This contribution proposes a tribological model within a three‐dimensional contact formulation considering structural anisotropy of the contact interface. A simple elastoplastic constitutive law is adopted for the description of the behavior on the anisotropic contact interface. Starting with the establishment of the thermodynamic framework of the contact problem, the dissipative, irreversible process

A recently proposed phase‐field model for cohesive fracture is examined. Previous investigations have shown stress oscillations to occur when using unstructured meshes. It is now shown that the use of nonuniform rational B‐splines (NURBS) as basis functions rather than traditional Lagrange polynomials significantly reduces this oscillatory behavior. Moreover, there is no effect on the global structural

Cable subsystems characterized by long, slender, and flexible structural elements are featured in numerous engineering systems. In each of them, interaction between an individual cable and the surrounding fluid is inevitable. Such a fluid‐structure interaction has received little attention in the literature, possibly due to the inherent complexity associated with fluid and structural semidiscretizations

We present an adaptive numerical treatment for a recently published model for brittle damage with gradient enhancement. We employ adaptive strategies both in time and space, yielding detailed investigations of the convergence behavior: the damage distribution can be resolved with very high accuracy, turning the damage behavior into cracks known from fracture mechanics. Although the localization is

Benefited from the accuracy improvement in modeling physical problem of complex geometry and integrating the discretization and simulation, the isogeometric analysis in boundary element method (IGABEM) has been drawn a great deal of attention. The nearly singular integrals of 2D potential problem in the IGABEM are addressed by a semi‐analytical scheme in the present work. We use the subtraction technique

Assessing the failure probability of complex aeronautical structure is a difficult task in presence of uncertainties. In this paper, active learning polynomial chaos expansion (PCE) is developed for reliability analysis. The proposed method firstly assigns a Gaussian Process (GP) prior to the model response, and the covariance function of this GP is defined by the inner product of PCE basis function

This contribution is concerned with a coupling approach for nonconforming NURBS patches in the framework of an isogeometric formulation for solids in boundary representation. The boundary representation modeling technique in CAD is the starting point of this approach. We parameterize the solid according to the scaled boundary finite element method and employ NURBS basis functions for the approximation

Modal expansion is a workhorse used in many engineering analysis algorithms. One example is the coupled boundary element‐finite element computation of the backscattering target strength of underwater elastic objects. To obtain the modal basis, a free‐vibration (generalized eigenvalue) problem needs to be solved, which tends to be expensive when there are many basis vectors to compute. In the above‐mentioned

Capturing the interaction between objects that have an extreme difference in Young's modulus or geometrical scale is a highly challenging topic for numerical simulation. One of the fundamental questions is how to build an accurate multiscale method with optimal computational efficiency. In this work, we develop a material‐point‐spheropolygon discrete element method (MPM‐SDEM). Our approach fully couples

We present an interpolation scheme for use with material models involving history‐dependent state variables. The interpolation scheme is based on the solution of a constrained optimization problem, to identify the smoothest monotone curve which produces an admissible solution. Unlike classical schemes used for transport equations, the proposed methodology accounts for the interdependence of the history

Fictitious domain methods, like the Cartesian grid finite element method (cgFEM), are based on the use of unfitted meshes that must be intersected. This may yield to ill‐conditioned systems of equations since the stiffness associated with a node could be small, thus poorly contributing to the energy of the problem. This issue complicates the use of iterative solvers for large problems. In this work

Mesh‐free properties are part of the superiority of cell‐based smoothed finite element method (CS‐FEM), but have yet to be fully exploited for computational fluid dynamics. A novel implementation of CS‐FEM for incompressible viscous fluid flows in stationary and deforming domains discretized by severely distorted bilinear four‐node quadrilateral (Q4) elements is presented in this article. The negative

This article introduces a novel error estimator for the proper generalized decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: it builds on concentration inequalities of Gaussian maps and an adjoint problem with random right‐hand side, which we approximate using the PGD. The effectivity of this randomized error estimator can be arbitrarily close to unity

Coupled diffusion of solvent molecules and mechanical stretching of polymeric networks induced swelling/deswelling in polymeric gels contributes to the ability of its “smart response” and “environmental sensitivity.” In this article, the coupled diffusion and large deformation of polymeric gels are clarified into three kinds of deformation conditions which all involve swelling/deswelling. The real

A challenge in engineering design is to choose suitable objectives and constraints from many quantities of interest, while ensuring an optimization is both meaningful and computationally tractable. We propose an optimization formulation that can take account of more quantities of interest than existing formulations, without reducing the tractability of the problem. This formulation searches for designs

