The Gazelle Optimization Algorithm (GOA) is an innovative metaheuristic inspired by the survival tactics of gazelles in predator-rich environments. While GOA demonstrates notable advantages in solving unimodal, multimodal, and engineering optimization problems, it struggles with local optima and slow convergence in high-dimensional and non-convex scenarios. This paper proposes the Hybrid Gazelle Optimization

The characterization of porous media via digital testing usually relies on intensive numerical computations that can be parallelized in GPUs. For absolute permeability estimation, Stokes flow simulations are carried out at the micro-structure to recover velocity fields that are used in upscaling with Darcy’s law. Digital models of samples can be obtained via micro-computed tomography (μCT) scans. As

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant

Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such operator learning models not only predict particular instances of a physical or biological system in real-time but also forecast classes of solutions corresponding to a distribution of

The Coherent Nodal Cluster (CoNC) model-reduction technique is used to construct an algebraic transformation from nodal degrees of freedom to generalized degrees of freedom for compact (coherent) clusters of nodes. The novel idea here is to construct a coarse-grid preconditioner for a conjugate gradient solver based on the CoNC technique, and integrate it into a two-level Schwarz algorithm. The finite

Traditional low-rank approximation is a powerful tool for compressing large data matrices that arise in simulations of partial differential equations (PDEs), but suffers from high computational cost and requires several passes over the PDE data. The compressed data may also lack interpretability thus making it difficult to identify feature patterns from the original data. To address these issues, we

Quasi-zero stiffness (QZS) is highly demanded in passive vibration isolators. Most of the existing design methods of QZS vibration isolators are typically based on mechanism designs, where pre-defined structural configurations, components, or mechanisms with certain features, such as negative stiffness, are required to synthesize the designs. This work introduces topology optimization for QZS structure

These days, deep learning (DL) techniques are regarded as an effective substitution of refined finite element models to conduct structural dynamics analysis. Nevertheless, the efficacy of DL methods overwhelmingly depends on the quality and quantity of the data. Since high-fidelity (HF) data are accurate enough but usually time-consuming and costly, while low-fidelity (LF) data are low-cost and efficient

Operator learning focuses on approximating mappings G†:U→V between infinite-dimensional spaces of functions, such as u:Ωu→R and v:Ωv→R. This makes it particularly suitable for solving parametric nonlinear partial differential equations (PDEs). Recent advancements in machine learning (ML) have brought operator learning to the forefront of research. While most progress in this area has been driven by

Corrosion-induced deterioration poses a significant threat to the serviceability of reinforced concrete (RC) structures. This study develops a comprehensive mesoscale model utilizing dual-phase field methods to capture the entire time-dependent chloride-induced corrosion and cracking mechanisms, incorporating interactive multi-physics. The model accurately delineates the evolution of corrosion morphology

A poroelastic medium is defined as a continuous system in which the mechanical response arises from the interaction between a deformable elastic solid skeleton and a pressurised fluid, fully saturating the interconnected porous network. The coupled theory of Poromechanics is effectively employed to solve a broad class of problems spanning various fields, ranging from its original application in Geomechanics

This paper develops an uncertainty-quantified parametrically upscaled continuum damage mechanics (UQ-PUCDM) model for efficient multiscale analysis of unidirectional composite structures. Its constitutive parameters explicitly incorporate representative aggregated microstructural parameters (RAMPs), connecting structural response to the local microstructure. Uncertainty quantification accounts for

This paper presents the formulation of a robust integrated framework for the coupled multiphysics and multiple fracture growth analysis in porous media. The finite element-based thermo-hydro-mechanical method for fracture growth with frictional contact (THMf-g) simultaneously solves monolithically coupled equations, incorporating contact and frictional constraints from fracture sliding. It also implements

Engineering design problems often involve solving parametric Partial Differential Equations (PDEs) under variable PDE parameters and domain geometry. Recently, neural operators have shown promise in learning PDE operators and quickly predicting the PDE solutions. However, training these neural operators typically requires large datasets, the acquisition of which can be prohibitively expensive. To overcome

Accurate modeling of fluid-particle interactions in geotechnical systems, particularly those involving irregular particles, presents significant challenges in computational mechanics, necessitating a versatile Eulerian-Lagrangian framework capable of handling diverse particle geometries. This paper presents a novel point cloud-based semi-resolved CFD-DEM coupling method to ensure accurate void fraction

Wildland fires pose a terrifying natural hazard, underscoring the urgent need to develop data-driven and physics-informed digital twins for wildfire prevention, monitoring, intervention, and response. In this direction of research, this work introduces a physics-informed neural network (PiNN) designed to learn the unknown parameters of an interpretable wildfire spreading model. The considered modeling

