A two-stage Bayesian model updating framework based on an affine-invariance sampling in Transitional Markov Chain Monte Carlo (TMCMC) algorithm is proposed. In the first stage, unknown modal coordinates are identified with an improved iterative model reduction technique. Subsequently, a modified TMCMC algorithm is proposed where obtaining the statistical estimators in the usual TMCMC algorithm is not

This paper formulates, analyzes and demonstrates numerically a method for the explicit partitioned solution of coupled interface problems involving combinations of projection-based reduced order models (ROM) and/or full order models (FOMs). The method builds on the partitioned scheme developed in Peterson et al. (2019), which starts from a well-posed formulation of the coupled interface problem and

For the first time the optimal local truncation error method (OLTEM) with 125-point stencils and unfitted Cartesian meshes has been developed in the general 3-D case for the Poisson equation for heterogeneous materials with smooth irregular interfaces. The 125-point stencils equations that are similar to those for quadratic finite elements are used for OLTEM. The interface conditions for OLTEM are

The microfluidic concentration gradient generator (μCGG) is an important biomedical device to generate concentration gradients (CGs) of biomolecules at the microscale. Nonetheless, determining their operational parameter values to generate complex, user-specific, biologically desired CGs is not trivial. This paper presents a neural-physics multi-fidelity model (NP-MFM) to predict CGs with equivalent

Interactions between fluids and particles are common in both natural and industrial fields. However, modeling these intricate interactions presents considerable challenges, especially when dealing with free surface flows and irregularly shaped particles. In this work, a hybrid approach that combines the Material Point Method (MPM) and the Metaball Discrete Element Method (MDEM) is proposed to address

This spreading of prion proteins is at the basis of brain neurodegeneration. This paper deals with the numerical modelling of the misfolding process of α-synuclein in Parkinson’s disease. We introduce and analyse a discontinuous Galerkin method for the semi-discrete approximation of the Fisher–Kolmogorov (FK) equation that can be employed to model the process. We employ a discontinuous Galerkin method

We present a hybrid discontinuous Galerkin method for the velocity/stress formulation of Zener’s model in dynamic viscoelasticity. Our approach utilizes a spatial discretization that enforces strongly the symmetry of the stress tensor, and that allows for efficient handling of heterogeneous materials comprising both purely elastic and viscoelastic components. We provide an hp error analysis of the

Plants can change their morphology upon environmental variations such as temperature. Inspired by plants’ morphological adaptability, we present a computational inverse design framework for systematically creating optimized thermo-active liquid crystal elastomers (LCEs) that spontaneously morph into arbitrary programmed geometries upon temperature changes. The proposed framework is based on multiphysics

Physics-informed neural networks (PINNs), which are promising tools for solving nonlinear equations in the absence of labeled data, have been successfully applied for continuum field approximation in fluid mechanics, solid mechanics, thermodynamics, and other scientific and engineering problems. However, it is equally necessary to solve discontinuous problems such as cracking behaviors in structures

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations

We propose a novel framework for investigating fluid–membrane interactions involving fracture, and apply it to simulate initial stages during the bursting of a balloon. Fluid flow is computed using a stabilized space–time finite element method over a body-fitted mesh. The membrane is modelled as a hyperelastic material and the equations are solved using the standard Galerkin method. Structural failure

Since the solutions of the multi-material diffusion problems are not smooth, the general physics-informed neural network (PINN) method does not work well for this problem. In this paper, we first give the interface continuity conditions which are necessarily added to the loss function as a loss term. Then, to adapt PINN for solving the multi-material diffusion problems with a single neural network

Hole control is an important issue in topology optimization. In this work, a comprehensive study is made to address four aspects related to the hole number, shape, size and spacing control. Hole features described by level-set functions (LSFs) are introduced as design primitives and constrained for the hole control requirements in topology optimization. To be specific, the hole number is controlled

Buckling resistance has gained significant attention in topology optimization due to its profound implications for structural designs. Despite considerable research on buckling-constrained topology optimization, maximizing the critical buckling load factor (BLF) still remains a challenging topic. In this study, an innovative algorithm that utilizes a linear material interpolation scheme is introduced

In deterministic topology optimization (TO), due to not taking into account the uncertainties of the structural system, explicitly, resulting optimal layouts may conclude in low reliable levels or unreliable optimum design conditions. The objective of reliability-based topology optimization (RBTO) is to integrate the reliability concept into topology optimization, finding the optimized structures priori

