論文

This study proposes an efficient framework for sequentially solving a series of boundary value problems (BVPs), each with a different material distribution, using a direct data-driven approach to reduce constitutive model evaluations in materials design tasks. In the direct data-driven approach, two stress–strain datasets are iteratively populated and reused across BVPs, reducing material model evaluations. In addition, the constant pseudo stiffness matrix of the data-driven solver avoids costly numerical decompositions. These features are particularly advantageous for evaluating sets of candidate microstructures in two-phase materials. In this study, we extend an adaptive data generation scheme to handle two separate datasets corresponding to each phase, adding new data when necessary. Comparison of the proposed method with conventional finite element analysis shows significant reduction in constitutive model evaluations, with close agreement in mechanical response observed. In the later stages of the sequential evaluation, many microstructure evaluations required no additional data, indicating increasing reusability of existing datasets. This trend demonstrates that the number of constitutive evaluations decreases as the evaluation progresses, leading to computational savings in large-scale material design problems. These results suggest that the proposed method can broaden the applicability of data-driven computational mechanics, particularly for composite materials involving high-cost constitutive models.

In this study, we use a coupled finite element method (FEM)–molecular dynamics (MD) methodology to examine the complex deformation response at fine and coarse scales of carbon dioxide hydrate pellets. While previous studies in this area have focused on simple deformations of fine-scale structures using MD simulations, none have attempted to model the stability of hydrate pellets under complex deformations. To accurately represent the geometry of hydrate pellets, we employ FEM to model these cylindrical shapes and extract deformation gradients at each integration point. Subsequently, MD simulations are carried out to capture the detailed fine-scale response to the imposed deformation at each integration point. Further study of constrained expansion within a hydrate pellet uncovers differing responses depending on the location of the integration points. We observe higher peaks of von-Mises equivalent stress where a shear deformation mode is dominant. In all cases, the hydrate cage structure remains intact at an total equivalent strain of around 0.14, which is already beyond the critical point, where the stress of hydrate reaches its maximum value. This indicates that gas hydrate pellets are safe for carbon storage applications when not subjected to deformations above the critical point.

In this study, we developed a method of estimating the correction terms that makes the Hamiltonian used in phase-field analysis by quantum annealing correspond to the free energy functional of the conventional phase-field analysis using the finite difference method. For the estimation of the correction terms, we employed a factorization machine. The inputs to the factorization machine were the phase-field variables in domain-wall encoding and the differences between the Gibbs free energy and Hamiltonian. We obtained the difference value in quadratic unconstrained binary optimization (QUBO) form as the output of learning using the factorization machine. The QUBO form difference was subjected to the original Hamiltonian as the correction term. The performance of this correction term was evaluated by calculating the energy for a equilibrium state of diblock copolymer. In phase-field analysis, the time evolution equation is formulated so that the total free energy decreases; hence, a lower the free energy means a more accurate result close to that of a conventional method. When we performed annealing with correction terms, the microstructure showed a Gibbs free energy that was lower than that obtained without the correction terms.

This study presents a gradient damage model for ductile fracture, in which the damage hardening modulus is degraded by the accumulation of plastic deformation and the volume expansion caused by negative hydrostatic pressure. The proposed model fulfills the thermodynamic requirements, and the governing equations are derived from energy minimization principles. Two parameter studies are carried out to confirm the basic performance of the proposed model, in which some typical ductile fracture responses are demonstrated by changing parameters for degrading the damage hardening modulus. Also, a series of numerical experiments are presented to reveal the ability of the proposed model to successfully simulate the fracture tests of advanced high strength steel sheets with different tensile strengths. It is indeed confirmed by the close agreement with experimental results that the proposed model is capable of realizing the breaking elongation, the transitional behavior from unstable to stable crack propagations, and the corresponding load–displacement curves. Also, the model successfully reproduces and predicts the crack initiation positions in notched specimens with different notch radii.