This work suggests a reliable contact algorithm for simulating adhesion between soft bodies based on the isogeometric analysis. To accurately characterize adhesion-contact regional effects, a modified exponential cohesive zone model is proposed by incorporating a real contact area influence factor into the original exponential cohesive zone model. Considering the nonlinear large-deformation effect

Numerical simulations are crucial for comprehending how engineering structures behave under extreme conditions, particularly when dealing with thermo-mechanically coupled issues compounded by damage-induced material softening. However, such simulations often entail substantial computational expenses. To mitigate this, the focus has shifted towards employing model order reduction (MOR) techniques, which

This work considers the nodal finite element approximation of peridynamics, in which the nodal displacements satisfy the peridynamics equation at each mesh node. For the nonlinear bond-based peridynamics model, it is shown that, under the suitable assumptions on an exact solution, the discretized solution associated with the central-in-time and nodal finite element discretization converges to a solution

Lattice structures offer significant advantages, including high strength-to-weight ratios, efficient material use, and customizable properties, making them ideal for applications ranging from aerospace components to biomedical implants. However, existing lattice structure design and optimization methods either do not consider the self-supporting property of the generated lattice structures or construct

In this study, a topology optimization technique with stress control is proposed for the composite laminates. The bi-directional evolutionary structural optimization (BESO) method is selected to avoid the stress singularity. The technique expresses the failure index based on the Tsai-Wu criterion, thereby ensuring a comprehensive consideration of the anisotropy. To address the local nature of stress

Model Order Reduction (MOR) is a core technology for the creation of comprehensive executable Digital Twins, since it efficiently reduces the computational burden of high-fidelity models. When dealing with nonlinear structural Finite Element analyses, several Hyper-Reduction (HR) approaches have been developed to reduce the computational cost. Nonetheless, HR approaches are typically intrusive in nature

In this contribution, a new design framework leveraging Bayesian optimisation is developed to enhance the efficiency and quality of material and structural design processes. The proposed framework comprises two main steps. The first step involves efficiently exploring the design space with a minimum number of sampled points to mitigate computational costs. In the subsequent step, a composite Bayesian

To alleviate the intensive computational burden of reliability analysis, a new parallel active learning reliability method is proposed from the multi-point look-ahead paradigm. First, in the framework of probability density evolution method, a global measure of epistemic uncertainty about Kriging-based failure probability estimation, referred to as the targeted integrated mean squared error (TIMSE)

In this study, a novel scaled coordinate transformation boundary element method (SCTBEM) is proposed to solve the transient heat transfer problem of three-dimensional (3D) functionally gradient materials. In order to compute the coefficient matrix only once when solving transient problems, the fundamental solution of Laplace operator is used to derive the boundary-domain integral equation. To maintain

Neurodevelopmental disorders (NDDs) have arisen as one of the most prevailing chronic diseases within the US. Often associated with severe adverse impacts on the formation of vital central and peripheral nervous systems during the neurodevelopmental process, NDDs are comprised of a broad spectrum of disorders, such as autism spectrum disorder, attention deficit hyperactivity disorder, and epilepsy

This paper introduces the Temporal Graph Neural Network-based Simulator (TGNNS), a novel physical-information-flow-constrained deep learning-based simulator for granular material modeling. The TGNNS leverages a series of frames, each representing material point positions, enabling particle dynamics to propagate through the sequence, resulting in a more physically grounded architecture for granular

AI for partial differential equations (PDEs) has garnered significant attention, particularly with the emergence of Physics-informed neural networks (PINNs). The recent advent of Kolmogorov–Arnold Network (KAN) indicates that there is potential to revisit and enhance the previously MLP-based PINNs. Compared to MLPs, KANs offer interpretability and require fewer parameters. PDEs can be described in

In this paper, the nodal-based continuous-discontinuous deformation analysis method (NCDDAM) is enriched to simulate the thermo-mechanical coupling effects in rock masses. A distance-based contact potential algorithm is first incorporated into NCDDAM to avoid the dependency of element shape and size on the calculation of contact force between different blocks. Then, three types of heat conduction models

Fatigue-constrained topology optimization (FCTO) is a currently research hotspot, and its fatigue constraints have material property dependency, highly nonlinear, and local features, which lead to challenges for the algorithm stability, computational efficiency, and different material application of FCTO. This research provides a FCTO method for structures subjected to variable-amplitude fatigue loading

