Peridynamics (PD) is a numerical analysis method that can analyze crack growth and propagation phenomena. However, much less PD studies have been done on the energy release rate, which is an important parameter for understanding fracture phenomena. Furthermore, because PD is a numerical analysis method that solves integral equations based on the nonlocal theory, it is known that the accuracy of calculation deteriorates near the boundary. To avoid that problem, we used four PD formulations in calculating the energy release rate using the E-integral formula, and compared it with the exact solution. As a result, we have shown that the energy release rate can be obtained with high accuracy for the NOSB-PD FEM coupled analysis, and furthermore, path-independent can be obtained with high accuracy by limiting the integral path to the FEM region.

This study proposes novel conservative filters for uniformly spaced grids. The original conservative filters, proposed by Vreman, are extended by developing a filter matrix that is symmetric stochastic and pentadiagonal, rather than tridiagonal. When the original conservative filters are applied to uniform grids, once the coefficients of the filters at the interior nodes are established, the coefficients of the filter at the boundary can be determined uniquely. This study improves the flexibility of adjusting the filter strength near the boundaries. The numerical results suggest that the developed filters can be applied when it is essential that filters neither increase the global maximum nor decrease the global minimum of a variable.

We propose an ellipsoidal particle model for the Moving Particle Hydrodynamics (MPH) method to reduce the computational cost in thin calculation geometries. The Lagrangian and dissipation functions of the MPH method are extended for an ellipsoidal particle model, which has an ellipsoidal influence domain. The governing equations of the ellipsoidal MPH method are derived from the extended Lagrangian with dissipation. The proposed ellipsoidal MPH method was applied to calculate a hydrostatic problem, the evolution of a droplet, and a dam break problem. The results of the former two calculations showed good agreement with the theoretical solutions. In the dam break calculation, the front position agreed well with the experiment, both with and without the ellipsoidal particle model. However, the dependence on the aspect ratio of the ellipsoidal particle was observed in the shape of splashes.

This study investigates simulations using particle methods for liquid mixing based on free surface wave phenomena. Periodic excitation waves were applied to the gas-liquid interface to induce waves, predicting the mixing process of two liquids. The cubic interpolated propagation (CIP) method was employed to predict the wave phenomena on the liquid surface. Additionally, the moving particle semi-implicit (MPS) method was used to predict the diffusion process of the stirred liquids. The MPS method also predicted the movement, coalescence, and breakup of bubbles introduced from the atmosphere. By utilizing flow velocity information from the CIP method's computational mesh, the MPS method efficiently predicted complex mixing phenomena with fewer meshes. The predicted mixing phenomena showed good agreement with experimental results regarding the size of the swirling flow and the vortex center position. Furthermore, it was revealed that bubbles introduced from the atmosphere affect the mixing process.

The seismic fragility curve (SFC) used for probabilistic seismic risk assessment adopts a theoretical probability distribution function in many previous studies. However, focusing on plural members consisting of the structure, it is possible that the members contributing to the damage change sequentially depending on the seismic intensity, and the shape of the SFC of the structural system is not always characterized as theoretical probability distribution. In this study, the SFC of the member is evaluated with the Monte Carlo simulation, then the SFC of the structural system is obtained as a composition of those SFCs of members, and the random variables of the SFC of structural system are evaluated.

In this paper the development of natural vibration analysis method for two types of thin-walled shell structures using the isolated element method is presented. The shell elements are a generalized quadrilateral thin-walled shell element with two orthogonal curvatures and a cylindrical thin-walled shell. The isolated element method (IEM) proposed by the authors is a discretized analysis method with divided elements. It extends the minimum potential energy principle without using nodes between elements, Lagrange multiplier method and penalty method. The continuity is satisfied by natural boundary conditions at the element boundaries. The admissible function in the element includes rigid body displacements and rotations using the local coordinate system is used and can be defined arbitrarily to some extent. On the other hand, noise and acoustic problems require analysis over a wide frequency range from low frequencies to high frequencies, requiring a large number of degrees of freedom in the analysis. By taking advantage of the characteristics of the isolating element method, natural vibration analysis in these wide frequency ranges can be performed with high accuracy using a small number of elements compared to the conventional FEM. In this presentation the basic theory of shell is based on Flügge's theory (Flügge-Goldenveizer-Novozhilov equations) and using the previously reported results for the basic plane stress field and plate bending, the equations for the generalized quadrilateral shell elements and the cylindrical shell are described. Numerical examples of the cylindrical shell are shown.

