This article investigates the convergence properties of the augmented finite element method (AFEM). The AFEM is here used to model weak discontinuities independently of the underlying mesh. One noticeable advantage of the AFEM over other partition of unity methods is that it does not introduce additional global unknowns. Numerical 2D experiments illustrate the performance of the method and draw comparisons

The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline‐online decomposition, a.k.a. a learning‐execution process. A key feature of the method is a greedy algorithm repeatedly scanning the training set, a fine discretization of the parameter domain, to identify the next dimension of the parameter‐induced solution manifold

The recent drive for producing lightweight and high performance designs on reduced timelines has promoted the need for computational design generation tools such as Multi‐Material Topology Optimization (MMTO). However, MMTO has drawn some industry skepticism as it assumes different material elements to be perfectly fused together. To address this concern, in this paper, a novel pseudo‐cost domain (PCD)

We present a powder‐scale computational framework to predict the microstructure evolution of metals in Powder Bed Fusion Additive Manufacturing (PBF AM) processes based on the Hot Optimal Transportation Meshfree (HOTM) method. The powder bed is modeled as discrete and deformable threedimensional bodies by integrating statistic information from experiments, including particle size and shape, and powder

In topology optimization, the treatment of stress constraints for very large scale problems (more than 100 million elements and more than 600 million stress constraints) has so far not been tractable due to the failure of robust agglomeration methods, i.e. their inability to accurately handle the locality of the stress constraints. This paper presents a three‐dimensional design methodology that alleviates

Smoothed finite element method with the node‐based strain smoothing domains (NS‐FEM) is remarkable for the upper‐bound feature and insensitivity to the volumetric locking. As a meshbased methodology, its application is limited by the burdensome meshing for which elements align with the physical domain. We extend the strain smoothing in NS‐FEM to the numerical manifold method (NMM) with unfitted meshes

This paper presents a novel, scalable parallel computing framework for large‐scale and multiscale simulations of granular media. Key to the new framework is an innovative thread‐blockwise representative volume element (RVE) parallelism, inspired by the resemblance between a typical multiscale computational hierarchy and the hierarchical thread structure of graphics processing units (GPUs). To solve

This article presents a new adaptive reduced order model for resolving the angular direction of the Boltzmann transport equation, based on proper orthogonal decomposition (POD) and the method of snapshots. It builds upon previous methods of applying POD to the angular dimension, with modifications to increase accuracy and solver stability. Previous methods used continuous global functions spanning

A novel explicit time integration method is proposed on the basis of cubic b‐spline interpolation and weighted residual method. Its calculation formulation and procedure are presented. Accuracy, algorithmic damping (AD), and period elongation (PE) are theoretically and numerically solved. The influence of two algorithmic parameters on basic properties of the proposed method is studied to obtain optimal

We present a novel rp‐adaptation strategy for high‐fidelity simulations of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimizer to r‐adapt the mesh and cluster degrees of freedom there. In regions of smooth flow, we locally increase or decrease the local resolution through increasing or decreasing the polynomial

This article proposes a formulation for the analysis of delamination and fracture propagation problems at the interelement interface, with perfect adhesion at the pre‐failure condition and with linear softening at the post‐failure regime. The proposed formulation is based on the hybrid equilibrium element (HEE) model, with stress fields which strongly verify the homogeneous equilibrium equations and

A novel, accurate, and computationally efficient integration approach is developed to integrate small strain viscoplastic constitutive equations involving nonlinear coupled first‐order ordinary differential equations. The developed integration scheme is achieved by a combination of the implicit backward Euler difference approximation and the implicit asymptotic integration. For the uniaxial loading

A novel mixed shell finite element (FE) is presented. The element is obtained from the Hellinger–Reissner variational principle and it is based on an elastic solution of the generalized stress field, which is ruled by the minimum number of variables. As such, the new FE is isostatic because the number of stress parameters is equal to the number of kinematical parameters minus the number of rigid body

