This article focuses on the computation of the solutions to periodic cell problems that arise in a number of homogenization schemes. Formulated in terms of a generic constitutive relation, encompassing the linear and non-linear cases, a model problem is intended to be discretized on a Fourier-basis and solved using a Fast Fourier Transform (FFT)-based iterative scheme. Such a spectral method, which

Fluid–structure-interaction (FSI) phenomena with multi-phase flow dynamics and structural damage commonly exist in engineering practice, which however bring great challenges to nowadays numerical FSI algorithms. A novel localized subdomain smoothing MMALE particle method (ls-ALEPM) is proposed in this paper for efficient and accurate simulations of large scale FSI problems. The MMALE method and the

When repeated evaluations for varying parameter configurations of a high-fidelity physical model are required, surrogate modeling techniques based on model order reduction are desirable. In absence of the governing equations describing the dynamics, we need to construct the parametric reduced-order surrogate model in a non-intrusive fashion. In this setting, the usual residual-based error estimate

Numerical prediction of melt pool morphology and temperature distribution of thermomechanical processes (welding, additive manufacturing) plays an important role in understanding the relationships between process parameters and the quality of manufactured parts. The heat conduction models are limited in their predictability because the transport phenomena relevant to the melt pool dynamic are ignored

This study aims to develop a simple yet robust time-integration scheme for configuration-interpolated beam finite elements. Geometrically exact theory is employed to model the beams. It utilises the rotations which belong to a non-commutative Lie group and thus require special attention. The configuration is interpolated using a two-node SE(3) interpolation or its generalised implicit variant which

In order to perform isogeometric analysis with increased smoothness on complex domains, trimming, variational coupling or unstructured spline methods can be used. The latter two classes of methods require a multi-patch segmentation of the domain, and provide continuous bases along patch interfaces. In the context of shell modelling, variational methods are widely used, whereas the application of unstructured

The work presents a node-moving algorithm for topology optimization (NMTO) in the arbitrarily shaped design domain. Also, we further enhanced a body-fitted mesh generation algorithm to express smooth boundaries more efficiently. In each optimization iteration, a narrowband offset from the structural profile is established, based on which a signed-distance function is constructed to determine the node-moving

Together with the rapid development in manufacturing technology, multiscale structural topology optimization presents opportunities for the design of components at both the structural and sub-structural scales. A few works on topological optimization based on FE2 computational homogenization to concurrently evolve the structure and sub-structure have been reported. However, significant expertise and

We utilize neural operators to learn the solution propagator for challenging systems of differential equations that are representative of stiff chemical kinetics. Specifically, we apply the deep operator network (DeepONet) along with its extensions, such as the autoencoder-based DeepONet and the newly proposed Partition-of-Unity (PoU-) DeepONet to study a range of examples, including the ROBERS problem

This contribution introduces a methodology for the detection of isolated branches of periodic solutions to the nonlinear mechanical equation of motion for systems featuring frictionless contact interfaces. This methodology relies on a harmonic balance method-based solving procedure combined with the application of the Melnikov energy principle. It is able to predict the location of isolated branches

This study provides a new formulation of gradient damage model which allows an efficient explicit numerical solution of dynamics problems. The proposed methodology is based on an ”extended Lagrangian approach” developed by one of the authors for the nondissipative and dispersive shallow water equation. By using this strategy, the global minimization problem commonly derived for gradient damage models

Detecting and characterising shocks is challenging because they do not occur in isolation but are instead superimposed onto underlying vehicle vibrations which themselves are a result of the interaction with uneven road surfaces. Consequently, shocks are buried within vehicle vibration response measurements (usually acceleration). This paper presents the development and validation of an automated algorithm

An efficient computational framework to model the growth of intersecting height-contained hydraulic fractures is proposed. The fracture in solids is modeled by the classical theory of linear elastic fracture mechanics, whereas the injection flow in hydraulic fractures is treated as channel flow. The governing equations of fracture mechanics are formulated in terms of weakly-singular weak-form boundary

In numerical analysis of frame structures, modeling of the connection between structural members often requires the introduction of rigid end offsets to correctly describe the stiffness of the joints. This is typical of beam-to-column connections in civil constructions but is also common in lattice materials, where the element overlapping at the joints locally increases the stiffness of the nodes.