This work presents a generalized substructuring‐based topology optimization method for the design hierarchical lattice structures to maximize the first eigenvalue. In this method, the macrostructure is assumed to be composed of substructures with a common artificial lattice geometry pattern. And two different yet connected scales are considered through a lattice geometry feature parameter. The feature

Optimal design of structures for fracture resistance is a challenging subject. This appears to be largely due to the strongly nonlinear governing equations associated with explicitly modeling fracture propagation. We propose a topology optimization formulation, in which low weight structures are obtained with significantly increased resistance to brittle fracture, in which crack propagation is explicitly

This work investigates matrix‐free algorithms for problems in quasi‐static finite‐strain hyperelasticity. Iterative solvers with matrix‐free operator evaluation have emerged as an attractive alternative to sparse matrices in the fluid dynamics and wave propagation communities because they significantly reduce the memory traffic, the limiting factor in classical finite element solvers. Specifically

Generalized or eXtended finite element methods (GFEM/XFEM) for crack problems have been studied extensively. The GFEM/XFEM are called extrinsic if additional functions are enriched at every node in certain domains, while they are called degree of freedom (DOF)‐gathering if the singular enriched functions are gathered using cutoff functions. The DOF‐gathering GFEM/XFEM save the additional DOFs compared

We propose a method to solve the acoustic wave equation on an immersed domain using the hybridizable discontinuous Galerkin method for spatial discretization and the arbitrary derivative method with local time stepping (LTS) for time integration. The method is based on a cut finite element approach of high order and uses level set functions to describe curved immersed interfaces. We study under which

This article describes a numerical method to reconstruct the stress field starting from strain data in elastoplasticity. Usually, this reconstruction is performed using the radial return algorithm, commonly implemented also in finite element codes. However, that method requires iterations to converge and can bring to errors if applied to experimental strain data affected by noise. A different solution

Fracture is one of the most common failure modes in brittle materials. It can drastically decrease material integrity and structural strength. To address this issue, we propose a level‐set (LS) based topology optimization procedure to optimize the distribution of reinforced inclusions within matrix materials subject to the volume constraint for maximizing structural resistance to fracture. A phase‐field

We study the application to compressible and incompressible three‐dimensional elasticity problems of the technique that we proposed in 2009 for the recovery of equilibrated stresses from compatible finite element solutions. The case of finite elements with linear displacement approximations, for which the partitioned systems of loads are not initially balanced in terms of rotational equilibrium, addressed

Effects of nonaffine elements on the accuracy of 3D H(div)‐conforming finite elements are studied. Instead of convergence order k+1 for the flux and the divergence of the flux obtained with Raviart‐Thomas or Nédélec spaces with normal traces of degree k, based on affine hexahedra or triangular prisms, reduced orders k for the flux and k−1 for the divergence of the flux may occur for distorted elements

A computational framework is developed to model and optimize the nonlinear multiscale response of three‐dimensional particulate composites using an interface‐enriched generalized finite element method. The material nonlinearities are associated with interfacial debonding of inclusions from a surrounding matrix which is modeled using C−1 continuous enrichment functions and a cohesive failure model.

An efficient optimization framework is developed in this study by integrating auxiliary projection‐based multigrid isogeometric reanalysis (MG‐IGR) and metaheuristic searching techniques. It is well known that the inherent characteristics of isogeometric analysis (IGA) are superior in shape optimization problems. Inheriting the characteristics of IGA, an auxiliary projection‐based MG reanalysis (MGR)

Cracks with quasibrittle behavior are extremely common in engineering structures. The modeling of cohesive cracks involves strong nonlinearity in the contact, material, and complex transition between contact and cohesive forces. In this article, we propose a novel contact algorithm for cohesive cracks in the framework of the extended finite element method. A cohesive‐contact constitutive model is introduced

The accuracy of the finite element model is essential for fatigue analysis and vibration of a flexible body. This paper presents a finite element model updating (FEMU) algorithm based on crows search algorithm incorporated with Levy flight (LFCSA). The proposed algorithm is tested on the updating of two different cases: a simple structure (beam) and a complex structure (gearbox housing). To verify

In this paper, a finite element method is proposed to analyze the microscopic and macroscopic mechanical behaviors of heterogeneous media with randomly distributed inclusions. A simple mesh partitioned the domain into regular quadrilateral or triangular elements, where one element may contain two phases. An assumed stress hybrid formulation is implemented in the finite element model and the functional

“Open‐close iteration” is a crucial algorithm for handling complex contacts in numerical manifold method (NMM) and discontinuous deformation analysis (DDA). This algorithm has proved to be robust and efficient for decades. However, as some researchers have pointed out, the original open‐close iteration may involve errors in sliding tests, especially in critical sliding tests with cohesive contacts