Cell membranes phase separate into ordered Lo and disordered Ld domains depending on their compositions. This membrane compartmentalization is heterogeneous and regulates the localization of specific proteins related to cell signaling and trafficking. However, it is unclear how the heterogeneity of the membranes affects the diffusion and localization of proteins in Lo and Ld domains. Here, using Langevin dynamics simulations coupled with the phase-field (LDPF) method, we investigate several tens of milliseconds-scale diffusion and localization of proteins in heterogeneous biological membrane models showing phase separation into Lo and Ld domains. The diffusivity of proteins exhibits temporal fluctuations depending on the field composition. Increases in molecular concentrations and domain preference of the molecule induce subdiffusive behavior due to molecular collisions by crowding and confinement effects, respectively. Moreover, we quantitatively demonstrate that the protein partitioning into the Lo domain is determined by the difference in molecular diffusivity between domains, molecular preference of domain, and molecular concentration. These results pave the way for understanding how biological reactions caused by molecular partitioning may be controlled in heterogeneous media. Moreover, the methodology proposed here is applicable not only to biological membrane systems but also to the study of diffusion and localization phenomena of molecules in various heterogeneous systems.

We investigate the possibility and current limitations of flow computations using quantum annealers by solving a fundamental flow problem on Ising machines. As a fundamental problem, we consider the one-dimensional advection-diffusion equation. We formulate it in a form suited to Ising machines (i.e. both classical and quantum annealers), perform extensive numerical tests on a classical annealer, and finally test it on an actual quantum annealer. To make it possible to process with an Ising machine, the problem is formulated as a minimization problem of the residual of the governing equation discretized using either the spectral method or the finite difference method. The resulting system equation is then converted to the quadratic unconstrained binary optimization (QUBO) form through the quantization of variables. It is found in numerical tests using a classical annealer that the spectral method requiring a smaller number of variables has a particular merit over the finite difference method because the accuracy deteriorates with the increase of the number of variables. We also found that the computational error varies depending on the condition number of the coefficient matrix. In addition, we extended it to a two-dimensional problem and confirmed its fundamental applicability. From the numerical test using a quantum annealer, however, it turns out that the computation using a quantum annealer is still challenging due largely to the structural difference from the classical annealer, which leaves a number of issues toward its practical use.

Advanced high-strength steels (AHSSs) are widely adopted in car body structures to achieve weight reduction for energy efficiency and crash safety. This study investigates the effects of material strength and notch shapes on crack initiation and propagation behaviors in AHSS sheets used in car body structures. Tensile tests were conducted for three types of Japanese grade AHSS (JSC590, JSC980, and JSC1180) specimens and two notch root radii (R0.5 and R5). The crack initiation and propagation behaviors were found to strongly depend on the material strength and notch root radius. The crack generated from the notch root for the R0.5 specimens, whereas it generated from 1 to 2 mm inside the notch root for the R5 specimens. Unstable crack propagation occurred beyond the maximum load for the R5 and JSC1180 specimens, whereas only stable crack propagation occurred for the R0.5 specimens. From the digital image correlation analyses, we found that the specimen notch radius affects the stress triaxiality and equivalent plastic strain around the notch root. The JSC980 material had the highest crack initiation energy, which correlates with the plastic dissipation energy utilized for thickness reduction. The JSC590 material exhibited the highest crack propagation energy, which correlates with the true fracture strain.

Carbon-fiber-reinforced plastic (CFRP) is a composite material whose base material is plastic and reinforcement material is carbon fibers. CFRP is widely used in various fields for laminating prepregs. The laminated plate tends to sustain damage, such as delamination, fiber breakage, and base material breakage; hence, we must conduct high-precision and efficient nondestructive testing (NDT). Examples of NDT are ultrasonic examination, X-ray tomography, and infrared stress analysis. With most NDT methods, it is difficult to easily obtain detailed correct information of defects, such as their depth, position, and size. To solve this problem, we develop a machine-learning-aided inverse analysis model that predicts the spatial information of defects from the sum of the principal stresses on the surface calculated from the temperature change measured by infrared analysis, and we propose it as an alternative method to the existing damage analysis. Applying the proposed method to the simulated stress distributions of quasi-isotropic CFRP laminates with defects, the results showed over 99% success to recognize the detail information of defects. Additionally, we examine the properties of the dataset using a forward analysis model and a variational autoencoder. Our method with a convolutional neural network enables us to successfully estimate the information of defects at high speed. Experimental data can be applicable as well as the simulation results to our proposed method, and we believe our method will be a powerful supporting tool for the current NDT for CFRPs.