Embedded and immersed methods have become essential tools in computational mechanics, as they allow discretizing arbitrarily complex geometries without the need for boundary-fitted meshes. One of their main challenges is the accurate numerical integration of cut elements. Among the various integration schemes developed for this purpose, moment fitting has proven to be a powerful technique that provides

This work presents a novel global digital image correlation (DIC) method, based on a newly developed convolution finite element (C-FE) approximation. The convolution approximation can rely on the mesh of linear finite elements and enables arbitrarily high order approximations without adding more degrees of freedom. Therefore, the C-FE based DIC can be more accurate than the usual FE based DIC by providing

We introduce the concept of physics-guided transfer learning to predict the thermal conductivity of an additively manufactured short-fiber reinforced polymer (SFRP) using micro-structural characteristics extracted from tensile tests. Developing composite manufacturing digital twins for SFRP composite processes like extrusion deposition additive manufacturing (EDAM) require extensive experimental material

Misfolded tau proteins play a critical role in the progression and pathology of Alzheimer’s disease. Recent studies suggest that the spatio-temporal pattern of misfolded tau follows a reaction–diffusion type equation. However, the precise mathematical model and parameters that characterize the progression of misfolded protein across the brain remain incompletely understood. Here, we use deep learning

We develop and implement finite element approximations for the coupled problem of cellular aggregate formation. The equation governing evolution of cell density is convective in nature, necessitating a modification of standard approaches to circumvent the instabilities associated with standard finite element approximations. To this end, a novel mean zero artificial diffusion approach is proposed, in

This paper presents an advanced approach for structural topology optimization by incorporating fatigue crack propagation analysis. The extended finite element method (X-FEM) is employed to model initial crack propagation, while the Paris model serves as the basis for simulating fatigue crack growth. The proposed methodology aims to optimize the structural design by minimizing compliance while considering

Numerical modeling of localizations is a challenging task due to the evolving rough solution in which the localization paths are not predefined. Despite decades of efforts, there is a need for innovative discretization-independent computational methods to predict the evolution of localizations. In this work, an improved version of the neural network-enhanced Reproducing Kernel Particle Method (NN-RKPM)

Probability distributions of structural responses have been widely used in many engineering applications and their accuracy could significantly affect the performance and credibility of these applications. To obtain accurate distributions, existing methods often need massive calculations of the original response function, especially for highly nonlinear problems. To alleviate the computational burden

Hydraulic fracturing and acidification techniques are important approaches for deep energy recovery engineering. However, the details of the interactions and impacts between acid fluids and solid porous media remain inadequately modelled, necessitating further research in this domain. Building on this need, we present a novel approach for modelling the chemo-hydro-mechanical response in sandstone during

This paper proposes novel and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). To address the modeling of Newtonian fluids with incompressibility constraints, a new mixed implicit MPM formulation is proposed. Here, instead of solving the velocity and pressure fields as the unknown variables like the typical Eulerian computational

The development of efficient optimization algorithms is crucial across various scientific disciplines. As the complexity and diversity of optimization problems continue to grow, researchers seek faster and stronger algorithms capable of optimizing a wide range of functions. This paper introduces Lung performance-based optimization (LPO), a novel and efficient algorithm inspired by the regular and intelligent

Structural designs in the engineering field commonly require the prior embedding of several fixed-shape components to satisfy desired performance or functional requirements. In the past few decades, topology optimization has been regarded as an effective approach to deal with the optimization problems of continuous structures embedded with multiple components. However, the interfaces between the host

This paper formulates a model order reduction method for electromagnetic boundary element analysis and extends it to computer-aided design integrated shape optimization of multi-frequency electromagnetic scattering problems. Firstly, a series expansion technique is adopted to decouple frequency-dependent terms from the integrands in boundary element formulation, and the second-order Arnoldi procedure

