Cohesive Element (CE) is a well‐established finite element for fracture, widely used for the modelling of delamination in composites. However, an extremely fine mesh is usually needed to resolve the cohesive zone, making CE‐based delamination analysis computationally prohibitive for applications beyond the scale of lab coupons. In this work, a new CE‐based method of modelling delamination in composites

We propose a surrogate model for two‐scale computational homogenization of elastostatics at finite strains. The macroscopic constitutive law is made numerically available via an explicit formulation of the associated macro‐energy density. This energy density is constructed by using a neural network architecture that mimics a high‐dimensional model representation. The database for training this network

A high‐order harmonic polynomial method (HPM) is developed for solving the Laplace equation with complex boundaries. The “irregular cell” is proposed for the accurate discretization of the Laplace equation, where it is difficult to construct a high‐quality stencil. An advanced discretization scheme is also developed for the accurate evaluation of the normal derivative of potential functions on complex

The accuracy of multiscale modeling approaches for the analysis of heterogeneous materials hinges on the representativeness of the micromodel. One of the issues that affects this representativeness is the application of appropriate boundary conditions. Periodic boundary conditions are the most common choice. However, when localization takes place, periodic boundary conditions tend to overconstrain

An algorithm is presented for discrete element method (DEM) simulations of energyconserving systems of frictionless, spherical particles in a reversed‐time frame. This algorithm is verified, within the limits of round‐off error, through implementation in the LAMMPS code. Mechanisms for energy dissipation such as interparticle friction, damping, rotational resistance, particle crushing or bond breakage

In the presence of strong added mass effects, partitioned solution strategies for incompressible fluid‐structure interaction are known to lack robustness and computational efficiency. A number of strategies have been proposed to address this challenge. However, these strategies are often complicated or restricted to certain problem classes and generally require intrusive modifications of existing software

This article presents an approach for characterizing and estimating statistical dependence between a large number of observables in a composite material system. Conditional regression is carried out using the estimated joint density function, permitting a systematic exploration of interdependence between fine scale and coarse observables that can be used for both prognosis and design of complex material

In Lagrangian particle‐based methods such as smoothed particle hydrodynamics (SPH), computing totally divergence‐free velocity field in a flow domain with the smallest error possible is the most critical issue, which might be achieved through solving pressure Poisson equation implicitly with higher particle resolutions. However, implicit solutions are computationally expensive and may be particularly

A novel method which combines the active learning Kriging (ALK) model with important sampling is proposed in this paper. The main aim of the proposed method is to solve problems with very small failure probability and multiple failure regions. A surrogate limit state surface (LSS) which strikes a balance between the Kriging mean and variance is proposed. In each iteration, important samples of the

In this article, a recovery by compatibility in patches (RCP)‐based a posteriori error estimator is proposed for the virtual element method (VEM), and it is utilized to drive adaptive mesh refinement processes in two‐dimensional elasticity problems. In RCP, recovered stresses are obtained by minimizing the complementary energy of patches of elements over a set of assumed equilibrated stress modes.

In this paper, a data assimilation method using a linear Kalman filter is presented to monitor the thermal state of a part during a fused deposition modeling process. The system model is found by discretizing the heat equation with the finite difference method. IR camera measurements are then combined with the system model via a linear Kalman filter. As a result of the data assimilation, the accuracy

Many of the commonly used methods in model order reduction do not guarantee stability of the reduced order model. This paper extends the eigenvalue reassignment method of stabilization of linear time‐invariant ROMs, to the more general case of linear time‐varying systems. Through a post‐processing step, the ROM is controlled to ensure the stability while enhancing/maintaining its accuracy using a constrained

This article proposes a new method for hybrid reliability‐based design optimization under random and interval uncertainties (HRBDO‐RI). In this method, Monte Carlo simulation (MCS) is employed to estimate the upper bound of failure probability, and stochastic sensitivity analysis (SSA) is extended to calculate the sensitivity information of failure probability in HRBDO‐RI. Due to a large number of

It is well known that the sensitivity analysis of the eigenvectors corresponding to multiple eigenvalues is a difficult problem. The main difficulty is that for given multiple eigenvalues, the eigenvector derivatives can be computed for a specific eigenvector basis, the so‐called adjacent eigenvector basis. These adjacent eigenvectors depend on individual variables, which makes the eigenvector derivative

To assess the influence of thermal stress on fracture deformation, a composite element algorithm of thermo‐mechanical coupling for fractured rock mass is developed based on the composite element method (CEM). This study aims to investigate coupled processes associated with the (i) effect of temperature on mechanical deformation and (ii) effect of fracture aperture on heat transfer. The composite element