A reduced order model designed by means of a variational multiscale stabilized formulation has been applied successfully to fluid‐structure interaction problems in a strongly coupled partitioned solution scheme. Details of the formulation and the implementation both for the interaction problem and for the reduced models, for both the off‐line and on‐line phases, are shown. Results are obtained for

An extended/generalized finite element method (XFEM/GFEM) for simulating quasistatic crack growth based on a phase‐field method is presented. The method relies on approximations to solutions associated with two different scales: a global scale, that is, structural and discretized with a coarse mesh, and a local scale encapsulating the fractured region, that is, discretized with a fine mesh. A stable

We present a novel method for computational design of adaptive shape‐memory alloy (SMA) structures via topology optimization. By optimally distributing a SMA within the prescribed design domain, the proposed algorithm seeks to tailor the two‐way shape‐memory effect (TWSME) and pseudoelasticity response of the SMA materials. Using a phenomenological material model, the thermomechanical response of the

A new C0 8‐node 48‐DOF hexahedral element is developed for analysis of size‐dependent problems in the context of the modified couple stress theory by extending the methodology proposed in our recent work (Shang et al., Int J Numer Methods Eng 119(9): 807‐825, 2019) to the three‐dimensional (3D) cases. There are two major innovations in the present formulation. First, the independent nodal rotation

In this article, a study of residual based a posteriori error estimation is presented for the partition of unity finite element method (PUFEM) for three‐dimensional (3D) transient heat diffusion problems. The proposed error estimate is independent of the heuristically selected enrichment functions and provides a useful and reliable upper bound for the discretization errors of the PUFEM solutions. Numerical

Finite element analysis of ductile fracture with tetrahedral elements faces two numerical issues: volumetric locking and mesh sensitivity. In this paper, two widely adopted remedies for volumetric locking (F‐bar and mixed field) are evaluated, and the superior performance of the mixed field method is demonstrated. Building on the mixed field formulation, a gradient enhancement is further incorporated

A new topology optimization scheme called the projection‐based ground structure method (P‐GSM) is proposed for linear and nonlinear topology optimization designs. For linear design, compared to traditional GSM which are limited to designing slender members, the P‐GSM can effectively resolve this limitation and generate functionally graded lattice structures. For additive manufacturing‐oriented design

Finite element stereo digital image correlation (FE‐SDIC) requires a crucial calibration phase in which the initial CAD needs to be updated to fit the actual shape of the specimen. On the one hand, the use of a FE mesh facilitates the coupling of measurements with simulation tools, while on the other hand, it provides a unique, fine description of both the geometry and the displacement, which often

In this work, the modally equivalent perturbed system (MEPS) which was originally developed for finding the parametrically rich solution space of linear time‐invariant systems is modified for time‐varying cases and applied to find the characteristically rich nonlinear solution space given arbitrary initial or boundary conditions, or system inputs. An integral form of the non‐Hamiltonian Liouville equation

Anisotropic diffusion is important to many different types of common materials and media. Based on structured Cartesian meshes, we develop a three‐dimensional (3D) nonhomogeneous immersed finite‐element (IFE) method for the interface problem of anisotropic diffusion, which is characterized by an anisotropic elliptic equation with discontinuous tensor coefficient and nonhomogeneous flux jump. We first

Sequentially linear analysis (SLA), an event‐by‐event procedure for finite element (FE) simulation of quasi‐brittle materials, is based on sequentially identifying a critical integration point in the FE model, to reduce its strength and stiffness, and the corresponding critical load multiplier (λcrit), to scale the linear analysis results. In this article, two strategies are proposed to efficiently

In this work we consider the numerical solution of incompressible flows on two‐dimensional manifolds. Whereas the compatibility demands of the velocity and the pressure spaces are known from the flat case one further has to deal with the approximation of a velocity field that lies only in the tangential space of the given geometry. Abandoning H1‐conformity allows us to construct finite elements which

In this work, we present an approach for the efficient treatment of parametrized geometries in the context of proper orthogonal decomposition (POD)‐Galerkin reduced order methods based on finite‐volume full order approximations. On the contrary to what is normally done in the framework of finite‐element reduced order methods, different geometries are not mapped to a common reference domain: the method

Defects such as gas pores can be formed and trapped in the fusion zone during laser welding. These defects can significantly affect the mechanical reliability of the welded joint. Current nondestructive inspection technologies are able to detect micro‐voids in a mass production context. Finite element analysis can therefore be used to assess the lifetime of an observed component via image‐based modeling

Following the so‐called cracking elements method (CEM), we propose a novel Galerkin‐based numerical approach for simulating quasi‐brittle fracture, named global cracking elements method (GCEM). For this purpose the formulation of the original CEM is reorganized. The new approach is embedded in the standard framework of the Galerkin‐based finite‐element method (FEM), which uses disconnected element‐wise

