論文

In this study, we develop a conditional diffusion model that proposes the optimal process parameters and predicts the microstructure for the desired mechanical properties. In materials development, it is costly to try many samples with different parameters in experiments and numerical simulations. The use of data-driven inverse design method can reduce the cost of materials development. This study develops an inverse analysis model that predicts process parameters and microstructures. This method can be used for any material, but in this study it is applied to polymeric material, which is the matrix resin of carbon fiber reinforced thermoplastics as an example. Matrix resins contain a mixture of dendrites, which are crystalline phases, and amorphous phases even after crystal growth is complete, and it is important to consider the microstructures consisting of the crystalline structure and the remaining amorphous phase to achieve the desired mechanical properties. Typically, the temperature during forming affects the microstructures, which in turn affect the macroscopic mechanical properties. The trained diffusion model can propose not only the processing temperature but also the microstructure when Young’s modulus and Poisson’s ratio are given. The capability of our conditional diffusion model to represent complex dendrites is also noteworthy. This model can be applied to other process parameters and mechanical properties. Furthermore, multiple process parameters and mechanical properties can be handled together.

In this study, the effect of ferrite grain size on the mechanical properties and dislocation behavior of dual-phase (DP) steel is investigated using dislocation-based crystal plasticity finite element analysis. DP steel, composed of a soft ferritic phase and a hard martensitic phase, shows mechanical properties that are significantly influenced by ferrite grain size. The mechanism underlying this grain size effect is clarified by analyzing the partitioning and distribution of stress, strain, and dislocations in each phase. Three models with the same volume fraction of martensitic phase but different ferrite grain sizes are subjected to tensile loading. Interestingly, even though only the ferrite grain size is changed, the stress in the martensitic phase exhibited a notable dependence on ferrite grain size. This can be explained as follows. Geometrically necessary (GN) dislocations accumulate on the ferrite side of the ferrite–martensite grain boundary, and the grain boundary occupancy per unit area increases as the ferrite grain size decreases. As a result, smaller ferrite grain sizes make the ferritic phase less deformable owing to the effect of GN dislocations, shifting more deformation to the martensitic phase. This behavior is confirmed by the more uniform strain distribution and partitioning observed with decreasing ferrite grain size. As the martensitic phase takes on greater deformation, the statistically stored dislocation density in the martensitic phase becomes ferrite grain size dependent, which in turn leads to the observed grain size dependence of stress in the martensitic phase.

Hamiltonian simulation is a fundamental algorithm in quantum computing that has attracted considerable interest owing to its potential to efficiently solve the governing equations of large-scale classical systems. Exponential speedup through Hamiltonian simulation has been rigorously demonstrated in the case of coupled harmonic oscillators. The question arises as to whether Hamiltonian simulations in other physical systems also accelerate exponentially. Schrödingerization is a technique that transforms the governing equations of classical systems into the Schrödinger equation. However, since the Schrödinger equation is a linear equation, Hamiltonian simulation is often limited to linear equations. The research on Hamiltonian simulation methods for nonlinear governing equations remains relatively limited. In this study, we propose a Hamiltonian simulation method for nonlinear partial differential equations (PDEs). The proposed method is named Carleman linearization + Schrödingerization (CLS), which combines Carleman linearization (CL) and warped phase transformation (WPT). CL is first applied to transform a nonlinear PDE into a linear differential equation. This linearized equation is then mapped to the Schrödinger equation via WPT. The original nonlinear PDE can be solved efficiently by the Hamiltonian simulation of the resulting Schrödinger equation. By applying this method, we transform the original governing equation into the Schrödinger equation. Solving the transformed Schrödinger equation then enables the analysis of the original nonlinear equation. As a specific application, we apply this method to the nonlinear reaction–diffusion equation to demonstrate that Hamiltonian simulations are applicable to nonlinear PDEs.

Establishing efficient methods to obtain quantitative data on crystal defect evolution is vital for understanding material properties. Dynamic Transmission Electron Microscopy (TEM) captures crystal defects in materials undergoing plastic deformation, generating vast datasets with high temporal and spatial resolution. However, manual analysis of these images is labor-intensive, and automated, unbiased analysis remains a challenge. In this study, we developed a U-net-based machine learning approach to analyze TEM videos of crystal defect evolution in Twinning-Induced Plasticity (TWIP) steels with different grain sizes. The method overcame challenges like field-of-view translation and nonuniform defect motion. This approach quantitatively measured defect evolution as a function of time and strain with the same temporal resolution as the original videos, detecting even minor changes with high accuracy. We use this technique to quantitatively reveal the switch of the dominant plastic deformation mechanism with grain size and the relaxation of elastic strain due to the rapid increase in stacking faults. Our results validate the use of U-net models for efficient semantic segmentation of TEM videos, enabling accurate quantitative analysis. This work advances TEM video analysis and provides new insights into the deformation mechanisms of materials.

This study presents a secant-based multiscale constitutive modeling framework coupling homogenized finite element method (FEM) and molecular dynamics (MD) for the nonlinear and strain-dependent mechanical behavior of polymeric materials. Representative unit cells governed by MD simulations are assigned to each FEM integration point and deformed consistently with the macroscopic deformation gradient. In conventional atomistic-to-continuum approaches, constitutive responses are often derived from analytically evaluated tangent stiffness at the reference configuration, which is feasible only for simple interatomic potentials. For realistic polymeric systems, however, analytical evaluation of tangent stiffness is generally intractable, and the discrepancy in boundary condition treatment between FEM and MD further complicates direct constitutive coupling. To overcome these difficulties, the proposed framework employs a secant-based approach that enables the extraction of physically meaningful secant properties, such as the secant modulus and transverse contraction coefficient, from temporally averaged MD stress and strain data, which in turn serve as effective constitutive descriptors within the homogenization framework. The proposed method is demonstrated through three numerical examples: uniform tensile simulation on a single-element model, non-uniform tensile simulation on a single-element model, and tensile simulation on a multi-element model of a quarter perforated structure. The results show that the framework successfully reproduces key features of the nonlinear stress–strain behavior obtained from pure MD simulations, while preserving the continuum-scale consistency required for FEM. Overall, the proposed approach provides a robust pathway for incorporating atomistic dynamics into continuum constitutive modeling of polymeric materials.

Quantum annealing is emerging as a practical tool for large-scale combinatorial optimization. We map continuum displacements and element densities to binary variables, turning both deformation analysis and topology optimization into quadratic unconstrained binary optimization (QUBO) problems that run on today's annealers. Two formulations are compared: one derived from the stiffness equation and another from the minimum total potential energy. Benchmarks show the energy-based QUBO matches finite-element displacements and stresses more closely and avoids the rapid term-count growth that slows the stiffness-based form. The numerical demonstrations reported here include deformation analysis of a 100-element plate model and topology optimization of cantilever beams discretized with up to 60 triangular elements or 32 rectangular elements. These examples are intended as proof-of-concept demonstrations under current hardware and encoding limitations rather than as large-scale industrial benchmarks. Leveraging this model, a single QUBO embedding density variables–implemented with combinatorial random-number sums and a quadratic volume penalty–yields two-dimensional beam layouts that are quantitatively compared with those obtained using the classical Optimality Criteria (OC) method.