This paper introduces a novel active learning kriging-based reliability analysis method that uses uniform sampling and local refinement, termed AK-UL, with a focus on problems involving small failure probabilities. Traditional methods, such as AK-MCS, struggle to identify failure regions efficiently because of the irregular distribution of candidate points and the high computational cost of generating

Efficient estimation of small failure probability subjected to multiple failure domains is one of the central and challenging issues in structural reliability analysis and other rare event analysis tasks, especially in case where the computational resource is quite limited but high accuracy is required. A new active learning scheme, named as Transitional Bayesian Quadrature (TBQ), is proposed to fill

With the growing application of deep learning techniques in computational physics, physics-informed neural networks (PINNs) have emerged as a major research focus. However, today’s PINNs encounter several limitations. Firstly, during the construction of the loss function using automatic differentiation, PINNs often neglect information from neighboring points, which hinders their ability to enforce

Computational homogenization methods open the possibility to simulate engineering structures on two scales simultaneously and to accurately describe complex macroscopic material behavior. Their intrinsically high computational cost can be alleviated through model order reduction methods in combination with hyper-reduction. The recently proposed E3C hyper-reduction method is applied to plane-strain

Multiscale structural design is an emerging field within the aerospace community driven by the need for innovative structural concepts capable of fulfilling ever-expanding performance requirements. However, exploring novel material systems or architectures at the preliminary design stage can be inefficient due to potential changes in objectives, boundary conditions, and constraints. Such changes often

Predicting the thermal fatigue life of flexoelectric components is of great engineering significance. In this study, an effective adaptive phase-field model combined with the cycle jump scheme is proposed to simulate thermo-electro-mechanical fatigue fracture in flexoelectric solids. To provide C1 continuity due to the presence of strain gradients, the phase-field model is implemented in the multi-patch

Design for continuous fiber-reinforced polymer additive manufacturing (CFRP-AM) has evolved from sequential approaches to concurrent design methods, enabling the simultaneous optimization of structural topology and fiber toolpaths. However, existing studies fails to consider the manufacturing constraints inherent to CFRP-AM, such as toolpath width consistency and fiber continuity, which are critical

Engineering shell structures have been extensively used in aerospace, automotive and other fields, whose aerodynamic performance is significant in structural design. In the current work, the primary intention is to propose an aerodynamic topology optimization design framework for arbitrary engineering shell structures using the T-splines-based panel method and isogeometric analysis. Firstly, the T-splines-based

The structural reliability analysis subject to epistemic uncertainty and multidimensional correlations among input variables signifies a crucial and demanding task. To address this challenge, a new evidence theory model capable of quantifying complex multidimensional correlations is proposed in this study; and further, an efficient reliability analysis method is developed. To start with, the multidimensional

Structures composed of multiple lattice materials have exceptional mechanical properties due to their rationally designed macrostructures and microstructures, which have enabled diverse engineering applications. However, existing topology optimization approaches for such structures often face challenges in achieving generality and flexibility, particularly in designing the thickness of interfacial

Physics-informed neural networks (PINNs) hold promise for solving partial differential equations (PDEs), but they often face challenges in achieving high accuracy, especially in complex, real-world scenarios. This paper presents an adaptive deep PINN (ad-PINN) framework designed to enhance the efficiency of both activation and loss functions. The proposed ad-PINN introduces two main innovations: (1)

The aim of this paper is to introduce, analyze and test in practice a new mathematical model describing the interplay between biological tissue atrophy driven by the diffusion of a biological agent, with applications to neurodegenerative disorders. This study introduces a novel mathematical and computational model comprising a Fisher–Kolmogorov equation for species diffusion coupled with an elasticity

We consider elliptic problems in multipatch isogeometric analysis (IGA) where the patch parameterizations may be singular. Specifically, we address cases where certain dimensions of the parametric geometry diminish as the singularity is approached — for example, a curve collapsing into a point (in 2D), or a surface collapsing into a point or a curve (in 3D). To deal with this issue, we develop a robust

Advances in additive manufacturing and tow-steered processes are now enabling the fabrication of fiber-reinforced composites (FRCs) with architected microstructures, via complex curvilinear fiber paths/layouts, for desired structural response at the macroscale. Engineers can leverage these advances, via multiscale topology optimization (MTO), to design structures with optimized macro and microstructures

