plate, subjected to a bending load of -10 mm, employing an extremely sparse sensor configuration. Through the application of the new methodology, thirteen deformation solutions were identified within the polynomial space. When the highest polynomial order was set to 2 or 3, the reconstructed full-field deformation exhibits a high degree of congruence with the actual conditions. Specifically, with the highest polynomial order of 2, the maximum deformation reconstructed at the end of the plate was -10.2146 mm. Compared with the value of -4.9595 mm obtained only by inverse finite element method, the reconstruction accuracy error has decreased from 50.4048% to -2.1460%. Additionally, the maximum spatial distribution reconstruction error was quantified at 2.7554%. The proposed method effectively addresses the issue of solution non-uniqueness in deformation reconstruction under sparse strain measurements, facilitates a comprehensive exploration of multiple feasible solutions, and achieves a substantial improvement in reconstruction accuracy. thereby exhibiting strong promise for practical engineering applications. 2026 Vol. 47 (2): 171-187 [Abstract] ( 6 ) HTML (1 KB)  PDF   (0 KB)  ( 2 ) 188 Design of truss lattice structures with free configuration based on the improved ESPSO algorithm Due to their excellent characteristics of light weight, high specific strength/stiffness, and good vibration and energy absorption, truss lattice structures have been widely used in the design of key load-bearing components of spacecraft. However, in view of the numerous topological configurations and significant difference in mechanical properties of truss lattice structures, the traditional empirical design method cannot achieve an optimal configuration under complex load conditions, and failing to meet the urgent performance requirements of ultra-lightweight and high load-bearing for high-end equipment. This paper proposes an intelligent design method of truss lattice structures with free configuration by two design strategy of fast restarting intelligent algorithm and deleting lattice struts. Firstly, a geometric parameterization model of a lattice unit cell is constructed by the explicit topological description function, achieving independent description of each strut of the lattice structures. Secondly, an energy homogenization method is employed to calculate its macroscopic effective properties of a lattice unit cell, to further perform efficient mechanical performance analysis for lattice structure. Finally, taking the geometric description parameters as design variables, allowable material usage as constraint conditions, and the overall compliance minimization of lattice structures as objective functions, an optimization mathematical model for lattice structures is established. And then an efficient surrogate-assisted particle swarm optimization algorithm is adopted to solve the above optimization model. To address the issue of traditional ESPSO algorithm tending to fall into local convergence, a fast restart strategy is applied to improve ESPSO algorithm, enhancing its global search capability. And to further expand the optimization space of ESPSO algorithm, a lattice strut deletion strategy is also designed, improving the design flexibility of lattice topological configurations and maximizing the material utilization rate. Numerical example results show that the proposed design method can significantly enhance the load-bearing capacity of truss lattice structures, and also provides a theoretical reference for the design of lattice structures for high-end equipment. 2026 Vol. 47 (2): 188-204 [Abstract] ( 5 ) HTML (1 KB)  PDF   (0 KB)  ( 2 ) 205 Research on the Crashworthiness Mechanism of Perforated CFRP Square Tubes under Carbon fiber reinforced polymer (CFRP) thin-walled tubes are widely used as lightweight energy-absorbing components in aerospace and transportation structures because of their high specific strength, high specific stiffness, and excellent crashworthiness. In practical engineering applications, CFRP tubes often require mechanical fastening, which inevitably introduces holes into the structure. These holes interrupt fiber continuity and cause severe stress concentration, which may significantly alter the crushing behavior, failure mechanisms, and energy absorption efficiency of the structure under axial compression. However, the combined effects of open-hole defects, ply angle, and stacking sequence on the crashworthiness of CFRP square tubes are still not fully understood, especially for complex layup configurations inspired by biological helicoidal structures. In this study, we investigate the quasi-static axial crushing behavior of perforated CFRP square tubes through a systematic numerical approach. A progressive damage finite element model is developed based on continuum damage mechanics. The model accounts for intralaminar damage initiation and evolution in fiber and matrix under tension and compression, as well as stiffness degradation associated with damage growth. Contact interactions between adjacent plies and between the tube and loading plates are also considered to realistically capture the crushing process. The numerical model is validated by comparing the predicted load–displacement response, failure modes, and energy absorption with available experimental results, showing good agreement and acceptable error in total absorbed energy. Based on the validated model, a comprehensive parametric study is conducted to examine the influence of ply angle and stacking sequence on the crashworthiness of perforated CFRP square tubes. Three categories of layup designs are considered: single-angle layups, gradient symmetric layups, and bio-inspired helicoidal layups with different angular variation patterns. Key crashworthiness indicators, including