This study investigates the relationship between composition, descriptors, and phase structure in nitride thin films and coatings using machine learning. A dedicated dataset of 79 systems, comprising 627 individual records, is analyzed using features derived from elemental properties and thermodynamic parameters. The Gradient Boosting model performs excellently on the 8 key features, achieving 0.94 mean accuracy in phase classification. Critical descriptors such as D-CR and C-N are identified as dominant predictors through feature importance analysis. Interpretable models reveal a pronounced preference for FCC phase formation at higher values of D-CR (>0.33) and C-N (>0.35). The study further proposes data inclusion principles to address the limitations of existing models under limited data conditions. By reformulating the classification task as a regression problem via a sigmoid function, an explicit predictive expression based on the key descriptors is derived. These findings highlight the value of diverse compositional databases and interpretable machine learning for understanding complex material systems and guiding the design of materials with stable structures.

This work develops a thermodynamically consistent thermo-elastic-damage model within a two-scale asymptotic homogenization framework, bridging microcrack dynamics and macroscopic fracture behavior. Starting from a representative volume element containing an embedded microcrack, the homogenized Helmholtz free and kinetic energy densities are rigorously derived through two-scale asymptotic expansion. Application of the first and second laws of thermodynamics yields a set of nonlocal thermo-elastic coupling equations, while incorporating Griffith's criterion leads to a dynamic damage evolution law linking microcrack growth with the macroscopic thermomechanical state (strain, strain gradient, strain rate, and temperature). During crack propagation, the excess internal energy beyond that required for new surface formation is dissipated as heat. The effective material properties are expressed as nonlinear functions of microcrack length and orientation via first-order cell functions, capturing anisotropic stiffness and conductivity degradation. The framework strictly satisfies the dissipation inequality, ensuring thermodynamic consistency. Numerical simulations successfully reproduce key experimental observations, including localized temperature rise near the crack front, anisotropic degradation of thermal conductivity, and strain-rate-dependent fracture responses. The predicted temperature evolution shows good quantitative agreement with reported experimental measurements.

The fracture behavior of geomaterials is largely governed by their internal microcrack structures, and establishing a link between microcrack evolution and macroscopic fracture remains a key challenge. In this work, a multiscale anisotropic phase field model is proposed to simulate the complex fracture processes of geomaterials with randomly distributed microcracks. Within the framework of asymptotic homogenization, the system energy under brittle fracture during microcrack opening and ductile fracture induced by frictional sliding during microcrack closure is characterized. By statistically describing the distribution of microcracks, the microstructural features are incorporated into the homogenized stiffness, plastic yield criterion, and phase field structure tensor, enabling the model to naturally capture the anisotropy of stiffness, plasticity, and fracture toughness arising from the preferential orientation of microcracks. Under the principle of energy conservation and the stability condition, the variationally consistent governing equations of the proposed model are derived. Numerical examples demonstrate that the model can accurately reproduce the brittle or ductile fracture behavior of geomaterials under tensile, compressive, and mixed-mode loading conditions, and can reasonably predict fracture anisotropy induced by the preferential orientation of microcracks.

The low efficiency and accuracy are the bottleneck problems that constrain neural network-based approaches from solving multi-scale problems. In this study, an innovative higher-order multi-scale method enhanced by physics-informed randomized neural network (HOMS-PIRNN) is proposed to efficiently and accurately compute transient thermal problems of composite materials with discontinuous and high-contrast material parameters, which inherits the respective high efficiency, accuracy, mesh-free and space–time advantages of higher-order multi-scale approach and PIRNN. To address the large complexity and Frequency Principle of multi-scale problems, higher-order multi-scale approach is employed to decouple and reduce complicated multi-scale thermal problem of heterogeneous materials as simpler macroscopic homogenized and small-scale lower-order and higher-order microscopic cell problems. Then, by using macroscopic homogenized and microscopic cell problems as new physical constraints, PIRNN are designed to efficiently solve homogenized equations and microscopic unit cell functions, for further assembling higher-order multi-scale asymptotic solutions for multi-scale heat problems via automatic differentiation. Moreover, the error estimate of the proposed HOMS-PIRNN method is rigorously demonstrated under some hypotheses. The efficiency and accuracy of the proposed HOMS-PIRNN are validated through multi-scale thermal simulations of high-contrast composites, three-dimensional composites, and porous materials. The efficient HOMS-PIRNN computational framework with strong potential for large-scale heat simulations of complex composites.