In this work, we have developed a state‐based peridynamics theory for nonlinear Reissener‐Mindlin shells to model and predict large deformation of shell structures with thick wall. The nonlocal peridynamic theory of solids offers an integral formulation that is an alternative to traditional local continuum mechanics models based on partial differential equations. This formulation is applicable for

We present an efficient adjoint‐based framework for computing sensitivities of quantities of interest with respect to material parameters for coupled fluid‐structural acoustic systems with explicit interface coupling. The fluid is modeled using the Helmholtz equation and the structure is modeled using the Navier‐Cauchy equations. Sensitivities are used to drive a gradient based optimization algorithm

Non‐ordinary state‐based peridynamics (NOSBPD) has instability issue due to zero‐energy modes during nodal integration. A zero‐energy mode controlling scheme of NOSBPD for laminated composite materials is derived by using the linearized bond‐based peridynamics (BBPD), which forms a stable force state formulation corresponding to the non‐uniform deformation. The proposed controlling scheme does not

Numerical model reduction is adopted for solving the microscale problem that arizes from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields. A reduced basis is obtained for the pressure field using (i) spectral decomposition (SD) and (ii) proper orthogonal decomposition (POD). This strategy has been used in previous work—the main contribution

The Fragile Points Method (FPM) is an elementarily simple Galerkin meshless method, employing Point‐based discontinuous trial and test functions only, without using element‐based trial and test functions. In this study, the algorithmic formulations of FPM for linear elasticity are given in detail, by exploring the concepts of point stiffness matrices and numerical flux corrections. Advantages of FPM

In this paper, we propose a virtual interface‐coupled technique to model the arbitrary discontinuous interface based on the three‐field dual mortar method. The computational domain is divided into several subdomains and the enriched nodes are individually introduced to construct the approximation of the displacement field. This method provides a flexible way to describe the multiple‐body contact with

Enriched finite element methods have gained traction in recent years for modeling problems with material interfaces and cracks. By means of enrichment functions that incorporate a priori behavior about the solution, these methods decouple the finite element discretization from the geometric configuration of such discontinuities. Taking advantage of this greater flexibility, recent studies have proposed

Interior‐point methods are well suited for solving convex non‐smooth optimization problems which arise for instance in problems involving plasticity or contact conditions. This work attempts at extending their field of application to optimization problems involving either smooth but non‐convex or non‐smooth but convex objectives or constraints. A typical application for such kind of problems is finite‐strain

This paper provides a method for the simultaneous topology optimization of parts and their corresponding joint locations in an assembly. Therein, the joint locations are not discrete and predefined, but continuously movable. The underlying coupling equations allow for connecting dissimilar meshes and avoid the need for remeshing when joint locations change. The presented method models the force transfer

In this paper, an implicit gradient force‐based beam element is developed for analysis of reinforced concrete structures. The element is settled on the framework of Timoshenko beam theory, and adopts force interpolations to construct the element formulation. The sectional constitutive relation is described by the well‐known fiber model, where the multi‐axial softened damage‐plasticity model is used

Brain tissues are known for exhibiting complex nonlinear and time‐dependent properties, which require visco‐hyperelastic constitutive models for proper simulation. In this paper, a Total Lagrangian Explicit Selective Smoothed Finite Element Method (Selective S‐FEM) is formulated to analyze the dynamic behavior of incompressible brain tissues undergoing extremely large deformation. The proposed Selective

An Iterative Reanalysis Approximation‐ (IRA) assisted Moving Morphable Components‐ (MMCs) based topology optimization is developed (IRA‐MMC) in this study. Compared with other classical topology optimization methods, Finite Element‐based solver is replaced with the suggested IRA. In this way, the expensive computational cost can be significantly saved by several nested iterations. In the suggested

A new multiphysics mode synthesis (MMS) is presented for the construction of reduced‐order models of acoustic fluid‐structure interaction systems. The present acoustic‐structure interaction model is symmetric and consists of the fluid pressure p, the fluid displacement potential φ, and the structural displacement u. In carrying out MMS, the structure is first reduced, which is then applied to the coupling