Observation of dynamic processes by transmission electron microscopy (TEM) is an attractive technique to experimentally analyze materials’ nanoscale phenomena and understand the microstructure-properties relationships in nanoscale. Even if spatial and temporal resolutions of real-time TEM increase significantly, it is still difficult to say that the researchers quantitatively evaluate the dynamic behavior of defects. Images in TEM video are a two-dimensional projection of three-dimensional space phenomena, thus missing information must be existed that makes image’s uniquely accurate interpretation challenging. Therefore, even though they are still a clustering high-dimensional data and can be compressed to two-dimensional, conventional statistical methods for analyzing images may not be powerful enough to track nanoscale behavior by removing various artifacts associated with experiment; and automated and unbiased processing tools for such big-data are becoming mission-critical to discover knowledge about unforeseen behavior. We have developed a method to quantitative image analysis framework to resolve these problems, in which machine learning and particle filter estimation are uniquely combined. The quantitative and automated measurement of the dislocation velocity in an Fe-31Mn-3Al-3Si autunitic steel subjected to the tensile deformation was performed to validate the framework, and an intermittent motion of the dislocations was quantitatively analyzed. The framework is successfully classifying, identifying and tracking nanoscale objects; these are not able to be accurately implemented by the conventional mean-path based analysis.

Quantum annealing machines are next-generation computers for solving combinatorial optimization problems. Although physical simulations are one of the most promising applications of quantum annealing machines, a method how to embed the target problem into the machines has not been developed except for certain simple examples. In this study, we focus on a method of representing real numbers using binary variables, or quantum bits. One of the most important problems for conducting physical simulation by quantum annealing machines is how to represent the real number with quantum bits. The variables in physical simulations are often represented by real numbers but real numbers must be represented by a combination of binary variables in quantum annealing, such as quadratic unconstrained binary optimization (QUBO). Conventionally, real numbers have been represented by assigning each digit of their binary number representation to a binary variable. Considering the classical annealing point of view, we noticed that when real numbers are represented in binary numbers, there are numbers that can only be reached by inverting several bits simultaneously under the restriction of not increasing a given Hamiltonian, which makes the optimization very difficult. In this work, we propose three new types of real number representation and compared these representations under the problem of solving linear equations. As a result, we found experimentally that the accuracy of the solution varies significantly depending on how the real numbers are represented. We also found that the most appropriate representation depends on the size and difficulty of the problem to be solved and that these differences show a consistent trend for two annealing solvers. Finally, we explain the reasons for these differences using simple models, the minimum required number of simultaneous bit flips, one-way probabilistic bit-flip energy minimization, and simulation of ideal quantum annealing machine.

We calculate the parameter that governs the width of the transition zone by molecular dynamics (MD) simulation and use it in a phase-field crack (PFC) simulation with the mechanical properties of iron. First, a quantitative evaluation of intactness is conducted by examining the change in atomic conformation induced by crack propagation, whose numerical data are taken from the result of the MD simulation. The spatial distribution of the intactness is fitted to the same function as the damage parameter in the PFC model, namely, an exponential function, by the least-squares method. From this distribution, the transition zone parameter is estimated. The result of the PFC simulation using this newly determined transition zone parameter is discussed in terms of the crack path by comparison with the result of crack propagation analysis based on the MD simulation.

A new substitution approach is proposed for decoupled two-scale analysis of a materially nonlinear composite plate with in-plane periodic meso-structures within the framework of computational homogenization. The macroscopic nonlinear mechanical behavior of the plate is characterized by numerical plate tests on an in-plane unit structure (IPUS), which enables us to obtain the relationship between macroscopic resultant stresses and generalized strains. Then, we postulate that the original composite plate can be substituted by an equivalent laminated plate that exhibits approximately the same macroscopic response. The material parameters of each lamina of this substitute, which is referred to as mesoscopic substitution model (meso-SM), are identified using an optimization method so that it could be equivalent to the original IPUS. After the parameter identification, the corresponding macroscopic substitution model (macro-SM) can be analyzed with appropriate analysis software that supports laminated plate elements. Representative numerical examples are presented to validate the appropriateness of the proposed approach by performing comparative calculations with the results obtained from the original composite plates.