The combination of topology optimization and laser powder bed fusion (LPBF), a kind of metal additive manufacturing, has attracted attention because of its ability to manufacture complex optimal structures with metal materials. However, LPBF must satisfy geometric constraints, e.g., overhang constraint and closed cavity exclusion constraint. Several previous studies proposed the fictitious physics

This paper presents an adaptive stochastic isogeometric method to incorporate material uncertainties in the nonlinear bending analysis of thin functionally graded material (FGM) shells. The gradient index is modeled as a second-order random field to describe the spatial randomness of material properties. An adaptive, nested, and non-intrusive Chebyshev interpolation process based on Leja sequences

The challenge of material surface damage and spalling, caused by high-frequency, high-pressure jets owing to cavitation, remains a substantial concern. To better understand the physical mechanisms of cavitation-induced cyclic impact, we developed a multi-field-coupling framework. This framework encapsulates polymer viscoelastic-viscoplastic deformation, thermal softening, strain softening, and damage

We present a multiscale computational framework for high-pressure resin transfer molding of fiber-reinforced composites. Due to the relatively rapid speed of resin flow and the significant convective effects, this process is governed by the nonlinear steady-state Navier–Stokes equations, as opposed to the linear Stokes equations commonly adopted for the simulation of classical resin transfer molding

Extensions to the Roe and HLL method have been previously formulated in order to solve the Shallow Water equations in the presence of source terms. These were named the Augmented Roe (ARoe) method and the HLLS method, respectively. This paper continues developing these formulations by examining how entropy corrections can be appropriately fitted in for the ARoe method and how the HLLS method can be

The construction of high-quality parameterizations for complex domains remains a significant challenge in isogeometric analysis. To address this issue, we propose a G1-smooth parameterization method for planar domains with arbitrary topology. Firstly, we generate a coarse decomposition of the given complex shape without internal singularities utilizing the extracted skeleton of the domain. We then

A hybrid Finite Volume Method (FVM)-Smoothed Particle Hydrodynamics (SPH) approach for shock capturing in compressible fluids is presented. The Python framework Pyro2 is employed to simulate a coarse FVM mesh, while the Python framework PySPH is utilized to model the fluid in regions with high gradients through SPH particles. New FVM-SPH coupling approaches are explored, including online SPH particle

Data-driven modeling in mechanics is evolving rapidly based on recent machine learning advances, especially on artificial neural networks. As the field matures, new data and models created by different groups become available, opening possibilities for cooperative modeling. However, artificial neural networks suffer from catastrophic forgetting, i.e. they forget how to perform an old task when trained

This article presents an innovative approach for developing an efficient reduced-order model to study the dispersion of urban air pollutants. The need for real-time air quality monitoring has become increasingly important, given the rise in pollutant emissions due to urbanization and its adverse effects on human health. The proposed methodology involves solving the linear advection–diffusion problem

The computational cost of the discrete element method (DEM)-population balance model (PBM) coupled framework is predominantly attributed to DEM simulations. To overcome this challenge, coarse-grained (CG) particles have been introduced in the DEM-PBM coupled framework. In this study, we proposed a new CG-enabled DEM-PBM coupled framework that builds upon the previous work of Das et al. (Proc. R. Soc

Isogeometric collocation methods have been introduced as an alternative to isogeometric Galerkin formulations, aiming at improving the computational cost of simulation by reducing the cost of assembly of the corresponding matrices. However, in contrast to their Galerkin counterparts, collocation formulations result in non-symmetric matrices of much higher dimensions, for a specified level of accuracy

In this paper, a peridynamic-enhanced finite element formulation is introduced for the numerical simulation of thermo–hydro–mechanical coupled problems in saturated porous media with cracks. The proposed approach combines the Finite Element (FE) method for governing heat conduction–advection and fluid flow in the fractured porous domain, and the Peridynamic (PD) method for describing solid phase deformation

Modern computational soft-tissue mechanics models have the potential to offer unique, patient-specific diagnostic insights. The deployment of such models in clinical settings has been limited however, due to the excessive computational costs incurred when performing mechanical simulations using conventional numerical solvers. An alternative approach to obtaining results in clinically relevant time

The effect of higher order continuity in the solution field by using NURBS basis function in isogeometric analysis (IGA) is investigated for an efficient mixed finite element formulation for elastostatic beams. It is based on the Hu–Washizu variational principle considering geometrical and material nonlinearities. Here we present a reduced degree of basis functions for the additional fields of the

