This paper is concerned with non-Hermitian degeneracy and exceptional points in a simple two-dimensional scattering system. We study resonant frequencies associated with multiple scattering between a sound-hard disk and an ellipse situated in the ambient air. To this end, a boundary integral equation is used to characterize the system’s resonant frequencies and is discretized by the Nyström method. This allows us to compute the scattering resonances with the help of a nonlinear eigenvalue solver. The system is parameterized by two geometric parameters: position and rotation angle of the ellipse. We define exceptional points of resonant frequencies and seek them numerically based on hierarchical subdivision of the two-dimensional parameter space. The proposed method, a combination of the boundary integral equation and hierarchical algorithm, does not rely on the sensitivity of resonant frequencies with respect to the system parameters. To illustrate the concepts of non-Hermitian degeneracy and exceptional points, we first study a simple mechanical model and show that the degeneracy is associated with perturbation theory, i.e., how eigenvalues of the system depend on the parameters. Subsequently, we formulate the scattering resonance problem and describe the proposed method for pinpointing exceptional points. Numerical results confirm that the proposed method provides strong numerical evidence of the existence of exceptional points.

Epoxy resin is widely used as a matrix resin of CFRP (Carbon Fiber Reinforced Plastics). It is known that the initial phase of the fatigue fracture of CFRP is the damage of matrix resin near fibers as well as interfacial debonding between fibers and matrix resin on the microscale. Thus, to understand the fatigue property of CFRP, it is necessary to consider the fatigue behavior of epoxy resin. However, permanent deformation occurs under the cyclic loading because of non-linear mechanical properties such as visco-elasticity, plasticity, and visco-plasticity. This research focused on the permanent strain, which is called “accumulated strain” in this research, under fatigue loading. Fatigue tests of epoxy resin were carried out to obtain the relationship between stress, number of cycles, and accumulated strain, in addition to S − N relationship. The test results showed that the values and increasing rates of the accumulated strain depend on the elapsed number of cycles and magnitude of stress. After that, a numerical simulation of CFRP was conducted considering the accumulated strain of the epoxy resin, and fatigue test of CFRP which matrix resin was the same as the previous tests was carried out under the same condition of the fatigue analysis. The results of analysis and test showed agreement except for the high stress condition. Focusing on the numerical results of the accumulated strain on the microscale, it was found that the maximum equivalent accumulated strain when first fatigue damage occurs is a similar value at each stress level and analysis model.

We propose a collocation-based NURBS-enhanced boundary element method in which NURBS surfaces are directly used for exact geometry representation, while piecewise-constant basis functions are employed for field approximation. In three-dimensional boundary element analyses, the accuracy of conventional BEM with piecewise-linear shape functions is often limited by geometric approximation errors. Although isogeometric BEM (IGBEM) naturally combines NURBS geometry with smooth basis functions, it encounters difficulties, for example, in Dirichlet problems when the unknown density is discontinuous at geometric singularities such as edges and corners. These discontinuities might not be handled naturally by smooth basis functions typically used in IGBEM. The proposed method resolves this issue through a simple strategy that adopts constant basis functions for the unknown density while preserving the exact CAD geometry via NURBS surfaces, allowing discontinuities to be represented accurately without special treatments. Numerical experiments demonstrate that the proposed BEM achieves substantially higher accuracy than the conventional one for a fixed number of degrees of freedom (DoFs) and improves the convergence rate of the solution from (DoFs)^−1/2 to (DoFs)⁻¹. Furthermore, the proposed method provides accurate solutions for scatterers with non-smooth edges without requiring additional treatments, making it a practical and efficient alternative to traditional BEM implementations.

Compliant morphing airfoils (CMAs) can improve aerodynamic efficiency and structural integrity through aeroelastic deformation in response to airflow. However, designing them is challenging owing to the coupling between aerodynamic forces and structural responses. This study presents an aerostructural topology optimization method for CMAs that explicitly accounts for static aeroelastic deformation to improve integrated aerostructural performance. A two-way coupled aerostructural analysis, combining the aerodynamic panel method with the structural finite element method, was developed to evaluate aeroelastic behavior. Design sensitivities were obtained using the discrete adjoint method, and topology optimization was applied to determine the internal compliant mechanisms. Numerical examples demonstrate that the optimized CMA achieves simultaneous increases in lift coefficient and actuator input energy through static aeroelastic deformation. The effects of static aeroelastic deformation were then analyzed in detail. These results suggest that allowing static aeroelastic deformation yields a more energy-efficient design than using excessively stiff structures, which demands higher actuator input with limited lift improvement.

