In engineering applications, the Metropolis-Hastings (M-H) algorithm with high rejection rates is employed to evaluate implicit response functions, making reliability analysis for small failure probabilities with multiple input random variables difficult and inefficient. To address the challenge and estimate highly nonlinear limit state functions in a more efficient and accurate way, a novel reliability

This work introduces an efficient methodology for: (i) predicting dynamic responses across a broad frequency band for large-scale, highly complex structures, and (ii) forecasting their high-frequency response using associated low-frequency information. Structures of interest are characterized by a large number of degrees of freedom (DOFs) and numerous local vibration modes that couple, within the frequency

We present a novel probabilistic approach for generating multi-fidelity data while accounting for errors inherent in both low- and high-fidelity data. In this approach a graph Laplacian constructed from the low-fidelity data is used to define a multivariate Gaussian prior density for the coordinates of the true data points. In addition, few high-fidelity data points are used to construct a conjugate

We study in detail the pressure stabilizing effects of the non-iterated fixed-stress splitting in poromechanical problems which are nearly undrained and incompressible. When applied in conjunction with a spatial discretization which does not satisfy the discrete inf–sup condition, namely a mixed piecewise linear–piecewise constant spatial discretization, the explicit fixed-stress scheme can have a

The mesh flexibility offered by the virtual element method has made it increasingly popular in the context of adaptive remeshing. There exists a healthy literature concerning error estimation and adaptive refinement techniques for virtual elements while the topic of adaptive coarsening (i.e. de-refinement) is in its infancy. The notion of a quasi-optimal mesh is based on the principle of quasi-even

Data-based uncertainty quantification plays a significant role in the design of various patterns of new materials and structures. However, significant challenges remain due to missing data, inherent uncertainties, and incomplete material properties arising from the manufacturing process. In this paper, we quantitatively investigate the uncertainty in the probability of the mechanical response of bio-inspired

The rapid advancement in technology and engineering leads to increasingly complex structural working conditions. Especially, in the field of aeronautics and astronautics, structures are frequently subjected to high temperatures together with external forces, posing great threat to structural health. Consequently, the identification of both mechanical and thermal loads is crucial for structural health

This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an appropriate state–space representation, in the projection step that underlies many reduced-order modeling methods, or as a byproduct of considerations made during training

In this paper, we propose several improvements to existing fictitious domain/distributed Lagrange multiplier (FD/DLM) type immersed fluid–structure interaction (FSI) methods targeted for FSI analysis of heart valve dynamics. We utilize the variational multiscale (VMS) method to improve accuracy and robustness on under-resolved grids expected with immersed FSI techniques, as well as for the wide range

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations by including in the cost function to minimise during training the residual of the differential operator. This paper proposes an adaptive inverse PINN applied to different transport models, from diffusion to advection–diffusion–reaction

In recent years, the architected structures have attracted extensive attention due to their lightweight feature and excellent mechanical properties. The development of additive manufacturing technologies has expedited the development of the computational design of architected structures. However, the parametric design and simulation of architected structures are full of challenges because of their

In this paper, we introduce a fully-monolithic, implicit finite element method designed for investigating fluid–structure interaction problems within a fully Eulerian framework. Our approach employs a coupled Navier–Stokes Cahn–Hilliard phase-field model, recently developed by Mokbel et al. (2018). This model adeptly addresses significant challenges such as large solid deformations, topology changes

This work introduces a new solution-transfer process for slab-based space–time finite element methods. The new transfer process is based on Hsieh–Clough–Tocher (HCT) splines and satisfies the following requirements: (i) it maintains high-order accuracy up to 4th order, (ii) it preserves a discrete maximum principle, (iii) it asymptotically enforces mass conservation, and (iv) it constructs a smooth

An incremental high-cycle fatigue damage model is combined with topology optimization to design structures subject to non-proportional loads. The optimization aims to minimize the mass under compliance and fatigue constraints. The fatigue model is based on the concept of an evolving endurance surface and a system of ordinary differential equations that model the local fatigue damage evolution. A recent