The rotation degree of freedom in discontinuous deformation analysis may cause false volume expansion when a block undergoes a large rotation. We propose a block displacement function to prevent this defect. Specifically, the degrees of freedom in a block are redefined by incremental displacements at its vertices, and displacement is formulated based on the mean value coordinates. In addition, the

The non‐probabilistic reliability theory is a promising methodology for implementing structural reliability analysis in case of scarce statistical data. One of the main obstacles to implement non‐probabilistic reliability analysis is the implication of the limit state function (LSF) for complex structures. This paper aims to establish a surrogate model of the LSF with higher simulation precision, and

This work proposes an approach that combines a library of component‐based reduced‐order models with Bayesian state estimation in order to create data‐driven physics‐based digital twins. Reduced‐order modeling produces physics‐based computational models that are reliable enough for predictive digital twins, while still being fast to evaluate. In contrast with traditional monolithic techniques for model

Material failure analysis are addressed by the continuum strong discontinuity approach within the implicit formulation of the boundary element method in this work. An automatic cell generation algorithm is used to track cracks during the loading processes in the nonlinear analysis. As a major novelty, a new class of cells with embedded discontinuity is developed in which nonuniform displacement jump

Barycentric rational interpolation collocation method (BRICM) for solving plane elasticity problems with high accuracy is presented. The plane elasticity problems on a circular or rectangular domain can be solved directly by BRICM. Embedded the irregular domain into a regular (circular or rectangular) domain, the governing equations of plane elasticity on regular domain are discretized by the differentiation

Spring analogies and the point‐by‐point interpolating approaches have been widely used for the grid deformation, and both require solution of a linear system of equations. Depending on the problem, the resulting system of equations may be defined by a large‐dimensional matrix. Thus, sampling for a subset of the grids is essential in order to achieve an efficient grid deformation. This article presents

This study establishes an innovative discontinuous deformation analysis by solving the problem of frictional and cohesive contact using an implicit cone complementary formulation. In order to handle singularity associated with the vertex‐vertex contact, resistances to motion trend are firstly estimated by introducing the concepts of total and partial contact forces. Based on principle of least effort

Owing to the severe technological competition and high demand for safety estimation in complex physic and engineering systems, reliability analysis has drawn more and more attention. The regular non‐probabilistic reliability analysis assumes that experimental data are enclosed by ellipse and rectangle; however, this appears inconsistent with various types of uncertain sources. In this article, a novel

3D rapid transient acoustic problems are difficult to solve numerically when dealing with large geometries, because numerical methods based on geometry discretisation (mesh), such as the boundary element method (BEM) or the finite element method (FEM), often require to solve a linear system (from the spacial discretisation) for each time step. We propose a numerical method to efficiently deal with

An adaptive scheme to generate reduced‐order models for parametric nonlinear dynamical systems is proposed. It aims to automatize the POD‐Greedy algorithm combined with empirical interpolation.At each iteration, it is able to adaptively determine the number of the reduced basis vectors and the number of the interpolation basis vectors for basis construction. The proposed technique is able to derive

A new orthogonal split of strain tensor into compressive and tensile parts is implemented within the phase field model to mimic unilateral contact condition with which any existing cracks and any crack propagation have to comply. The resulting phase field model offers several advantages as compared to other available schemes. First, it involves rigorous orthogonality between traction and compression

A method of constructing parameterized Non‐Intrusive Reduced Order Models (NIROMs) is given. The approach relies on a geometrical interpretation of NIROM, requires only a single layer of interpolation to be applied for both system state and parametric dependence of the model and is applicable to systems characterized by any number of parameters spanning arbitrary orders of magnitude. The method is

With the development of parallel computing architectures, larger and more complex finite element analyses (FEA) are being performed with higher accuracy and smaller execution times. Graphics processing units (GPUs) are one of the major contributors of this computational breakthrough. This work presents a three‐stage GPU‐based FEA matrix generation strategy with the key idea of decoupling the computation

We propose a new discrete element method supporting general polyhedral meshes. The method can be understood as a lowest‐order discontinuous Galerkin method parametrized by the continuous mechanical parameters (Young's modulus and Poisson's ratio). We consider quasi‐static and dynamic elasto‐plasticity, and in the latter situation, a pseudo‐energy conserving time‐integration method is employed. The

We present an adaptive isogeometric‐analysis approach to elasto‐capillary fluid‐solid interaction (FSI), based on a diffuse‐interface model for the binary fluid and an Arbitrary‐Lagrangian‐Eulerian formulation for the FSI problem. We consider approximations constructed from adaptive high‐regularity truncated hierarchical splines, as employed in the isogeometric analysis (IGA) paradigm. The considered