Three-node isoparametric elements are widely used for solving various one-dimensional problems with finite element discretization. However, it is not well known that the value of the Jacobian at either end of an element can be zero or negative when the interior node is placed at particular positions inside the element. In this study, we propose a simple remedy to fix this problem, and the proposed method is applied to the discretization of the one-dimensional advection-diffusion equation. With the use of this proposed scheme, accurate numerical results are obtained on two types of unequally spaced meshes, whereas the numerical solution obtained using isoparametric elements diverges from the analytical solution on one of the meshes, whose nodes are more concentrated in the vicinity of the edges of the domain. This proves the robustness of the proposed method on any unequally divided mesh.

The purpose of this study is to develop a more general and accurate empirical formula of ballistic limit velocity than the conventionally used Ballistic Research Laboratory (BRL) formula. After presenting a unified description of the conventional empirical formulae, an empirical formula including fitting parameters is proposed. Then, the parameters of the proposed formula are determined using the results of perforation tests and finite element analyses considering the strain rate dependence of material strength and fracture in SUS304 steel plates, and it is shown that it is possible to develop a penetration evaluation equation that enables highly accurate evaluation than the BRL formula.

Gurson model is capable of describing the plastic deformation of Mises metal with the plastic ductile damage. It has been extended to take the nucleation, the growth and the coalescence of the voids into account. However, it is incapable of describing the plastic strain rate for the change of stress inside the yield surface, since the interior of the yield surface is assumed to be the purely-elastic domain. Further, it is incapable of describing the accumulation of plastic strain during the cyclic loading of stress inside the yield surface. Furthermore, it is incapable of describing the rate-dependent behavior, i.e. the viscoplastic deformation. Then, in this article, Gurson model is extended to describe the viscoplastic deformation with the viscoplastic ductile damage by incorporating the subloading-overstress model, which is capable of describing not only the monotonic but also the cyclic loading behavior. The validity of the present model is verified by the comparison with test data.

Accurate bending energy modeling is crucial for morphogenetic simulations using cell-center models, especially on anisotropic meshes where remeshing is precluded because vertices represent biological cells. This study addresses the open question of which bending-energy discretization methods are most suitable by evaluating 13 distinct models. Accuracy was first assessed by comparing numerically computed bending energy and forces against theoretical values for static wrinkled planar and smooth spherical sheets with varying mesh anisotropy. Subsequently, dynamic simulations of wrinkle formation driven by anisotropic (uniaxial) and isotropic (random) cell division were performed, analyzing the resulting wavenumber patterns against theoretical scaling predictions. Results indicate that model suitability depends on the application: least-squares fitting methods, particularly the Hamann model, demonstrate superior accuracy for quantitative predictions, while the computationally efficient Jülicher model suffices for capturing qualitative morphological trends. These findings guide the selection of bending-energy discretizations, facilitating more accurate and efficient modeling of morphogenesis involving anisotropic tissues.

Recently, a machine learning model called Physics-Informed Neural Network (PINN) was proposed to address the black box problem of machine learning. This study applied PINN to the flow field behind a simple two-dimensional block. We designed PINN that incorporates the continuity equation and the Navier-Stokes equations for incompressible fluids into the loss function and outputs the flow velocities and pressure in the block wake. We demonstrated the performance of PINN in accurately predicting the flow field in the block wake. Furthermore, a comparison between the PINN and a conventional neural network model highlighted the superiority of the PINN in achieving high prediction accuracy even with a small amount of training data, as its outputs inherently comply with the physical laws of fluid dynamics.