Embedded or immersed boundary methods (IBM) are powerful mesh-based techniques that permit to solve partial differential equations (PDEs) in complex geometries circumventing the need of generating a mesh that fits the domain boundary, which is indeed very difficult and has been the main bottleneck of the simulation pipeline for decades. Embedded methods exploit a simple background mesh that covers

Data assimilation combines (imperfect) knowledge of a flow’s physical laws with (noisy, time-lagged, and otherwise imperfect) observations to produce a more accurate prediction of flow statistics. Assimilation by nudging (from 1964), while non-optimal, is easy to implement and its analysis is clear and well-established. Nudging’s uniform in time accuracy has even been established under conditions on

Data-driven surrogate modeling has surged in capability in recent years with the emergence of graph neural networks (GNNs), which can operate directly on mesh-based representations of data. The goal of this work is to introduce an interpretability enhancement procedure for GNNs, with application to unstructured mesh-based fluid dynamics modeling. Given a black-box baseline GNN model, the end result

A novel Isogeometric topology optimization (ITO) method considering stress constraint and load uncertainties is proposed for the fiber reinforced composite structures. Firstly, with the density and fiber orientations at the control points of Non-Uniform Rational B-Splines (NURBS) defined as design variables while the magnitudes and direction angles of uncertain external loads described as interval

This paper develops a novel Hybrid Particle Element Method (HPEM) to model large deformation problems in solid mechanics, combining the strengths of both mesh-based and particle approaches. In the proposed method, the computational domain is discretized into two independent components: a set of finite elements and a set of particles. The finite elements serve as a temporary tool to compute the spatial

High-temperature oxidation damage in C/SiC composite, alongside mechanical failure, has becoming a focal point of developing high performance motor components. However, most of existing models focus on only one field and thus can hardly to simulate a complete process. To address this, a thermodynamically consistent phase field model tailored specifically for C/SiC composites is proposed. This model

A complete understanding of the wrinkling of compressed films on curved substrates remains illusive due to the limitations of both analytical and current numerical methods. The difficulties arise from the fact that the energetically minimal distribution of deformation localizations is primarily influenced by the inherent nonlinearities and that the deformation patterns on curved surfaces are additionally

The phase field model (PFM) has emerged as a popular computational framework for analyzing and simulating complex fracture problems. Despite PFM's inherent capacity to model relatively complex fracture phenomena such as nucleation, branching, deflection, etc., the computational costs involved in the analysis are quite high. Hence, a multi-level adaptive mesh refinement framework is proposed for a unified

In this paper, a novel time-weighted residual methodology is developed in the two-field form of structural dynamics problems to enable generalized class of optimal zero-order overshooting Linear Multi-Step (LMS) algorithms by design. For the first time, we develop a novel time-weighted residual methodology in the two-field form of the second-order time-dependent systems, leading to the newly proposed

We propose a novel framework of generalised Petrov–Galerkin Dynamical Low Rank (DLR) Approximations in the context of random PDEs. It builds on the standard Dynamical Low Rank Approximations in their Dynamically Orthogonal formulation. It allows to seamlessly build-in many standard and well-studied stabilisation techniques that can be framed as either generalised Galerkin methods, or Petrov–Galerkin

The First-Order Reliability Method (FORM) is renowned for its high computational efficiency, but its accuracy declines when addressing the nNar Limit-State Function (LSF). The Second-Order Reliability Method (SORM) offers greater accuracy; however, its approximation formula can sometimes introduce errors. Additionally, SORM requires extra calculations involving the Hessian matrix, which can reduce

We propose a relatively simple and mesh-independent approach to model crack branching and merging using the Shifted Fracture Method (SFM), within the class of Shifted Boundary Methods. The proposed method achieves mesh independency by accurately accounting for the area of the fracture surface, in contrast to traditional element-deletion/node-release techniques. In the SFM, the true fracture is embedded

We consider the coupled Navier–Stokes/transport equations with nonlinear transmission conditions, which constitute one of the most common models utilized to simulate a reverse osmosis effect in water desalination processes when considering feed and permeate channels coupled through a semi-permeate membrane. The variational formulation consists of a set of equations where the velocities, the concentrations

We propose a randomized data-driven solver for multiscale mechanics problems which improves accuracy by escaping local minima and reducing dependency on metric parameters, while requiring minimal changes relative to non-randomized solvers. We additionally develop an adaptive data-generation scheme to enrich data sets in an effective manner. This enrichment is achieved by utilizing material tangent

High fidelity modeling of multiphysical systems is typically achieved using nonlinear coupled differential equations, often with multiscale model coefficients. These simulations are performed using finite-element methods with implicit time stepping. Within each time step, nonlinearities are numerically linearized using Newton-like iterative solvers, which increases the computational complexity. For