peak crushing force, total energy absorption, specific energy absorption, mean crushing force, and crushing force efficiency, are evaluated. The results show that introducing an appropriate amount of 30° plies significantly improves both energy absorption capacity and crushing stability. Single-angle 45° layups tend to promote global buckling and unstable failure, while gradient and helicoidal designs can effectively suppress catastrophic fracture by promoting progressive damage. Furthermore, the study reveals that inner plies play a dominant role in load bearing and energy dissipation during axial crushing. Structures with smaller angular differences between adjacent inner plies exhibit more stable damage evolution and higher energy absorption efficiency. In bio-inspired helicoidal configurations, concentrating larger angular gradients in the outer plies while maintaining smoother angular transitions in the inner plies leads to superior crashworthiness performance. The findings of this work provide clear design guidelines for optimizing the stacking sequence of perforated CFRP tubes. The proposed strategies are expected to be valuable for the crashworthy design of lightweight composite structures in aerospace, automotive, and other energy-absorbing engineering applications. 2026 Vol. 47 (2): 205-216 [Abstract] ( 5 ) HTML (1 KB)  PDF   (0 KB)  ( 2 ) 217 Thermal Conductivity Regulation and Multifunctional Design for Irregular Thermal Metamaterials Thermal metamaterials represent an advanced paradigm for heat flow manipulation through microstructural design, offering novel pathways for customizing thermal functionalities in engineering applications. This study introduces a microstructure design methodology based on the thermal resistance method, which establishes an explicit analytical relationship between equivalent thermal conductivity and geometric parameters. This framework enables precise control over non-uniform, anisotropic thermal conductivity distributions. By integrating transformation theory, we further develop a structured design process applicable to arbitrarily shaped thermal devices. The proposed approach is validated through the design and numerical simulation of six distinct thermal concentrators and rotators, demonstrating its effectiveness and adaptability in achieving targeted thermal responses. 2026 Vol. 47 (2): 217-229 [Abstract] ( 7 ) HTML (1 KB)  PDF   (0 KB)  ( 2 ) 230 Study on compressive mechanical behavior and energy absorption of square hollow structure filled with negative Poisson's ratio cells When compressed, materials with a negative Poisson's ratio contract laterally, causing the structure to shrink uniformly. This phenomenon involves cooperative deformation across the internal architecture, which sustains a relatively constant and high stress level during the compression process. This mechanism enables exceptionally efficient energy dissipation, making these materials highly resistant to impact. Therefore, employing them as filler material can substantially improve the protective capability of energy-absorbing structures. In this study, the two-dimensional curved concave cells with excellent performance were extended and applied to the filling design of three-dimensional energy-absorbing boxes through the classic and reliable construction method of orthogonal stacking. Based on the proposed two-dimensional curved edge re-entrant negative Poisson's ratio cell, this paper constructs a three-dimensional curved edge re-entrant negative Poisson's ratio cell and designs a negative Poisson's ratio multi-cell filled square hollow structure. The compression deformation failure mode of this energy-absorbing structure was numerically and experimentally studied, and its energy absorption effect was discussed. Research shows that the negative Poisson's ratio multi-cell filled square hollow structure undergoes plastic buckling instability during compression. Its deformation mechanism is mainly manifested as a regular layered fold deformation mode. The generation of each fold corresponds to a specific critical buckling mode, marking the change of the energy absorption process from elastic energy storage to plastic dissipation. The number, formation position and deformation mode of wrinkles in energy-absorbing structures during the collision process are extremely important. During the compression process of the square hollow filled energy-absorbing structure, the energy absorption curve presents a "dual-platform" feature, demonstrating high energy absorption efficiency and stability. The design method and results obtained in this paper provide theoretical basis and technical support for the design of new impact-resistant materials and lightweight energy-absorbing devices, which is conducive to the development and application of lightweight porous negative Poisson's ratio structures with excellent energy absorption performance in the field of vehicle engineering. 2026 Vol. 47 (2): 230-239 [Abstract] ( 6 ) HTML (1 KB)  PDF   (0 KB)  ( 2 ) 240 Research on High-Temperature Longitudinal Compression Failure Behavior of UD-CF/Al Composite Containing Fiber Misalignment Defect This paper presents experimental and finite element simulation investigation into the longitudinal compressive failure behavior of unidirectional carbon fiber reinforced aluminum matrix (UD-CF/Al) composites at room and elevated temperatures. First, UD-CF/Al composites with M40J carbon fibers as reinforcement and Al-10Mg alloy as matrix were prepared via the vacuum pressure infiltration process, and longitudinal compression tests were carried out at 25?℃ and 300?