Smoothed Particle Hydrodynamics (SPH) simulations of violent sloshing flows characterized by a strong fragmentation of free-surface can be affected by volume conservation errors. These errors can accumulate in time and preclude the possibility of using such models for long-time simulations. In the present work, different techniques to measure directly the particles’ volumes by their positions are displayed

A new numerical continuum one-domain approach (ODA) solver is presented for the simulation of the transfer processes between a free fluid and a porous medium. The solver is developed in the mesoscopic scale framework, where a continuous variation of the physical parameters of the porous medium (e.g., porosity and permeability) is assumed. The Navier–Stokes–Brinkman equations are solved along with the

The scope of this paper is to propose an appropriate numerical strategy to extend the Mixed Finite Element–Finite Volume (MEV) scheme to adapted meshes composed of both triangular and quadrangular elements, called hybrid meshes (Kallinderis and Kavouklis, 2005; Ito et al., 2013) (also named mixed-element meshes (Marcum and Gaither, 1999; Mavriplis, 2000)). Convective, diffusive and source terms require

Dehomogenization techniques are becoming increasingly popular for enhancing lattice designs of compliant mechanical systems with ultra-large resolutions. Their effectiveness hinges on computing a deformed periodic grid that enable to reconstruct fine-scale designs with modulated and oriented patterns. In this paper, we propose an approach for extending dehomogenization methods to laminar fluid systems

This paper presents an approach to the numerical estimation of effective properties of highly porous materials based on the scaled boundary finite element method (SBFEM). The latter can be formulated on quadtree meshes with hanging nodes and thus facilitates the efficient mesh generation and analysis of a large number of randomly created samples. To generate the corresponding Representative Volume

The nonconforming Morley-type virtual element method for the incompressible Navier–Stokes equations formulated in terms of the stream-function on simply connected polygonal domains (not necessarily convex) is designed. A rigorous analysis by using a new enriching operator is developed. More precisely, by employing such operator, we provide novel discrete Sobolev embeddings, which allow to establish

This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. We leverage the proper generalized decomposition (PGD) to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation. In contrast with the standard incremental approach, which solves the (non-linear and computationally

The turbulent flow characteristics, such as its multiscale and nonlinear nature, make the solution to turbulent flow problems complex. To simplify these problems, traditional methods have employed simplifications, such as RANS and LES models for dealing with the multiscale aspect and linear approximation theories for dealing with the nonlinear aspect. We designed a multiscale and nonlinear turbulence

This paper deals with the numerical analysis of ductile damage and fracture behavior under non-proportional biaxial reverse loading conditions. A two-surface anisotropic cyclic elastic–plastic-damage continuum model is adequately presented, which takes into account the Bauschinger effect, the stress-differential effect, and the change of hardening rate after reverse loading. An efficient Euler explicit

This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating appropriate training data, cost-accuracy trade-offs, and nontrivial hyperparameter tuning. The unpredictability of the accuracy of neural operators impacts their applications

In recent years operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions, and boundary data to the solution of a PDE. This work describes a new architecture for operator networks, called the variationally mimetic operator network (VarMiON

The method of smoothed particle hydrodynamics (SPH) has been recently developed to study the coupled flow-deformation problems in porous material and considerable success has been achieved comparing to traditional mesh-based method, especially for treating large deformation and post-failure. However, computational challenges remain for the hydro-mechanical boundary treatment as well as the accuracy

This paper presents a novel computational approach for modelling fluid-driven fracturing in quasi-brittle solids using peridynamics. The approach leverages a rigorous coupling of the total- and semi-Lagrangian formulations of peridynamics. Specifically, the total-Lagrangian formulation, whch is based on classical peridynamics theory used for modelling fractures in solids, is combined with the semi-Lagrangian

With the diversification of engineering structure performance requirements and the continuous development of structural design refinement, structural design methods are facing more and more factors to be considered. It is necessary to develop advanced design technology. In this paper, a sensitivity mapping technique is proposed to improve the effect of topology optimization based on a gradient optimization