Thin structures and shells in particular are well-known to be highly sensitive to manufacturing imperfections such as perturbations on the profile of a shell of revolution. The main result of this study is that one cannot expect to apply standard models for perturbations, such as Karhunen–Loève expansions, without careful consideration on how the applied model depends on the regularity of the random

This work formulates compact and efficient surrogates of the stress field for sheet-network, triply periodic minimal surface (TPMS) lattices, which have been gaining popularity due to advancements in additive manufacturing methods. The proposed surrogates can be employed to determine, for example, the largest von Mises or principal stresses in a TPMS lattice as a function of the wall thickness, base

The discrete quasi-static response of rate-independent dissipative granular media is addressed. Granular systems are conventionally simulated with methods that are intrinsically dynamic, such as the discrete element (DEM) and discontinuous deformation (DDA) methods, with the particles’ accelerations and damping being essential aspects. In contrast, quasi-static methods derive from the static stiffness

Bayesian updating, as a useful tool for system identification and model calibration, has gained signification traction in recent years. However, for time-dependent models, the number of observations will increase rapidly with the increase of the number of time nodes, resulting in Bayesian updating problems facing serious challenges. To settle this issue, this paper proposes an efficient Bayesian updating

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary

Similar to quasi-brittle materials, it has been recently shown that elastomers can exhibit a macroscopically diffuse damage zone that accompanies the fracture process. In this study, we introduce a stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm

We consider iterative algebraic solvers for saddle-point mixed finite element discretizations of the model Darcy flow problem. We propose a posteriori error estimators of the algebraic error as well as a nonoverlapping domain decomposition algorithm. The estimators control the algebraic error from above and from below in a guaranteed and fully computable way. The distinctive feature of the domain decomposition

In this work, we present a novel isogeometric topology optimization (TO) method for shell structures that involve complex design domains. In particular, analysis-suitable unstructured T-splines (ASUTS) are used to represent complex design domains in a smooth and watertight manner. On top of such domains, minimum compliance is studied as the model problem, where the Kirchhoff–Love shell is used to compute

The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input

We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of boundary observations for typical solutions (collective data) and a bulk measurement of a specific realization. To leverage this collective data, we first compress the

A data-free predictive scientific AI model, termed Tensor-decomposition-based A Priori Surrogate (TAPS), is proposed for tackling ultra large-scale engineering simulations with significant speedup, memory savings, and storage gain. TAPS does not require any training data and can effectively obtain surrogate models for high-dimensional parametric problems with equivalently zetta-scale (1021) degrees

In this work, we develop a hybrid phase-field modeling approach, enhanced by a higher-order nonlocal operator method (NOM) to simulate dynamic brittle fracture in fiber-reinforced composites. This approach captures dynamic fracture patterns in composite materials, including matrix cracking, interfacial debonding, and the interaction between these failure modes. A crack surface density function is applied

Equidistant fiber placement structures exhibit significant advantages in both mechanical performance and manufacturability. This paper addresses the challenge of forming continuous, manufacturable fiber paths from discrete fiber optimization results. Leveraging the ability of B-splines to represent complex shapes and offer local control, we propose a method that uses B-spline as the base curve for

This study proposes a novel porosity-based mechanics model for investigating the crack evolution in concrete under uniaxial compression. This model accounts for the porosity gradient and heterogeneous mechanical properties within the concrete’s interfacial transition zone (ITZ). Validation against experimental results from the literature and international standards demonstrates the model’s accuracy

Time-dependent reliability analysis has proven to be an invaluable tool for assessing the safety levels of engineering structures subject to both randomness and time-varying factors. In this context, single-loop active learning Kriging methods have demonstrated a favorable trade-off between efficiency and accuracy. However, there remains significant potential for further improvement, particularly in

Modeling dynamic behavior and large deformation in porous media, encompassing coupled fluid flow, solid deformation, and heat transfer, remains a critical challenge in geomechanics. While the two-phase material point method (MPM) combined with the semi-implicit fractional step method (FSM) has demonstrated efficacy for saturated porous media under large deformation, traditional FSM is constrained to