This study presents a procedure for creating a surrogate model for the transient electrochemical potential analysis of solid oxide fuel cells (SOFCs) by applying proper orthogonal decomposition (POD), which takes into account the characteristics of the spatial distribution of oxygen potential. In the proposed procedure, the time-variation of oxygen potential distributions in an SOFC are determined by numerical simulations under various analytical conditions with different explanatory variables or, equivalently, input parameters, and the results are stored in a separate data matrix for each component in accordance with certain rules. Then, POD is applied to each data matrix to create an individual surrogate model for the corresponding component using the dominant modes on the basis of contribution rates and/or mean square errors. The created models are used separately to obtain the oxygen potential distribution in the entire domain of the SOFC for an arbitrary set of input parameters at a low computational cost. A notable aspect of the proposed approach is that the positions and values of oxygen potential in two electrodes and interconnectors are data points and responses, respectively, but play opposite roles in the electrolyte region where the oxygen potential changes abruptly. Therefore, before combining the responses from the individual surrogate models, the oxygen potential values must be calculated backward from the coordinate values in the electrolyte. Representative numerical examples are presented to validate the appropriateness of the analysis procedure by applying the surrogate models with input parameters other than those used in the training process in comparison with the results obtained using the transient electrochemical potential.

In this study, the Fe–Pt binary system was critically reassessed by means of the CALPHAD technique for the applications of the next-generation data storage media. The liquid and A2 phases were modeled as substitutional solutions. The fcc-based phases (L12–Fe3Pt, L10–FePt, L12–FePt3 and A1) were modeled using the split-compound energy formalism (split-CEF) with four sublattices, where the effect of short-range ordering was taken into account through the reciprocal parameters. The formation enthalpies of the fcc-based phases were reproduced well by introducing the regular terms that represent the second-nearest-neighbor interactions in the fcc lattice. The magnetic excess Gibbs energies described by the Inden model were assessed for the fcc-based ordered and disordered phases. The obtained parameter set in the present work can reproduce satisfactorily the key theoretical and experimental data in this system.

In this paper, we propose a framework of nondestructive testing for predicting the 3D structure of internal defects in carbon-fiber-reinforced plastic (CFRP) from the distribution of the sum of principal stresses on surfaces (DSPSS) through transfer learning. DSPSS is obtained from both the finite element method and infrared stress measurement results. Infrared stress measurements are based on Kelvin's theory to convert surface temperature changes to DSPSS changes. The machine learning model used in this framework is a 3D convolutional neural network (CNN). The transfer learning method employed in this framework is as follows. First, a CNN that predicts the 3D structure of defects is trained using the DSPSS dataset by the finite element method and the 3D structure of internal defects. DSPSS is used with noise that imitates the noise generated by experimental factors such as temperature fluctuations in infrared stress measurements and differences in physical properties between the polymer resin and the carbon fiber bundle of CFRP. Next, the CNN is trained using the DSPSS dataset obtained by infrared stress measurement and the 3D structure of defects. The accuracy of the trained CNN is evaluated using DSPSS infrared stress measurements. We discuss the factors that enable us to predict the 3D defect data from the two-dimensional DSPSS using a variational autoencoder. The proposed method makes it possible to estimate internal defect information.

This study aims to enhance the crack phase-field model for ductile fracture by introducing a novel degrading fracture toughness to reflect damage evolution based on the phenomenological justification for the failure mechanism in elastoplastic materials. The free energy consists of elastic, pseudo-plastic and crack components. The governing equations are derived as stationary conditions for the corresponding local and global optimization problems within the continuum thermodynamics framework. Then, we introduce a degrading fracture toughness to reflect the evolution of micro-defects and their coalescences that are caused by both plastic deformation and negative hydrostatic pressure. Equipped with this implement, the proposed crack phase-field model realizes the reduction of both stiffness and fracture toughness to simulate the failure phenomena of elastoplastic materials. Two numerical examples are presented to demonstrate the capability of the proposed model in reproducing typical ductile fracture behaviors.