We present an efficient approach to compute the matrices used in finite element formulations where self‐equilibrated (zero divergence) approximations of the stress field are used. The fundamental aspect of this approach is that it is applicable to polynomial approximations of high degree (it was tested up to degree 10), providing closed form expressions for the elementary matrices involved. The components

Numerical analysis of the hyperelastic behavior of polymer materials has drawn significant interest from within the field of mechanical engineering. Currently, hyperelastic models based on the energy density function, such as the Neo‐Hookean, Mooney‐Rivlin, and Ogden models, are used to investigate the hyperelastic responses of materials. Conventionally, constants relating to materials were determined

The surface energy a phase‐field approach to brittle fracture in anisotropic materials is also anisotropic and gives rise to second‐order gradients in the phase field entering the energy functional. This necessitates C 1 continuity of the basis functions which are used to interpolate the phase field. The basis functions which are employed in IsoGeometric Analysis, such as Non‐Uniform Rational B‐Splines

This paper proposes an algorithm for express solutions in nonlinear structural dynamics. Our strategy is to adopt a typical time integrator and accept the solution after a constant number of iterations using a constant Jacobian matrix. Its success may not be initially obvious, but we demonstrate that the proposed algorithm not only is fully operational but also inherits the advantages of the host time

Embedded Boundary Methods (EBMs) are robust solution methods for highly nonlinear Fluid‐Structure Interaction (FSI) problems. They suffer however some disadvantages because they perform their computations on embedding, non body‐fitted fluid meshes. In particular, they tend to generate discrete events that introduce discontinuities in the semi‐discretization process and lead to numerical solutions that

The objective of this study is to present an eXtended IsoGeometric formulation for cohesive fracture. The approach exploits the higher‐order inter‐element continuity property of Non‐Uniform Rational B‐Splines (NURBS), in particular the higher accuracy that results for the stress prediction, which yields an improved estimate for the direction of crack propagation compared to customary Lagrangian interpolations

Amethod for efficient computational homogenization of hyperelastic materials under finite strains is proposed. Multiple spatial scales are homogenized in a recursive procedure: starting on the smallest scale, few high fidelity FE computations are performed. The resulting fields of deformation gradient fluctuations are processed by a snapshot POD resulting in a Reduced Basis model (RB). By means of

This paper presents an approach to build a multi‐fidelity kriging metamodel from finite element computations on different meshes for stuctural reliability assessment. The proposed method takes advantage of the computation of bounds on the discretization error, which enables to guarantee the state (safe or failure) of each computation of the performance function. An algorithm to build the meta‐model

The Proper Generalized Decomposition is a well established reduced order method, used to efficiently obtain approximate solutions of multi‐dimensional problems in a procedure that controls the effects of the "curse of dimensionality".The question of assessing the quality of the solutions obtained and adapting the approximations assumed, for example the finite element meshes used, so that the best result

In virtue of their intrinsic integro‐differential formulation of underlying physical behavior of materials, discontinuous computational methods are more beneficial over continuum‐mechanics‐based approaches for materials failure modeling and simulation. However, application of most discontinuous methods is limited to elastic/brittle materials, which is partially due to their formulations are based on

Composite manufacturing processes usually proceed from pre‐impregnated preforms that are consolidated by simultaneously applying heat and pressure, so as to ensure a perfect contact compulsory for making molecular diffusion possible. However, in practice, the contact is rarely perfect. This results in a rough interface where air could remain entrapped, thus affecting the effective thermal conductivity

A parametrized reduced order modeling methodology for cracked two dimensional solids is presented, where the parameters correspond to geometric properties of the crack, such as location and size. The method follows the offline‐online paradigm, where in the offline, training phase, solutions are obtained for a set of parameter values, corresponding to specific crack configurations and a basis for a

Unfitted mesh finite element approximations of immersed incompressible fluidstructure interaction problems which efficiently avoid strong coupling without compromising stability and accuracy are rare in the literature. Moreover, most of the existing approaches introduce additional unknowns or are limited by penalty terms which yield ill‐conditioning issues. In this paper, we introduce a new unfitted

Numerical simulation of cable systems remain delicate due to their geometrical non‐linearity and also to their intrinsic unilateral constitutive law. Indeed Finite Element approaches (if not implemented carefully) fail to predict accurate equilibrium for cable structures. The major issue to be addressed is the ill‐conditioning, starting configuration and wrong choice of descent direction during iterative

We present novel coupling schemes for partitioned multi‐physics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative coupling, support for multi‐rate time stepping, and higher‐order convergence in time. To achieve this, we combine waveform relaxation – a known method to achieve higher