This paper presents a concurrent optimization method for structural topology and fabrication sequence, aiming at designing for multi-axis additive manufacturing. The proposed method involves two fields: the density field representing the structure, and the time field representing the manufacturing sequence. In addition, angle variables are introduced to represent the designable build directions. The

Enriched finite element methods (e-FEMs) have become a popular choice for modeling problems containing material discontinuities (e.g., multi-phase materials and fracture). The main advantage as compared to the standard finite element method (FEM) remains the versatility in the choice of discretizations, since e-FEMs resolve discontinuities by completely decoupling them from the finite element mesh

This paper presents a novel equilibrium-based approach to the linear homogenization of shear-deformable beams and plates with periodic heterogeneity. The proposed approach leverages the fact that, under equilibrium, the stress resultants and sectional strains in beams and plates vary at most linearly with respect to the axial or in-plane coordinates. Consequently, the displacement fields within a representative

A phase-field monolithic scheme based on the gradient projection method is developed to model crack propagation in brittle materials under cyclic loading. As a type of active set method, the gradient projection method is particularly attractive to enforce the irreversibility condition imposed on the phase-field variables as bound constraints, or box constraints. This method has the advantages of allowing

We develop H(div)-conforming mixed finite element methods for the unsteady Stokes equations modeling single-phase incompressible fluid flow. A projection method in the framework of the incremental pressure correction methodology is applied, where a predictor problem and a corrector problem are sequentially solved, accounting for the viscous effects and incompressibility, respectively. The predictor

Modeling cardiovascular blood flow is central to many applications in biomedical engineering. To accommodate the complexity of the cardiovascular system, in terms of boundary conditions and surrounding vascular tissue, computational fluid dynamics (CFD) often are coupled to reduced circuit and/or solid mechanics models. These allow for realistic simulations of hemodynamics in the heart or the aorta

Geometry projection-based topology optimization has attracted a great deal of attention because it enables the design of structures consisting of a combination of geometric primitives and simplifies the integration with computer-aided design (CAD) systems. While the approach has undergone substantial development under the assumption of linear theory, it remains to be developed for non-linear hyperelastic

Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and enhance score-based diffusion models in field reconstruction tasks, where the goal is to estimate complete spatial fields from partial observations. We introduce a

This work presents a matrix-free finite element solver for finite-strain elasticity adopting an hp-multigrid preconditioner. Compared to classical algorithms relying on a global sparse matrix, matrix-free solution strategies significantly reduce memory traffic by repeated evaluation of the finite element integrals.

This study presents an approach to solving an inverse problem through the application of Deep Reinforcement Learning (DRL) coupled with homogenization. The underlying objective is to determine the micro-structural parameters of a composite material, including particle radius, Young’s moduli and Poisson’s ratios in order to achieve a specific target bulk modulus at the macro-scale using DRL. This approach

The original computational framework of elasto-plastic localizing gradient damage, also called as the localizing gradient plasticity (LGP) model, considers that damage in a material causes reduction of yield strength alone. It does not account for the physical process of stiffness-degradation due to damage of ductile materials. Therefore, in this work, a new constitutive model of elasto-plastic localizing

Peridynamics (PD) is a nonlocal continuum mechanics theory over two scales, where the macro-scale material responses are built based on the interaction forces among meso-scale material points. Unlike molecular dynamics, where the pairwise bond forces consist only of normal components along the bonds, the peridynamics bond forces proposed in our recent work can have both normal and tangential components

Euler’s elastica is a classical model of flexible slender structures relevant in many industrial applications. Static equilibrium equations can be derived via a variational principle. The accurate approximation of solutions to this problem can be challenging due to nonlinearity and constraints. We here present two neural network-based approaches for simulating Euler’s elastica. Starting from a data