The collapse mechanism identification and limit load calculation of block composite structures are essential tasks in practical engineering. In this work, the discontinuity layout optimization (DLO) is utilized to simulate a stable blocky system structure under static and pseudostatic loading by considering soil–structure interaction effects. The program refers to the discretization of the system

In Jakeman et al,1 Figures 10 and 11 were corrected to: FIGURE 1 Open in figure viewerPowerPoint The number of simulations (left) and fraction of total work (right) assigned to each approximate advection diffusion model at the point labeled 1 in Figure 9. Here M 𝒦 𝒥 | α = card 𝒵 𝒦 𝒥 | α is the number of samples, of the random variables, at which f ^ α is evaluated. The number on top of the bars

The primary objective of this study is three‐fold: (1) to present a general higher‐order shell theory to analyze large deformations of thin or thick shell structures made of general compressible hyperelastic materials; (2) to formulate an efficient shell theory using the orthonormal moving frame, and (3) to develop and apply the nonlinear weak‐form Galerkin finite element model for the proposed shell

Contact detection significantly affects the computational efficiency of discrete element simulations, especially for irregularly shaped elements. The dilated polyhedron is constructed by the Minkowski sum of a dilated sphere and a core convex polyhedron. One of the greatest advantages of using the dilated polyhedron in contact detection lies in its ability to be solved by calculating the nearest distance

Phase‐field modeling, which introduces the regularized representation of sharp crack topologies, provides a convenient strategy for tackling 3D fracture problems. In this work, an adaptive isogeometric‐meshfree approach is developed for the phase‐field modeling of brittle fracture in a 3D polycrystalline material. The isogeometric‐meshfree approach uses moving least‐squares approximations to construct

Peridynamics is a nonlocal theory which has been successfully applied to solid mechanics and crack propagation problems over the last decade. This methodology, however, may lead to large computational calculations which can soon become intractable for many problems of practical interest. In this context, a technique to couple—in a global/local sense–three‐dimensional peridynamics with one‐dimensional

Digital twins can be defined as digital representations of physical entities that employ real‐time data to enable understanding of the operating conditions of these entities. Here we present a particular type of digital twin that involves a combination of computer vision, scientific machine learning and augmented reality. This novel digital twin is able, therefore, to see, to interpret what it sees—and

In this study, we integrate the advantages of differential quadrature method (DQM) and finite element method (FEM) to construct a C1‐type four‐node quadrilateral element with 48 degrees of freedom (DOF) for strain gradient Mindlin micro‐plates. This element is free of shape functions and shear locking. The C1‐continuity requirements of deflection and rotation functions are accomplished by a fourth‐order

This paper presents a comment to the article “A method for smoothing multiple yield functions” by Andy Wilkins, Benjamin W. Spencer, Amit Jain and Bora Gencturk. The article was published in International Journal for Numerical Methods in Engineering, 2020, issue 121, pages 434–449.

In the discrete element method (DEM) simulation for wear prediction, structural boundary is now represented extensively by triangular meshes with high resolution, which brings a huge computational cost. A DEM‐based method for predicting the wear evolution of structural boundary has been developed for computational efficiency. The structural boundary subjected to wear is represented by the spherical

This article proposes an efficient approach for solving three‐dimensional (3D) topology optimization problem. In this approach, the number of design variables in optimization as well as the number of degrees of freedom in structural response analysis can be reduced significantly. This is accomplished through the use of scaled boundary finite element method (SBFEM) for structural analysis under the

We show that under suitable hypotheses on the nonporous material law and a geometric regularity condition on the pore space, Moulinec‐Suquet's basic solution scheme converges linearly. We also discuss for which derived solvers a (super)linear convergence behavior may be obtained, and for which such results do not hold, in general. The key technical argument relies on a specific subspace on which the