The macroscopic fracture strength and crack propagation behavior of heterogeneous materials are strongly governed by their underlying microstructures. When the characteristic scale of microstructures becomes comparable to that of the macroscopic structure, strain rate and strain gradient effects play a crucial role in dynamic fracture. In this work, we extend our recently proposed quasi-static strain gradient phase field model to the dynamic regime. The framework consistently integrates microstructural size, strain gradient, strain rate, and phase field evolution within a unified variational energy formulation, and provides mathematically consistent definitions of higher-order constitutive tensors without relying on empirical assumptions. A penalty-based computational strategy is adopted to ensure numerical efficiency while avoiding higher-order continuity requirements. Benchmark simulations demonstrate that the model accurately captures key features of dynamic fracture, including crack branching and propagation velocity, with excellent mesh objectivity. Applications to fiber-reinforced composites and porous materials further confirm the model’s capability to reproduce fracture anisotropy, porosity-dependent dynamic fracture behavior, and experimentally observed damage zones and free-surface velocity histories in spallation problems.

In this paper, a constructive second-order three-scale analysis method is proposed to analyze the Dirichlet eigenvalue problems for periodic hierarchically perforated materials. The perforated domains with three different scale configurations(macroscopic, mesoscopic and microscopic) are considered. Between the macro-mesoscopic scale, the second-order two-scale asymptotic expansion is performed, where the first cell eigenpair is introduced. Following a successive two-scale expansion strategy, the mesoscopic cell functions are developed at the microscopic level, and the meso-microscopic two-scale expansion is carried out for the mesoscopic eigenpair. Multiscale analyses are performed for eigenvalue problems under two void distribution patterns: mesoscaleonly and dual-scale (meso-micro) configurations. For different cases, the corresponding eigenvalue three-scale asymptotic expansions are derived according to the "corrector equation". The finite element(FE) algorithm of the three-scale asymptotic model is developed, and numerical experiments are carried out for the two cases. The results are compared with the two-scale and the classical finite element results, which demonstrate the convergence and effectiveness of the algorithm. It is shown that the three-scale finite element algorithm can greatly improve computing efficiency while ensuring the accuracy of the result. It is worth noting that the cell eigenpair plays an important role in the correction of the solution and the second-order asymptotic cell eigenfunction can capture small-scale variation. The second-order asymptotic cell eigenvalue acts as the main term of the asymptotic eigenvalues and with the addition of higher-order corrections, the asymptotic behavior of the structure can be reflected more accurately.

In this study, we propose a framework for the inverse design of amorphous alloys based on multi-objective properties, which not only constructs the potential relationship between material properties and composition, but also verifies the inherent constraints between different objective properties. The framework uses the variational autoencoder and conditional variational autoencoder as the core generation model, and combines the grid filter, quantum network, and machine learning algorithm to filter and recommend the generated data, thereby improving the feasibility of practical applications. To validate and analyze the performance of the proposed framework, we implemented an amorphous alloy design scheme covering three key properties: saturation magnetic strength, coercivity, and glass transition temperature. The experimental results show that the framework can generate alloy compositions that are extremely similar to the experimental data under the same property conditions, thus validating its excellent generation capability. More importantly, our material inverse design framework has good scalability. This allows it to flexibly respond to the increasingly complex and specific property requirements of various materials in the future.

Efficiently predicting the thermal responses of composite materials with complex, random, and highly heterogeneous microstructures remains challenging due to the high computational cost of traditional numerical methods. Existing numerical and data-driven methods still struggle to balance computational efficiency, full-field prediction accuracy, and data efficiency for highly heterogeneous random composites with sharp material-property contrasts. This work proposes a novel wavelet-neural network method, which achieves highly efficient and accurate prediction of the temperature field in random composite materials. First, high-fidelity databases with high-dimensional and highly complex mappings are established by multiscale computer modeling and finite element simulation of random composite materials across a wide range of random microstructural configurations and material properties. This study introduces the wavelet transform technique to preprocess raw large-scale databases, thereby achieving data dimensionality reduction, feature extraction, and noise filtering. Furthermore, optimized deep neural networks are employed to establish predictive models from the dimension-reduced data. These networks integrate three techniques: Squeeze-and-Excitation (SE) block, spatial attention module (SAM), and residual connection, which improve feature representation and predictive performance compared with conventional neural networks. Finally, the computational efficiency and accuracy of the proposed wavelet-neural network approach are validated via extensive numerical experiments. Numerical results demonstrate that, under the reported hardware configuration, the proposed method achieves a wall-clock speedup of approximately 93–266 times for the 2D cases and 19–37 times for the 3D cases compared with FEM. Across the eight cases, the average coefficient of determination (R2) exceeds 0.9988, and the relative L1 errors remain below 5%. Under spatially correlated Gaussian input noise, the relative L1 errors range from 0.28% to 1.85%; under 3% Gaussian perturbations of the thermal-conductivity parameters, the errors at the largest evaluated training scale remain below 2% for the 2D cases and are approximately 2.03% for the 3D cases. Overall, this framework offers an efficient and accurate tool for data-driven thermal prediction of random composite materials. Its scalability and robustness support extension to other material-response prediction tasks.