In this paper, we propose a convolutional neural network (CNN) based reduced-order modeling (ROM) to solve parametric nonlocal partial differential equations (PDEs). Our method consists of two main components: dimensional reduction with convolutional autoencoder (CAE) and latent-space modeling with CNN or long short-term memory (LSTM) networks. Our neural network-based ROM bypasses the main challenges

This paper presents an efficient and accurate methodology for computing displacement and stress fields in laminated thick plates using two-dimensional models. The approach begins with a novel one-dimensional finite element analysis across the thickness to derive transverse shear warping functions for a given layup. This preliminary analysis ensures accuracy for generic laminations, including asymmetric

Advancements in computational fluid mechanics have largely relied on Newtonian frameworks, particularly through the direct simulation of Navier–Stokes equations. In this work, we propose an alternative computational framework that employs variational methods, specifically by leveraging the principle of minimum pressure gradient, which turns the fluid mechanics problem into a minimization problem whose

In engineering structures and mechanical systems, the arrangement of supports or Dirichlet boundary conditions determines the constraint conditions and the distribution of degrees of freedom, thereby exerting a critical influence on performances. This paper proposes a novel integrated design method for structures and supports. First, a hybrid explicit–implicit topology description framework is developed

Single-material topology optimization designs struggle to achieve the free selection of multiple materials in vibro-acoustic structures while adhering to budgetary and spatial constraints to obtain optimal objective performance. To address this challenge, this paper proposes a novel topology optimization approach tailored for multi-material vibro-acoustic structures based on the multi-material floating

We present variational sequential optimal experimental design (vsOED), a novel method for optimally designing a finite sequence of experiments within a Bayesian framework with information-theoretic criteria. vsOED employs a one-point reward formulation with variational posterior approximations, providing a provable lower bound to the expected information gain. Numerical methods are developed following

In this work, we generalize the mass-conserving mixed stress (MCS) finite element method for Stokes equations (Gopalakrishnan et al., 2019), involving normal velocity and tangential-normal stress continuous fields, to incompressible finite elasticity. By means of the three-field Hu–Washizu principle, introducing the displacement gradient and 1st Piola–Kirchhoff stress tensor as additional fields, we

Traditional constitutive models rely on hand-crafted parametric forms with limited expressivity and generalizability, while neural network-based models can capture complex material behavior but often lack interpretability. To balance these trade-offs, we present monotonic Input-Convex Kolmogorov-Arnold Networks (ICKANs) for learning polyconvex hyperelastic constitutive laws. ICKANs leverage the Kolmogorov-Arnold

This paper focuses on the numerical solution of elliptic partial differential equations (PDEs) with Dirichlet and mixed boundary conditions, specifically addressing the challenges arising from irregular domains. Both finite element method (FEM) and finite difference method (FDM), face difficulties in dealing with arbitrary domains. The paper introduces a novel nodal symmetric ghost method based on

This paper introduces a novel computational design framework for topology and fiber path optimization of variable stiffness laminated composites. Based on the finite element discretization of the design domain, the topology and material stiffness are represented using elemental densities and lamination parameters (LPs), respectively. The density distribution is optimized via the discrete-variable topology

Many materials, such as clays, fresh concrete, and biological fluids, exhibit elasto-viscoplastic (EVP) behaviour, transitioning between solid and fluid states under varying stress conditions. Among EVP models, Saramito’s constitutive law stands out for its thermodynamic consistency, smooth solid-to-fluid transition, and ability to accurately represent diverse materials with only four easily determinable

We introduce an FFT-based Galerkin homogenization scheme, which, in combination with the level-set method, allows us to study the evolution of ferroelectric domain nuclei in the experimentally relevant stress-driven setting. Our proposed framework includes an accelerated FFT-solver for solving the electromechanically coupled balance laws and a unified regularized driving force formulation for the level-set

Adaptive Kriging model has gained growing attention for its effectiveness in reducing the computational costs in time-dependent reliability analysis (TRA). However, the existing methods struggle to identify critical sample regions, leverage parallel computational resources, and assess the value for sample trajectories, thus restricting improvement in accuracy and efficiency. To address the challenges