We present a numerical method for the solution of nonlinear geomechanical problems involving localized deformation along shear bands and fractures. We leverage the boundary element method to solve for the quasi‐static elastic deformation of the medium while rigid‐plastic constitutive relations govern the behavior of displacement discontinuity (DD) segments capturing localized deformations. A fully

The topology optimization problem of a continuum structure is further investigated under the independent position uncertainties of multiple external loads, which are now described with an interval vector of uncertain‐but‐bounded variables. In this study, the structural compliance is formulated with the quadratic Taylor series expansion of multiple loading positions. As a result, the objective gradient

In this paper, we present an algorithm to construct high‐order fully symmetric cubature rules for tetrahedral and pyramidal elements, with positive weights and integration points that are in the interior of the domain. Cubature rules are fully symmetric if they are invariant to affine transformations of the domain. We divide the integration points into symmetry orbits where each orbit contains all

The design of multibody systems involves high fidelity and reliable techniques and formulations that should help the analyst to make reasonable decisions. Given that constrained equations of motion for the simplest of multibody systems are highly nonlinear, determining the sensitivity terms is a computationally intensive and complex process that requires the application of special procedures. In this

The standard Fluid‐Structure Interaction (FSI) coupling, that uses as unknowns velocity and pressure for the fluid and displacements for the solid, is compared against two novel types of coupling, the first one a three‐field coupling (velocity–pressure–stress/displacement–pressure–stress) introduced by the authors in a recent work, and a two‐field coupling (velocity–pressure/displacement–pressure)

Conventional offline training of reduced‐order bases in a predetermined region of a parameter space leads to parametric reduced‐order models that are vulnerable to extrapolation. This vulnerability manifests itself whenever a queried parameter point lies in an unexplored region of the parameter space. This article addresses this issue by presenting an in situ, adaptive framework for nonlinear model

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

The material point method (MPM) combines Eulerian method and Lagrangian method and thus both Lagrangian particle position and interaction between neighboring Eulerian grid cells will affect the simulation stability. However, the original critical time step formula in the standard MPM does not reflect the effect of particle position and neighboring cell interaction on stability and overestimates the

In this study, a computational framework is proposed to investigate multiscale dynamic fracture phenomena in materials with microstructures. The micro‐ and macro‐scales of a composite material are integrated by introducing an adaptive microstructure representation. Then, the far and local fields are simultaneously computed using the equation of motion, which satisfies the boundary conditions between

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 macroenergy 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

The rotation degree of freedom in discontinuous deformation analysis (DDA) 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

An adaptive scheme to generate reduced‐order models for parametric nonlinear dynamical systems is proposed. It aims to automatize the proper orthogonal decomposition (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

Unfitted mesh finite element approximations of immersed incompressible fluid‐structure 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

To consistently coarsen arbitrary unstructured meshes, an adaptive mesh morphogenesis process is used in conjunction with the virtual element method. The morphogenesis procedure is performed by clustering elements based on a posteriori error estimation. Additionally, an edge straightening scheme is introduced to reduce the number of nodes and improve accuracy of solutions. The adaptive morphogenesis

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. Infrared (IR) camera measurements are then combined with the system model via a linear Kalman filter. As a result of the data assimilation

The immersed moving boundary (IMB) scheme has been extensively used to couple the discrete element method (DEM) with the lattice Boltzmann method (LBM). In the literature, only the formulation of IMB for lattice nodal cells covered by a single‐solid particle was given. The treatment of situations where a nodal cell is covered by two or more solid particles is seldom discussed. It is found that some

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

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

We present novel coupling schemes for partitioned multiphysics 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 multirate time stepping, and higher‐order convergence in time. To achieve this, we combine waveform relaxation—a known method to achieve higher‐order

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

Energy‐conserving integrations are widely used in long‐time simulations of mechanical systems because they exhibit excellent stability and conserve the discrete energy in conservative systems. However, in many applications, their errors of other quantities, for example, trajectory errors, are generally not bounded and increase with time. This article develops a parameter‐preadjusted energy‐conserving