International Journal for Numerical Methods in Engineering最新文献

Topology optimization (TO) has been a cornerstone of advanced structural design for decades, yet it continues to face challenges in terms of convergence, optimality, and numerical stability, particularly for complex, non-convex problems like stress minimization. This paper introduces a novel approach to stress-based topology optimization through the development of neural-reparameterized topology optimization using the convolutional Kolmogorov-Arnold network (KATO). KATO uses the neural network to reparameterize the optimization problem, offering a unique solution to the challenges posed by stress minimization in TO. It also simplifies the penalization scheme by reducing sensitivity to certain parameters, which reduces the non-convexity of the stress minimization problem, enhancing convergence and stability. Our method demonstrates better performance in stress minimization compared to conventional approaches and a different neural network-based approach, achieving up to 10% lower maximum stress in common benchmark cases. KATO also shows remarkable efficiency, reducing computational time by up to 67% compared to conventional methods for stress minimization problems. We conduct a comprehensive analysis of KATO's performance, computational cost, scalability, and the impact of various neural network architectures. Our results indicate that KATO not only improves stress optimization but also offers insights into the relationship between neural network design and topology optimization performance, paving the way for more efficient and effective structural design processes.

Simulations of blood flow in patient-specific models of heart ventricles is a rapidly developing field of research, showing promise to improve future treatment of heart diseases. Fluid-structure interaction simulation of the mitral valve, with its complex structure including leaflets, chordae tendineae, and papillary muscles, provides additional prospects as well as challenges to such models. In this study, we combine a patient-specific model of the left ventricle with an idealized unified continuum fluid-structure interaction model of the mitral valve, to simulate the intraventricular diastolic blood flow. To the best of our knowledge, no monolithic fluid-structure interaction model, without the need for remeshing, has ever been used before to simulate the native mitral valve within the left ventricle. The chordae tendineae are simulated as a region of porous medium, to partially hinder the flow. Simulation results from this model are compared to those of a model with the same patient-specific left ventricle, but with the mitral valve simply modeled as a time-variant inflow boundary condition. The blood flow is analyzed with the E-wave propagation index, and by use of the triple decomposition of the velocity gradient tensor, which decomposes the flow into rigid body rotational flow, shearing flow, and irrotational straining flow. The triple decomposition enables analysis of the formation of initially large dominant flow features, such as the E-wave jet and the vortex ring around it, and their subsequent decay into smaller turbulent flow structures. This analysis of the development of flow structures over the duration of diastole appears to be in general agreement with the theory of the stability of rotation, shear, and strain structures. Elevated shear levels are investigated, but are found only in limited amounts that do not indicate significant risks of thrombus formation or other blood damage, which is to be expected in this healthy ventricle. The highest shear levels are localized at the leaflets in the fluid-structure interaction model, and at the ventricle wall in the planar model. The computed E-wave propagation indices are 1.21 for the fluid-structure interaction model and 1.90 for the planar valve model, which indicates proper washout in the apical region with no significant risk of blood stasis that could lead to left ventricular thrombus formation.

Assessing the safety and environmental impacts of subsurface resource exploitation and management is critical and requires robust geomechanical modeling. However, uncertainties stemming from model assumptions, intrinsic variability of governing parameters, and data errors challenge the reliability of predictions. In the absence of direct measurements, inverse modeling and stochastic data assimilation methods can offer reliable solutions, but in complex and large-scale settings, the computational expense can become prohibitive. To address these challenges, this paper presents a deep learning-based surrogate model (SurMoDeL) designed for seismic data assimilation in fault activation modeling. The surrogate model leverages neural networks to provide simplified yet accurate representations of complex geophysical systems, enabling faster simulations and analyses essential for uncertainty quantification. The work proposes two different methods to integrate an understanding of fault behavior into the model, thereby enhancing the accuracy of its predictions. The application of the proxy model to integrate seismic data through effective data assimilation techniques efficiently constrains the uncertain parameters, thus bridging the gap between theoretical models and real-world observations.

This study develops a chemo-damage-mechanical coupled phase-field method for modeling two-dimensional and/or three-dimensional hydrogen-assisted transient dynamic cracking in metallic materials. In this method, hydrogen diffusion in solids is described by the evolution of bulk hydrogen concentration governed by the diffusion equation with an extended Fick's law. The hydrogen concentration and the inertial force of solids are incorporated into the governing equations of a non-standard quasi-brittle phase-field model (known as the phase-field regularized cohesive zone model, PF-CZM) capable of modeling complicated multiple crack nucleation, initiation, and propagation with insensitivity to mesh size and length scale. The resultant displacement-damage-hydrogen concentration coupled three-field equation is derived by the finite element Galerkin method and solved using a staggered Newton–Raphson iteration algorithm with an unconditionally stable implicit Newmark integration scheme. The new method was verified by four benchmark examples with hydrogen-free numerical/experimental results for comparison, including quasi-static/dynamic fracture of a notched plate under uniaxial tension, a dynamic crack branching experiment under constant traction, the Kalthoff-Winkler impact fracture experiment, and dynamic fragmentation of a cylinder under internal pressures, with the effects of loading velocity, initial bulk hydrogen concentration, and diffusion time on crack propagation investigated in detail. It is found that the present method is capable of modeling complex 2D and 3D hydrogen-assisted dynamic crack propagation and bifurcation under impact or internal pressure loadings, and thus holds the potential to be used for the structural design of hydrogen storage.

We introduce an approach to computational homogenization which unites the accuracy of interface-conforming finite elements (FEs) and the computational efficiency of methods based on the fast Fourier transform (FFT) for two-dimensional thermal conductivity problems. FFT-based computational homogenization methods have been shown to solve multiscale problems in solid mechanics effectively. However, the obtained local solution fields lack accuracy in the vicinity of material interfaces, and simple fixes typically interfere with the numerical efficiency of the solver. In the work at hand, we identify the extended finite element method (X-FEM) with modified absolute enrichment as a suitable candidate for an accurate discretization and design an associated fast Lippmann-Schwinger solver. We implement the concept for two-dimensional thermal conductivity and demonstrate the advantages of the approach with dedicated computational experiments.