With the continuous improvement of structural performance requirements of advanced equipment, the multiscale design of materials and structures is increasingly developing towards refinement and multi-function. Metamaterials have broad application prospects due to their superior mechanical properties. In this paper, a robust topology optimization design strategy for mechanical metamaterials with multiple

We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) on GPUs. The method is integrated with a widely used differential equation solver library in a high-level language (Julia’s DifferentialEquations.jl) and enables GPU acceleration without requiring code changes by

A time fractional-step method is presented for numerical solutions of the incompressible non-Newtonian fluids for which the viscosity is non-linear depending on the shear-rate magnitude according to a generic model. The method belongs to a class of viscosity-splitting procedures and it consists of separating the convection term and incompressibility constraint into two time steps. Unlike the conventional

This paper introduces a scalable computational framework for optimal design under high-dimensional uncertainty, with application to thermal insulation components. The thermal and mechanical behaviors are described by continuum multi-phase models of porous materials governed by partial differential equations (PDEs), and the design parameter, material porosity, is an uncertain and spatially correlated

The LATIN method has been developed and successfully applied to a variety of deterministic problems, but few work has been developed for nonlinear stochastic problems. This paper presents a stochastic LATIN method to solve stochastic and/or parameterized elastoplastic problems. To this end, the stochastic solution is decoupled into spatial, temporal and stochastic spaces, and approximated by the sum

This paper proposes a variable timestep-strategy that can speed up the peridynamic modeling of thermomechanical cracking in both homogeneous and heterogeneous materials. A piecewise continuous time-step variation function is incorporated into the peridynamic framework that dynamically adjusts the time-step size, which ranges from a small value to a maximum value that remains below the critical stable

Ensuring a high degree of dimensional accuracy of the printed part is critical in the development of additive manufacturing techniques. The advent of computational tools to simulate additive manufacturing has provided a robust way to predict part quality during the entire process. In this paper, a multiphysics model is introduced for the novel additive manufacturing technique of frontal polymerization-based

The rapid identification of unknown objects by their thermo-fluid flow field signature is becoming increasingly more important. In this work, a machine-learning framework is developed that efficiently simulates and adapts object geometries in order to match the thermo-flow field signature generated by an unknown object, across a time series of voxel-frames. In order to achieve this, a thermo-fluid

Physics-informed neural network (PINN) is an innovative universal function approximator which adds physical constraints to neural network to make the fitting results satisfy the physical laws better. In this paper, a physics-informed residual network (PIResNet) is proposed to solve the single-phase seepage equation without labeled data. The loss function is constructed by summarizing the residuals

We consider nonsmooth partial differential equations associated with a minimization of an energy functional. We adaptively regularize the nonsmooth nonlinearity so as to be able to apply the usual Newton linearization, which is not always possible otherwise. We apply the finite element method as a discretization. We focus on the choice of the regularization parameter and adjust it on the basis of an

We present and analyze a methodology for numerical homogenization of spatial networks models, e.g. heat conduction and linear deformation in large networks of slender objects, such as paper fibers. The aim is to construct a coarse model of the problem that maintains high accuracy also on the micro-scale. By solving decoupled problems on local subgraphs we construct a low dimensional subspace of the

The digital twin concept represents an appealing opportunity to advance condition-based and predictive maintenance paradigms for civil engineering systems, thus allowing reduced lifecycle costs, increased system safety, and increased system availability. This work proposes a predictive digital twin approach to the health monitoring, maintenance, and management planning of civil engineering structures

This paper provides an orientation angle optimization method for the design of fiber-reinforced composite materials using topology optimization. The orientation angle optimization is based on a topological derivative, which measures the sensitivity of an objective function with respect to a topological change of anisotropic materials. The sensitivity is incorporated into a new gradient-based optimization

A numerical framework is presented to predict the transport of soft elastic capsules immersed in an incompressible fluid with the aim of simulating inertial microfluidics applications. The flow evolution is modeled by a fully incompressible lattice Boltzmann method whereas a finite element model is considered for describing the dynamics of deformable structures. An immersed boundary technique is adopted