We propose an innovative isogeometric space–time method for the heat equation, with smooth splines approximation in both space and time. To enhance the stability of the method we add a stabilizing term, based on a linear combination of high-order artificial diffusions. This term is designed in order to make the linear system lower block-triangular, that is, lower triangular with respect to time. In

Inverse homogenization in combination with contact modeling, topology optimization and shape optimization is used to design metamaterials with optimized macroscopic response. The homogenization assumes length scale separation which allows the non-linear macroscopic behavior to be obtained by analyzing a single unit cell in a lattice structure. Self contact in the unit cell, which is modeled using a

Accurately evaluating derivatives poses a key challenge when numerically implementing complex constitutive models. This work presents an implicit stress update algorithm that utilizes the hyper dual step derivative approximation to address derivative evaluations in elastoplastic problems. Initially, the performance of various numerical differentiation methods is discussed and compared by examining

We propose a novel approach to the linear viscoelastic problem of shear-deformable geometrically exact beams. The generalized Maxwell model for one-dimensional solids is here efficiently extended to the case of arbitrarily curved beams undergoing finite displacement and rotations. High efficiency is achieved by combining a series of distinguishing features, that are: (i) the formulation is displacement-based

The eXtended Finite Element Method (X-FEM) is a versatile technique to model discontinuities by enriching the trial functions with a prior solution. In the X-FEM, a crack can be explicitly represented by a set of triangles or implicit signed distances, i.e., level set functions, of the points of interest from the crack surface and the crack front. In the explicit representations, it is crucial to accurately

In this research, a numerical framework for hydraulic fracturing has been formulated, incorporating thermo-hydro-mechanical (THM) coupled effects. While previous studies have reported various hydraulic fracturing models based on the phase-field method, a THM coupling scheme grounded in the variational phase-field approach remains unexplored. The THM coupling is of paramount importance for understanding

We resort to game theory in order to formulate Data-Driven methods for solid mechanics in which stress and strain players pursue different objectives. The objective of the stress player is to minimize the discrepancy to a material data set, whereas the objective of the strain player is to ensure the admissibility of the mechanical state, in the sense of compatibility and equilibrium. We show that,

Physics-Informed Neural Networks (PINNs) have recently gained increasing attention in the field of topology optimization. The fusion of deep learning and topology optimization has emerged as a prominent area of insightful research, where minimization of the loss function in neural networks can be comparable to minimization of the objective function in topology optimization. Inspired by concepts of

The concurrent design of different lattice material microstructures and their corresponding macro-scale distributions has great potential in achieving both lightweight and desired multiphysical performances. In such design problems, the lattice microstructures are usually separately optimized on the basis of the homogenization method, and the possibly poor connectivity between them is a key factor

A data-driven discrepancy modeling method is presented that variationally embeds measured data in the modeling and analysis framework. The proposed method exploits the variationally derived loss function that is comprised of the residual between the first-principles theory and sensor-based measurements to augment the physics-based model. The method was first developed in the context of linear elasticity

Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts to immersed boundary methods, which perform simulations on a regular background mesh cut by a boundary representation that defines the domain of interest. Therefore, we present a novel concept to divide the support of cut

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting accuracy in the training data set, their out-of-sample predictions can be highly inaccurate. This paper investigates this problem by reformulating the problem on

When certain polymer amphiphiles and phospholipids are dispersed in a liquid, these molecules combine to form various closed bilayer structures known as multiple vesicles. The specific structures of these vesicles play fundamental roles in cytobiology and drug transportation. To model the multiple lipid vesicles in a fluid environment, we use the multi-phase conservative Allen–Cahn-type equations with

This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for representing the high-dimensional system states in a reduced-dimensional coordinate system. While these approximations respect the symplectic nature of Hamiltonian

Patient-specific models of blood flow in the coronary arteries have entered clinical practice worldwide to aid in the diagnosis and management of heart disease. This technology leverages modern AI-based image segmentation methods to extract the geometry of the coronary arteries from noninvasive computed tomography volumetric imaging, computational physiology methods to define boundary conditions and

Using the equivalent inclusion method (a method strongly related to the Hashin–Shtrikman variational principle) as a surrogate model, we propose a variance reduction strategy for the numerical homogenization of random composites made of “inclusions” (or rather inhomogeneities) embedded in a homogeneous matrix. The efficiency of this strategy is demonstrated within the framework of two-dimensional,