This paper discusses a fast direct solver using boundary integral equations for Helmholtz transmission problems involving multiple inclusions in two dimensions. Efficiently addressing scattering problems in the presence of numerous inclusions remains a key challenge for various practical applications. For problems involving a large number of scatterers, the number of iterations in Krylov subspace methods is known to increase significantly. This occurs even when using second-kind boundary integral equations, which are typically recognized for their rapid convergence. We consider a fast direct solver as an alternative, an approach that has been less commonly explored for transmission problems with disjoint multiple inclusions. The low-rank approximation based on the proxy method achieves speedup by calculating interactions between disjoint scatterers without the terms derived from the internal integral representation. Notably, this advantage applies to the Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) formulation but breaks down in the Burton–Miller case. Numerical examples demonstrate that the proposed solver can compress the system of linear algebraic equations to a size of O(ωD), where ω is the frequency of the incident wave and D is the diameter of the (smallest) bounding box enclosing the multiple inclusions. The total computational cost scales as O(N^1.5) (= O(√N³)) at most for a fixed ω when the inclusions are arranged on a grid. Moreover, the PMCHWT formulation, that omits the interior term in the proxy method, is approximately six times faster than the Burton–Miller formulation when treating each inclusion as a cell. Furthermore, in the same setting, the former can compress the size of the system of linear algebraic equations by half compared to the latter.

Hydrogen segregation to strengthening precipitates (γ′′, γ′, and δ) is often invoked to explain hydrogen embrittlement (HE) in Ni-based superalloy 718 (Alloy718); however, its quantitative significance remains insufficiently validated. In this study, we reassess precipitate-related hydrogen trapping by combining first-principles calculations with thermal desorption analysis (TDA) of specimens with controlled precipitation states. Density functional theory (DFT) calculations indicate that energetically favorable sites exist at specific 6Ni octahedral environments in γ′-Ni3Al and at precipitate/matrix interfaces, whereas most sites inside γ′′, γ′-Ni3Ti and δ are not stabilized relative to the γ matrix. When the interface energetics are summarized using the median and interquartile range, the typical trapping strength is shallow, while deeper sites are limited to specific local environments. TDA measurements show only minor changes in macroscopic hydrogen uptake among the specimens, suggesting that equilibrium hydrogen partitioning to precipitates and their interfaces is quantitatively limited. A first-order equilibrium partitioning analysis indicates that precipitate-related trapping is dominated by shallow, reversible traps, and that the extent of hydrogen enrichment at precipitates may have been overstated in simplified interpretations. By integrating theoretical predictions with experimental observations, this study clarifies the intrinsic characteristics and quantitative significance of precipitate-related H trapping in Alloy 718.

Synchrotron X-ray nano-computed tomography (nano-CT) was employed to achieve high-resolution four-dimensional (3D + deformation step) visualization of deformation-induced martensitic transformation (DIMT) in a metastable austenitic steel during interrupted tensile deformation. The identical region of interest was precisely aligned and tracked at each deformation step, enabling direct three-dimensional observation of nucleation, growth, and coalescence of individual martensite plates. With an effective voxel size of 40.4 nm and a spatial resolution of approximately 180 nm, needle-like martensite plates were resolved, and their evolution along multiple habit-plane traces was visualized. Complementary projection-type micro-CT provided a wide-field overview of the transformation distribution in the bulk specimen; the martensite phase was identified as darker grey objects owing to contrast between the austenite and martensite phases, and grey-value profiles enabled discrimination between martensite and microvoids. The combined micro- and nano-CT approach provides multi-scale 4D visualization of DIMT, linking overall transformation progression to high-resolution plate evolution in the same specimen.