The Hagstrom–Warburton (HW) boundary operators play an important role in the development of high-order computational schemes for problems in unbounded domains. They have been used on truncating boundaries in the formulation of a sequence of high-order local Absorbing Boundary Conditions (ABCs) and in the Double Absorbing Boundary (DAB) method. These schemes proved to be very accurate, efficient, and

Fast-Fourier Transform (FFT) methods have been widely used in solid mechanics to address complex homogenization problems. However, current FFT-based methods face challenges that limit their applicability to intricate material models or complex mechanical problems. These challenges include the manual implementation of constitutive laws and the use of computationally expensive and complex algorithms

We develop a mixed finite element domain decomposition method on non-matching grids for the Biot system of poroelasticity. A displacement–pressure vector mortar function is introduced on the interfaces and utilized as a Lagrange multiplier to impose weakly continuity of normal stress and normal velocity. The mortar space can be on a coarse scale, resulting in a multiscale approximation. We establish

In the paper we develop the optimal local truncation error method (OLTEM) with the non-diagonal and diagonal mass matrices on unfitted Cartesian meshes for the 3-D time-dependent wave and heat equations for heterogeneous materials with irregular interfaces. 27-point stencils that are similar to those for linear finite elements are used with OLTEM. There are no unknowns for OLTEM on interfaces between

For many important problems it is essential to be able to accurately quantify the statistics of extremes for specific quantities of interest, such as extreme atmospheric weather events or ocean-related quantities. While there are many classical approaches to perform such modeling tasks, recent interest has been increasing in the usage of generative models trained on available data. Despite the sporadic

This work presents a straightforward and efficient isogeometric phase-field framework for predicting creep crack propagation in elasto-plastic materials. In contrast to conventional models that utilize viscous strain energy as the driving force, the proposed approach introduces an asymptotic degradation function for fracture toughness, effectively quantifying material damage resulting from creep strain

We present neural network-based constitutive models for hyperelastic geometrically exact beams. The proposed models are physics-augmented, i.e., formulated to fulfill important mechanical conditions by construction, which improves accuracy and generalization. Strains and curvatures of the beam are used as input for feed-forward neural networks that represent the effective hyperelastic beam potential

Structural lightweight is a core technical requirement for the structural design of aerospace and new energy power equipment structures. For multi-scale variable stiffness design optimization of discrete fiber-reinforced composite laminates, one of the challenges is how to avoid the explosion of design variable combinations caused by the increase in the number of candidate discrete fiber laying angles

Friction Stir Welding (FSW) is a solid-state joining process that has several benefits over conventional welding techniques. A major challenge is its high sensitivity to process parameters such as advancing and rotational speed. Simulations are a key tool for understanding the material flow and temperature evolution and help to find the best processing parameters for a given FSW task. This work proposes

The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mechanical systems. A direct computation of SSMs requires explicit knowledge of nonlinear coefficients in the equations of motion, which limits their applicability to generic finite-element (FE) solvers. Here, we propose a non-intrusive

A seamless integration of neural networks with Isogeometric Analysis (IGA) was first introduced in [1] under the name of Hierarchical Deep-learning Neural Network (HiDeNN) and has systematically evolved into Isogeometric Convolution HiDeNN (in short, C-IGA) [2]. C-IGA achieves higher order approximations without increasing the degree of freedom. Due to the Kronecker delta property of C-IGA shape functions

Motivated by the mismatch between the mechanical performance calculated numerically in topologically optimized designs and that observed in the associated parts fabricated by additive manufacturing (AM) processes, we integrate material characteristics produced via AM processes into topology optimization at low computational cost, by introducing a density-based topology optimization formulation that

Thanks to advances of techniques like digital image correlation (DIC), the virtual fields method (VFM) has become a common approach to identifying mechanical parameters of materials when full-field displacement data are available. However, it is limited to a priori selected classical material models. Recently, machine learning and model discovery has become a promising alternative for non-parametric

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