℃, respectively. Then, based on micromechanics, we develop a finite element model that incorporates fiber strength dispersion (Weibull distribution), initial fiber misalignment defects, interfacial damage evolution, and the elastoplastic mechanical behavior of the matrix. The effects of fiber strength dispersion on simulation accuracy, the influence of room and high temperatures on the compressive mechanical response, as well as the progressive damage evolution and corresponding failure mechanisms of the composites are systematically analyzed. The results demonstrate that the model accounting for fiber strength dispersion yields a macroscopic longitudinal compressive response that is in better agreement with experimental measurements, thereby significantly enhancing the accuracy of numerical predictions. At both room and elevated temperatures, the composite exhibits a typical progressive failure sequence: interfacial damage initiates first, followed by the emergence and development of matrix damage, and fiber kinking acts as the dominant final failure mechanism. Compared with room temperature, under high-temperature conditions, matrix softening and interfacial degradation lead to a significant decrease in the longitudinal compressive modulus and strength of the composite. Interfacial damage initiates earlier but propagates slowly, accompanied by relatively minor matrix damage. The fiber misalignment angle increases rapidly during the evolution process but remains small at the final failure state. Moreover, the composite is more prone to structural instability under high temperature, resulting in the formation of a wider kink band. This study provides a reliable numerical analysis approach and theoretical foundation for the structural design, mechanical performance evaluation, and reliability assessment of fiber-reinforced metal matrix composites serving in high-temperature environments. 2026 Vol. 47 (2): 240-253 [Abstract] ( 5 ) HTML (1 KB)  PDF   (0 KB)  ( 2 ) 254 Study on the Compressive Damage Mechanism of Laminated Composites with Protective Layer after Lightning Strike This study focuses on the lightning protection design and effectiveness evaluation of composite laminates with protective layers. Through electro-thermal-ablation coupled numerical simulation and experimental testing, the damage areas and failure modes of the materials under Zone 2 lightning current were analyzed. Compression tests were conducted on post-lightning specimens to assess the protective performance. The results show that the designed protection scheme effectively maintains the mechanical properties of the material after lightning strike, with only a 4.51% reduction in compressive residual strength, indicating a controllable level of degradation. Regarding the damage mechanism, lightning strike did not alter the core failure path of the material, which remains "uniform compression–shear dominance–composite failure." The final failure mode is still composite failure dominated by shear with supplemental compression, demonstrating that the main load-bearing mechanism remains intact. Lightning-induced damage only introduces local effects, such as residual microcracks leading to slightly uneven stress distribution, accelerated local strain growth in later stages, and slight reduction in shear band integrity. The overall mechanical behavior did not undergo qualitative changes, confirming good protective performance and controllable impact. This work provides a feasible solution for lightning protection design of composite materials. 2026 Vol. 47 (2): 254-267 [Abstract] ( 8 ) HTML (1 KB)  PDF   (0 KB)  ( 2 ) 268 Damage Mechanism of Cement Sheath Ring Penetrated by a Shaped Charge Jet: An SPH-Based Study As oil exploration and development advance to greater depths, reservoir rock strength increases, and perforation detonation energy rises, exacerbating damage to the cement sheath ring and compromising its integrity. Existing research has primarily focused on the properties and parameters of the cement sheath itself, with limited studies investigating cement sheath damage specifically from the perspective of shaped charge jet parameters. Leveraging the advantages of the Smoothed Particle Hydrodynamics (SPH) method in simulating crack propagation and damage accumulation, this study establishes an SPH model to investigate the effects of reflected wave strength under both free and fixed boundary conditions, as well as different jet parameters, on damage to cement targets. A self-programmed method was developed to quantify the extent of target damage, termed the damage ratio.Analysis results indicate that the damage ratio of targets with free boundaries is 9.35% lower than that with fixed boundaries. As jet density increases, the target damage ratio also increases: when penetration does not occur, the damage ratios are 10.8% and 15.9%; upon penetration, the damage ratio rises significantly to 55.0% and 64.7%. When the jet diameter increases from 1 mm to 2 mm, the damage ratio shows a substantial increase; however, further increases in jet diameter result in negligible changes to the damage ratio. At jet velocities between 2000 m/s and 3000 m/s, targets are not fully penetrated, and the damage ratio exhibits an increasing trend. At higher velocities that achieve penetration, the damage ratio decreases rapidly.The findings demonstrate that jet density and velocity are the primary factors influencing target damage. Under the condition that jet penetration is achieved, the extent of target damage increases with density but decreases with velocity. This study establishes a methodology for analyzing crack propagation and damage in cement targets and proposes a self-programmed quantitative analysis method for assessing damage. The results can also provide valuable insights for the optimized design of low-damage shaped charges and the optimization of perforation parameters. 2026 Vol. 47 (2): 268-280 [Abstract] ( 5 ) HTML (1 KB)  PDF   (0 KB)  ( 2 )

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