We develop an energetically consistent framework for modeling dynamic deformation and fracture of brittle materials, in which both the elastodynamic equation and the damage/fracture law are derived from the same E1-order two-scale asymptotic approximation of the strain and kinetic energy functions, with strain gradient and strain rate effects naturally embedded. Based on these energy functions, Hamilton's principle is applied to derive a strain gradient elastodynamic equation that naturally accounts for damage-induced softening. Concurrently, applying the Griffith criterion yields a microcrack evolution equation driven by macroscopic strain, strain gradient, and strain rate. The resulting brittle fracture model is shown to rigorously satisfy the Clausius-Duhem inequality. Moreover, both the elastodynamic equation and the damage/fracture law are governed by a concise set of coefficients, formulated as integrals over microscopic cell functions that depend exclusively on intrinsic material parameters-namely the elastic moduli, microcrack size, and microcrack spacing. Numerical simulations show that neglecting strain-gradient and strain-rate terms in the elastodynamic governing equations leads to unphysical phenomena such as infinite wave speeds at short wavelengths and stress singularities at macrocrack notch tips. In contrast, the present energetically consistent modeling approach effectively eliminates these spurious effects. Furthermore, simulations based on the proposed model quantitatively reproduce results from dynamic fracture experiments, including damage zone characteristics, free surface velocity profiles, and the strain-rate dependence of dynamic fracture strength.

A new third-order multiscale expansion is proposed for the elliptic problem with mixed boundary conditions in arbitrarily heterogeneous domains. The field variable is expanded in terms of a homogenized solution and its derivatives up to the third order. The so-called first to third-order functions are defined to give the homogenized coefficients and correct the differences between the homogenized and original solution both in the domain and on the boundaries. Error estimations are derived, and a typical numerical example is presented demonstrating the high accuracy of the multiscale model. This multiscale analysis presented in this paper generalizes the asymptotic expansion method and can be extended to other problems in non-homogeneous domains.

Smoothed Finite Element Method (S-FEM) has been widely used in many engineering simulations. However, there are still a lot of theoretical problems to be solved, especially with regard to composite materials and convergence proof. Based on a novel least-squares approximation and conservation property, we extend S-FEM to heterogeneous materials. Firstly, the orthogonality, Softening Effect, and energy function are checked. Secondly, the interpolation error in the maximum norm is estimated in any dimension. Consequently, we get a theoretical convergence rate which has been sought since the year 2010. When restricted to one-dimensional problems, we construct a special test function to prove the superconvergence: (1) S-FEM flux is exact in the meaning of element-wise integral; (2) numerical flux is exact at some point in each element; (3) physical flux can be quadratically approximated at the center of each element. At last, we present two numerical experiments: (1) conventional S-FEM fails in high-contrast composite materials while our new scheme performs well; (2) our flux converges quadratically.

Understanding the material response and material strength under dynamic loading is crucial for optimized design of advanced material serving in extreme conditions. Flow stress and spall strength are typical measured material strengths in shock loading. However, the correlation of the two strengths is not well understood. Here we use large-scale molecular dynamics simulations to demonstrate that flow stress and spall strength of nanocrystalline Cu have obviously different variation tendencies upon grain refinement at nanoscale. The flow stress reveals a transition from Hall-Petch (HP) to inverse Hall-Petch (IHP) behaviors as grain size decreases. The HP - IHP transition of flow stress is mainly attributed to the competition of grain boundaries strengthening effect by blocking and absorbing dislocations and the grain boundaries weakening effects including GB sliding and grain rotations. However, the grain size dependence of spall strength mainly shows an inverse Hall-Petch relationship, i.e., spall strength generally decreases as grain size decreases. This is mainly due to the role of grain boundaries as preferred void nucleation sites. For finer grain size, the larger volume fraction of grain boundaries and junctions facilitates damage nucleation and results in larger amount of voids and lower tensile strength.