This paper presents a nonlinear augmented finite element method (N‐AFEM) for the analysis of arbitrary crack initiation and propagation in large deformation plates and shells. The FE formulations for plate/shell elements and a shell‐like cohesive zone element, both with explicit consideration of geometric nonlinearity, have been derived in detail. The geometrically nonlinear shell‐like cohesive element

Particles suspension is considerably prevalent in petroleum industry and chemical engineering. The efficient and accurate simulation of such a process is always a challenge for both the traditional computational fluid dynamics (CFD) and lattice Boltzmann method (LBM). Immersed moving boundary (IMB) method is promising to resolve this issue by introducing a particle‐fluid interaction term in the standard

Computational analyses of gradient‐elasticity often require the trial solution to be C1 yet constructing simple C1 finite elements is not trivial. This article develops two 48‐dof 4‐node tetrahedral elements for 3D gradient‐elasticity analyses by generalizing the discrete Kirchhoff method and a relaxed hybrid‐stress method. Displacement and displacement‐gradient are the only nodal dofs. Both methods

Methods to compute the stress intensity factors along a three‐dimensional crack front often display a tenuous rate of convergence under mesh refinement or, worse, do not converge, particularly when applied on unstructured meshes. In this work, we propose an alternative formulation of the interaction integral functional and a method to compute stress intensity factors along the crack front which can

Nouy and Clement [1] introduced the stochastic extended finite element method to solve linear elasticity problem defined on random domain. The material properties and boundary conditions were assumed to be deterministic. In this work, we extend this framework to account for multiple independent input uncertainties, viz., material, geometry and external force uncertainties. The stochastic field is represented

A longstanding challenge in additive manufacturing (AM), the presence of void regions in additively manufactured components cause two main issues: the enclosing of build material powder in powder bed fusion techniques, and limiting tool access in critical post‐processing operations to remove sacrificial support structures. As topology optimization (TO) has embraced and overcome many of the obstacles

The study of dynamic soil‐structure interaction is significant to civil engineering applications, such as machine foundation vibration, traffic‐induced vibration, and seismic dynamic response. The scaled boundary finite element method (SBFEM) is a semi‐analytical algorithm, which is used to solve the dynamic response of a three‐dimensional infinite soil. It can automatically satisfy the radiation boundary

A second‐order face‐centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to solve a set of problems, independent cell‐by‐cell, to retrieve the local values of the solution and its gradient. The main novelty of this approach is the introduction

Numerical treatment of complicated wall geometry has been one of the most important challenges in particle methods for computational fluid dynamics. In this study, a novel wall boundary treatment using analytical volume integrations has been developed for two‐dimensional (2D) incompressible flow simulations with the moving particle semiimplicit method. In our approach, wall geometry is represented

We introduce a goal‐oriented model reduction framework for rapid and reliable solution of parametrized nonlinear partial differential equations with applications in aerodynamics. Our goal is to provide quantitative and automatic control of various sources of errors in model reduction. Our framework builds on the following ingredients: a discontinuous Galerkin finite element (FE) method, which provides

An accurate absorbing boundary condition (ABC) is developed in frequency domain for finite element analysis of scalar wave propagation in unbounded layered half space. The proposed ABC is H‐shaped line that consists of two parts, a new ABC at horizontal bottom boundary of finite domain to replace semi‐infinite strip below horizontal boundary and between two vertical boundaries, and a general consistent

This paper [1] addresses a topic that we have previously approached: the determination of solutions that are strictly equilibrated for plates modelled with the Kirchhoff theory. We start by noting that a simple search on the index of this journal for “Kirchhoff” and “equilibrium” or “Statically admissible” leads to the paper on the general degree equilibrium formulation for Kirchhoff plates that we

This article proposes an approach to resolve the dynamic fracture of brittle materials by incorporating eigenerosion into the material point method (MPM) framework. The eigenerosion approach links the crack propagation to energy conservation based on the variational theory of fracture mechanics. This idea closely resembles the conventional treatment for the phase‐field method. The major difference

This article presents a localizing gradient damage model with evolving micromorphic stress‐based anisotropic nonlocal interactions. The objective is to model mesh independent fracture behavior of quasi‐brittle materials, and to avoid the issues associated with the existing gradient‐enhanced damage models. In the proposed model, an evolving anisotropic nonlocal interaction domain governs the spatial

In this article, a new take on the concept of an active subspace for reducing the dimension of the design parameter space in a multidisciplinary analysis and optimization (MDAO) problem is proposed. The new approach is intertwined with the concepts of adaptive parameter sampling, projection‐based model order reduction, and a database of linear, projection‐based reduced‐order models equipped with interpolation