We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates

This work outlines a Lattice Boltzmann Method (LBM) for geometrically and constitutively non-linear solid mechanics to simulate large deformations under dynamic loading conditions. The method utilises the moment chain approach, where the non-linear constitutive law is incorporated via a forcing term. Stress and deformation measures are expressed in the reference configuration. Finite difference schemes

Shakedown analyses require a precise evaluation of pointwise elastic stresses and, at the same time, an accurate representation of the elastoplastic solution for capturing the ratcheting mechanisms effectively. However, existing discretization methods often face a trade-off: techniques that optimize plasticity performance may compromise elastic accuracy, and vice versa. The Hybrid Virtual Element Method

This paper proposes an effective and robust decoupled approach for addressing reliability-based design optimization (RBDO) problems. The method iteratively performs a parallel constrained Bayesian optimization (PCBO) with deterministic parameters based on the most probable point (MPP) underpinning limit-state functions (LSFs) sequentially updated through an enhanced active learning-based reliability

In density-based topology optimization of flow problems, flow in the solid domain is generally inhibited using a penalization approach. Setting an appropriate maximum magnitude for the penalization traditionally requires manual tuning to find an acceptable compromise between flow solution accuracy and design convergence. In this work, three penalization approaches are examined, the Darcy (D), the Darcy

In this paper, a time-dependent reliability-based double-scale topology optimization (TO) framework considering manufacturability is proposed. The proposed TO model focuses on the structural transient dynamic performance subjected to general dynamic loads. A time-dependent interval non-probabilistic reliability theory based on the idea of first-passage is introduced into the double-scale TO model to

We present a quantum computing formulation to address a challenging problem in the development of probabilistic learning on manifolds (PLoM). It involves solving the spectral problem of the high-dimensional Fokker–Planck (FKP) operator, which remains beyond the reach of classical computing. Our ultimate goal is to develop an efficient approach for practical computations on quantum computers. For now

The Multiscale Finite Element Method (MsFEM) decomposes the problem of solving partial differential equations with multiscale characteristics into two subproblems at two discrete resolution levels, i.e., the macroscopic one on a coarse mesh and the microscopic one on a fine mesh. The microscopic subproblems are used for constructing the Equivalent Stiffness Matrices (ESMs) of the coarse elements, and

A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on localized meshes of elements (or cells) directly. To facilitate mesh-based GNN representations in a manner similar to spectral (or finite) element discretizations

The fracture of flexoelectric materials involves strain gradients, which pose challenges for theoretical and numerical analysis. The phase-field model (PFM) is highly effective for simulating crack propagation. However, PFM within the finite element method (FEM) framework faces certain challenges in simulating the fracture behavior of flexoelectric materials since the conventional FEM can only provide

Locally resonant metamaterial structures have gained significant attention across multiple engineering disciplines due to their ability to exhibit vibration stop bands not found in regular materials. These structures are composed of an assembly of unit cells, which are often discretized into large finite element models due to their sub-wavelength nature and intricate design. Moreover, due to the contribution

Interfacial debonding, a critical failure mechanism in heterogeneous materials, is often characterized by mixed-mode fracture. This study develops a numerical framework to simulate bulk and interfacial fractures in composite materials. A phase-field cohesive zone model, incorporating a directional energy decomposition scheme and a modified toughness method, is employed to capture complex fracture behaviors

Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress–strain relation. However, discovering these constitutive material laws remains a significant challenge, in particular when only material deformation data is available. To address this challenge

Surrogate models are critical for accelerating computationally expensive simulations in science and engineering, particularly for solving parametric partial differential equations (PDEs). Developing practical surrogate models poses significant challenges, particularly in handling geometrically complex and variable domains, which are often discretized as point clouds. In this work, we systematically

We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate reconstructions, leveraging conditional diffusion models to draw samples, and also honors the symmetries of the underlying physics of wave-propagation. The procedure

In this study, we present a new framework of physics-informed non-intrusive reduced-order modeling (ROM) of dynamical systems modeled by parametric, partial differential equations (PDEs). Given new time and parameter values of a PDE, the framework utilizes trained physics-informed ML models to quickly estimate high-fidelity solutions while simultaneously observing the constraints and dynamics of the