We study the numerical approximation of advection–diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method (MsFEM). The latter method is a now classical, finite element type method that performs a Galerkin approximation on a problem-dependent basis set, itself precomputed in an offline stage. The approach is implemented

The statistics obtained from turbulent flow simulations are generally uncertain due to finite time averaging. Most techniques available in the literature to accurately estimate these uncertainties typically only work in an offline mode, that is, they require access to all available samples of a time series at once. In addition to the impossibility of online monitoring of uncertainties during the course

This paper proposes a new infill criterion for the optimization of expensive black-box design problems. The method complements the classical Efficient Global Optimization algorithm by considering the distribution of improvement instead of merely the expectation. During the optimization process, we maximize a penalized expected improvement acquisition function from a specially collected infill candidate

Understanding uncertainty is critical, especially when data are sparse and variations are large. Bayesian neural networks offer a powerful strategy to build predictable models from sparse data, and inherently quantify both, aleatoric uncertainties of the data and epistemic uncertainties of the model. Yet, classical Bayesian neural networks ignore the fundamental laws of physics, they are non-interpretable

The advantages of data science have inspired the development of data-driven approaches for solving constitutive modeling problems, which have become a new research focus in engineering mechanics. These approaches help fully utilize the information inherent in the data, bypassing the traditional modeling processes.

This paper presents a convolution tensor decomposition based model reduction method for solving the Allen–Cahn equation. The Allen–Cahn equation is usually used to characterize phase separation or the motion of anti-phase boundaries in materials. Its solution is time-consuming when high-resolution meshes and large time scale integration are involved. To resolve these issues, the convolution tensor

In this paper, we introduce a novel, data-driven approach for solving high-dimensional Bayesian inverse problems based on partial differential equations (PDEs), called Weak Neural Variational Inference (WNVI). The method complements real measurements with virtual observations derived from the physical model. In particular, weighted residuals are employed as probes to the governing PDE in order to formulate

Non-probabilistic convex models are powerful tools for structural model updating with uncertain‑but-bounded parameters. However, existing non-probabilistic model updating (NPMU) methods often struggle with detecting parameter correlation due to limited prior information. Worth still, the unique core steps of NPMU, involving nested inner layer forward uncertainty propagation and outer layer inverse

Time-dependent deformation and damage in viscoelastic materials exhibit distinct characteristics compared to purely brittle or ductile materials, especially under large deformations. These behaviours become even more complex in the presence of pre-cracks. To model this process, we propose an improved non-ordinary state-based peridynamics (NOSB-PD) with implicit adaptive time-stepping (IATS). The proposed

The computational cost associated with structural reliability analysis increases substantially when dealing with multiple response metrics and high-dimensional input spaces. To address this challenge, an innovative global prediction framework is proposed which leverages multi-output Gaussian process (MOGP) modeling. This framework reduces the computational burden for high-dimensional, multi-response

Uncertainty quantification (UQ) and inference involving a large number of parameters are valuable tools for problems associated with heterogeneous and non-stationary behaviors. The difficulty with these problems is exacerbated when these parameters are statistically dependent requiring statistical characterization over joint measures. Probabilistic modeling methodologies stand as effective tools in

Pulmonary capillary perfusion and gas exchange are physiological processes that take place at the alveolar level and that are fundamental to sustaining life. Present-day computational simulations of these phenomena are based on low-dimensional mathematical models solved in idealized alveolar geometries, where the chemical reactions between O2-CO2 and hemoglobin are simplified. While providing general

This paper presents an innovative methodology that seamlessly integrates the peridynamic method with advanced deep learning techniques, specifically utilizing the Gated Recurrent Unit (GRU) neural network. This integration results in the development of a highly accurate and efficient model for predicting fatigue cracking and life. This model can effectively forecast the fatigue crack patterns and fatigue

The aim of the present work is to design, analyze theoretically, and test numerically, a generalized Dryja–Smith–Widlund (GDSW) preconditioner for composite Discontinuous Galerkin discretizations of multicompartment parabolic reaction–diffusion equations, where the solution can exhibit natural discontinuities across the domain. We prove that the resulting preconditioned operator for the solution of

Modeling damage and failure behaviors of hyperelastic composites under large deformations is pivotal for advancing the design of cutting-edge elastomers used in biomedical engineering and soft robotics. However, existing methods struggle with capturing the non-linearities and singularities in the displacement field under such conditions. To address these difficulties, we propose a novel bond-based