In this study, a framework that deals with the inverse design of material structures based on macroscopic properties using deep learning models is proposed. For the framework, “polymer alloy's phase separation structures” as material structures and “stresses” as macroscopic properties are considered. The results of self-consistent field analysis are used as structure data, in particular, the analysis result of two-dimensional phase separation structures of a diblock copolymer melt in the equilibrium state. For the stress data, the results of finite element analysis are used, in particular, the analysis results of average stresses over the system under the small-enforced-displacement condition. This framework consists of two deep learning models—one aimed at generating phase separation structures, and the other at predicting properties from structures. For the second model, we incorporate a convolutional neural network. By implementing a random search toward a model that combines these two deep learning models, we constructed the framework for the inverse design of phase separation structures that possess desired macroscopic properties. This framework is demonstrated to be able to suggest phase separation structures that realize desired stresses that are input to the framework through examples. The innovation of the method is the development of framework to propose the optimal structure of polymer alloys by using machine learning. The main novelties of this method are the construction of generative adversarial network that reproduces the phase-separation structure of polymer alloy specified by label information, realization of inverse analysis based on mechanical properties, and the simultaneous optimization of multiple mechanical properties.

In this work, we introduce implicit Finite Operator Learning (iFOL) for the continuous and parametric solution of partial differential equations (PDEs) on arbitrary geometries. We propose a physics-informed encoder-decoder network to establish the mapping between continuous parameter and solution spaces. The decoder constructs the parametric solution field by leveraging an implicit neural field network conditioned on a latent or feature code. Instance-specific codes are derived through a PDE encoding process based on the second-order meta-learning technique. iFOL employs a purely physics-informed loss function derived via the Method of Weighted Residuals. The predicted neural field serves as the test function, resulting in the backpropagation of discrete residuals during the PDE encoding and decoding stages. Compared to the state-of-the-art neural operators, iFOL introduces several key innovations: (1) it bypasses the costly multi-network and supervised encode–process–decode pipeline of conditional neural fields for parametric PDEs; (2) it yields accurate parametric fields and solution-to-parameter gradients, enabling efficient sensitivity analysis regardless of response count; (3) it effectively captures sharp solution discontinuities, which are often challenging for some neural operator models; and (4) it is mesh and geometry agnostic, enabling zero-shot generalization to arbitrary domains. We critically assess these features and analyze the network's ability to generalize to unseen samples across both stationary and transient PDEs. The method is also compared against baseline operator-learning approaches, demonstrating its potential for tackling complex problems in computational mechanics.

Topology optimization is an essential tool in computational engineering, for example, to improve the design and efficiency of flow channels. At the same time, Ising machines, including digital or quantum annealers, have been used as efficient solvers for combinatorial optimization problems. Beyond combinatorial optimization, recent works have demonstrated applicability to other engineering tasks by tailoring corresponding problem formulations. In this study, we present a novel Ising machine formulation for computing design updates during topology optimization with the goal of minimizing dissipation energy in flow channels. We explore the potential of this approach to improve the efficiency and performance of the optimization process. To this end, we conduct experiments to study the impact of various factors within the novel formulation. Additionally, we compare it to a classical method from the literature using the number of optimization steps and the final values of the objective function as indicators of the time intensity of the optimization and the performance of the resulting designs, respectively. Our findings show that the proposed update strategy can accelerate the topology optimization process while producing comparable designs. However, it tends to be less exploratory, which may lead to lower performance of the designs. These results highlight the potential of incorporating Ising formulations for optimization tasks but also show their limitations when used to compute design updates in an iterative optimization process. In conclusion, this work provides an efficient alternative for design updates in topology optimization and enhances the understanding of integrating Ising machine formulations in engineering optimization.