We develop a strain gradient elastodynamics model for heterogeneous materials based on the two-scale asymptotic homogenization theory. Utilizing only the first-order cell functions, the present model is more concise and more computationally efficient than previous works with high-order truncations. Furthermore, we rigorously prove that the coefficient tensors, including the homogenized elasticity tensor, the strain gradient stiffness tensor, and the micro-inertial tensor are symmetric positive definite, thereby establishing the well-posedness of the strain gradient elastodynamics model, i.e., the existence and uniqueness of solutions. Numerical simulations are performed to confirm the theoretical findings and illustrate the characteristics of the present model in comparison with classical elastodynamics model (without strain gradient terms) and strain gradient models with higher-order truncations. The results indicate that the strain gradient model derived based on the first-order truncation can achieve an optimal balance between accuracy and computational cost.

This study introduces a hybrid network model for phase classification, integrating quantum networks and complex-valued neural networks. This architecture uses elemental composition as its only input, eliminating complex feature engineering. Parameterized quantum networks handle sparse elemental data and convert data from real to complex domains, increasing information dimensionality. Complex-valued neural networks process data in the complex domain, significantly reducing information loss during transitions. The experimental results show that the hybrid model achieves a phase classification accuracy of 94.93%, outperforming the best machine learning model by 2.27% and the quantum model by 8.67%. Precision, recall, and F1-score are also excellent at 0.9494, 0.9493, and 0.9500, respectively. Additional tests on phase transitions in Al x CoCrFeNi alloys confirm the model's robust generalization, identifying transition thresholds at 0.46 and 0.88, closely matching the 0.45 and 0.88 reported in related studies.

Multi-component thin films and coatings (MCTFCs) with stable structure and excellent capability are gradually being applied to more complex extreme environment. In the review paper, we summary the recent research progress of MCTFCs and build the comprehensive datasets from composition, experiment condition, microstructure and macro-properties. By searching the keywords, more than 30,000 relevant articles are found, including at least 600 systems of MCTFCs and involving 73 elements. Statistical analysis shows that the researched system is evolving from simple 4-element to 12-element to composite materials, and the research focus are extending from mechanical properties to chemical properties to medical and industrial applications. The results of comparing with high entropy alloys show that the theories of distinguishing solid solution phase and other structure are only explicable for part MCTFCs. Further, the building multivariate datasets that takes multiple factors into consideration will facilitate the development of optimal MCTFCs.

An accurate prediction of nonlinear hydro-mechanical (HM) coupling in subsurface structures with pronounced heterogeneity at multiple spatial scales is still an open topic and crucial for numerous engineering applications, for example, hydraulic fracturing and enhanced geothermal systems. In this study, novel high-order multi-scale asymptotic solutions are developed to accurately capture the locally oscillating characteristics of gas flow and solid displacement fields at multiple scales. First, the formal macro-meso two-scale asymptotic expansion is performed to establish the homogenized solutions and macro-meso high-order models which can predict the HM coupling problems at the macroscale and mesoscale. By directly expanding the cell functions defined at the mesoscale to the microscopic levels, the high-order two-scale expansion for the mesoscopic cell functions is built, and the upscaled relations for the flow parameters and constitutive coefficients from the microscale to the mesoscale and macroscale are developed correspondingly. The multi-scale low/high-order models are established by combining the high-order expansion of all cell functions at the mesoscale and the developed macro-meso two-scale models. The main contributions are that the present approaches follow the reverse thought processes of reiteration homogenization methods, and offer a very innovative and efficient way to establish high-accuracy high-order models for the nonlinear HM coupling problems in the heterogeneous porous medium with any number of spatial scales. The effectiveness and accuracy of the present solution are validated by several representative cases with different constitutive coefficient contrasts. The results demonstrate that the high-order solutions provide an accurate prediction for gas transport and solid deformation of heterogeneous porous media with multi-scale configurations.

The quantum circuit is a pivotal component of the hybrid classical-quantum neural network, and its efficacy influences the network’s overall performance. Given the vast number of potential combinations of quantum gates, designing simple yet effective quantum circuits has become a significant challenge. To improve the performance of hybrid networks through the design of suitable quantum circuits, we propose a training framework that utilizes quantum architecture search to enhance hybrid classical-quantum neural networks. This framework employs a Monte Carlo tree search algorithm to optimize quantum circuits and integrates multiple neural network architectures to improve the performance of hybrid networks. Furthermore, this work considers the quantum circuit architecture of two-qubit quantum circuits as the search target, constructing distributed quantum circuits that significantly reduce the search space. Experiments conducted on a coronary artery stenosis detection dataset validate the proposed scheme and analyze the impact of varying search spaces on circuit design. The results demonstrate that, compared to several prevalent quantum circuit architectures, the quantum circuit designed using this search strategy exhibits superior performance across multiple evaluation metrics.