In this paper, an incompatible unsymmetric 8-node hexahedral solid-shell element is proposed with different sets of trial and test functions. The trial functions used in the 8-node hexahedral solid element in our previous work are adopted with minor revision. In addition, to eliminate the transverse shear and trapezoidal locking in the calculation of thin shell structures, the test functions are revised

This work proposes a filtering technique for the concurrent and sequential finite element-based topology and discrete fiber orientation optimization of composite structures. The proposed filter is designed to couple the morphology with the topology of the structural domain throughout the optimization process in a way such that it suppresses the impact of the close-to-void finite elements’ morphology

Uncertainty quantification (UQ) has been widely recognized as of vital importance for reliability-oriented analysis and design of engineering structures, and three groups of mathematical models, i.e., the probability models, the imprecise probability models and the non-probabilistic models, have been developed for characterizing uncertainties of different forms. The propagation of these three groups

Computational fluid dynamics (CFD) is the cornerstone of the design and analysis process in many engineering applications. Not only has it been applied in the design phase, but it has also been employed for analyzing the fluid flow phenomena during the operation phase for many in-use structures, such as vehicles, buildings, and landscapes. However, creating a 3D mesh-based model of in-use structures

We explore how recent advances in Isogeometric analysis, Galerkin Least-Squares methods, and Augmented Lagrangian techniques can be applied to solve nonstandard problems, for which there is no classical stability theory, such as that provided by the Lax–Milgram lemma or the Banach-Necas-Babuska theorem. In particular, we consider continuation problems where a second-order partial differential equation

The efficient representation of random fields on geometrically complex domains is crucial for Bayesian modelling in engineering and machine learning, including Gaussian process regression and statistical finite element analysis. Today’s prevalent random field representations are either intended for unbounded domains or are too restrictive in terms of possible field properties. Because of these limitations

We are witnessing a rapid transition from Software 1.0 to 2.0. Software 1.0 focuses on manually designed algorithms, while Software 2.0 leverages data and machine learning algorithms (or artificial intelligence) for optimized, fast, and accurate solutions. For the past few years, we have been developing Convolution Hierarchical Deep-learning Neural Network Artificial Intelligence (C-HiDeNN-AI), which

We develop two new stabilized methods for the steady advection-diffusion-reaction equation, referred to as the Streamline GSC Method and the Directional GSC Method. Both are globally conservative and perform well in numerical studies utilizing linear, quadratic, cubic, and quartic Lagrange finite elements and maximally smooth B-spline elements. For the streamline GSC method we can prove coercivity

The article is aimed to provide an effective digital solution in support of the infill microstructural design within objectives generated from normal computer aided design (CAD) systems. The key here is to deploy the microstructure and to analyse the performance of the resulting multiscale objective in the parameter domain, from which a CAD objective is mapped, usually by means of Non-Uniform Rational

Simulation of wave propagation in poroelastic half-spaces presents a common challenge in fields like geomechanics and biomechanics, requiring Absorbing Boundary Conditions (ABCs) at the semi-infinite space boundaries. Perfectly Matched Layers (PML) are a popular choice due to their excellent wave absorption properties. However, PML implementation can lead to problems with unknown stresses or strains

This contribution proposes a second-order computational homogenisation formulation for natural and architected materials in the presence of voids. The macro-scale is described by a second gradient continuum theory in the finite strain regime, and the micro-scale is modelled by the concept of representative volume element (RVE) within the classical first-order continuum mechanics. The Method of Multi-scale

We present a quasi-conforming embedded reproducing kernel particle method (QCE-RKPM) for modeling heterogeneous materials that makes use of techniques not available to mesh-based methods such as the finite element method (FEM) and avoids many of the drawbacks in current embedded and immersed formulations which are based on meshed methods. The different material domains are discretized independently

We give an analytical justification of the determination of an important parameter involved in Feng and Wu’s solution of the Helmholtz equation by an Interior Penalty Discontinuous Galerkin (IPDG) method (Feng and Wu, 2009). This parameter was determined in this reference from a large number of numerical tests for a mesh composed of equal equilateral triangles at a fixed frequency. It plays an essential

Compared with conventional symmetric sandwich structures with two identical face-sheets and uniform core, geometrically asymmetric sandwich structures (GASSs) enable better dynamic performance due to the expanded design space provided by two unidentical face-sheets and graded cellular cores (GCCs). This paper proposes a dynamic response-oriented multiscale topology optimization method for the GASSs