In this article, we present a numerical discretization of the coupled elastoacoustic wave propagation problem based on a discontinuous Galerkin spectral element approach in a three‐dimensional setting. The unknowns of the coupled problem are the displacement field and the velocity potential, in the elastic and the acoustic domains, respectively, thereby resulting in a symmetric formulation. After stating

A generalized multiscale finite element method is introduced to address the computationally taxing problem of elastic fracture across scales. Crack propagation is accounted for at the microscale utilizing phase field theory. Both the displacement‐based equilibrium equations and phase field state equations at the microscale are mapped on a coarser scale. The latter is defined by a set of multinode coarse

In this paper, we construct new high‐order numerical integration schemes for tetrahedra, with positive weights and integration points that are in the interior of the domain. The construction of cubature rules is a challenging problem, which requires the solution of strongly nonlinear algebraic (moment) equations with side conditions given by affine inequality constraints. We present a robust algorithm

This contribution proposes the first three‐dimensional (3D) beam‐beam interaction model for molecular interactions between curved slender fibers undergoing large deformations. While the general model is not restricted to a specific beam formulation, in the present work, it is combined with the geometrically exact beam theory and discretized via the finite element method. A direct evaluation of the

In low Mach number aeroacoustics, the known disparity of length scales makes it possible to apply well‐suited simulation models using different meshes for flow and acoustics. The workflow of these hybrid methodologies include performing an unsteady flow simulation, computing the acoustic sources, and simulating the acoustic field. Therefore, hybrid methods seek for robust and flexible procedures, providing

Smooth particle hydrodynamics (SPH) is gaining popularity for the simulation of solids subjected to machining, wear, and impacts. Its attractiveness is due to its abilities to simulate problems, involving large deformations resulting from the absence of mesh as well as the development of the total‐Lagrangian version of SPH (TLSPH) to solve tensile instabilities and an hourglass control algorithm to

This article describes a numerical solution to the topology optimization problem using a time‐evolution equation. The design variables of the topology optimization problem are defined as a mathematical scalar function in a given design domain. The scalar function is projected to the normalized density function. The adjoint variable method is used to determine the gradient defined as the ratio of the

The hybrid‐Trefftz stress element is used to emulate conventional finite elements for analysis of Kirchhoff and Mindlin‐Reissner plate bending problems. The element is hybrid because it is based on the independent approximation of the stress‐resultant and boundary displacement fields. The Trefftz variant is consequent on the use of the formal solutions of the governing Lagrange equation to approximate

A new strategy for the mass matrix lumping of enriched elements for explicit transient analysis is presented. It is shown that to satisfy the kinetic energy conservation, the use of zero or negative masses for enriched degrees of freedom of lumped mass matrix may be necessary. For a completely cracked element, by lumping the mass of each side of the interface into the finite element nodes located at

A local grid refinement scheme for the material point method with B‐spline basis functions (BSMPM) is developed based on the concept of bridging domain approach. The fine grid is defined in the local large‐deformation regions to accurately capture the complex material responses, whereas other spatial domains are discritized by coarse grids. In the overlapping domain between the fine and coarse grids

Accurate numerical modeling of fracture in solids is a challenging undertaking that often involves the use of computationally demanding modeling frameworks. Model order reduction techniques can be used to alleviate the computational effort associated with these models. However, the traditional offline‐online reduction approach is unsuitable for complex fracture phenomena due to their excessively large

This paper discusses the concepts of auto‐ and cross‐interdependence in interval field finite element analysis. In classic interval analysis, independent intervals are used to construct hyper‐rectangular input spaces that correspond to the bounded uncertainty that is present on some model parameters. This is a direct result from the inability of modeling interdependence. Such assumption of complete

In this article, we present a novel nodal integration scheme for meshfree Galerkin methods, which draws on the mathematical framework of the virtual element method. We adopt linear maximum‐entropy basis functions for the discretization of field variables, although the proposed scheme is applicable to any linear meshfree approximant. In our approach, the weak form integrals are nodally integrated using

This study considers an efficient method for the estimation of quantiles associated to very small levels of probability (up to O(10−9)), where the scalar performance function J is complex (eg, output of an expensive‐to‐run finite element model), under a probability measure that can be recast as a multivariate standard Gaussian law using an isoprobabilistic transformation. A surrogate‐based approach

The authors proposed a quadrilateral shell element enriched with degrees of freedom to represent thickness‐stretch. The quadrilateral shell element can be utilized to consider large deformations for nearly incompressible materials, and its performance is demonstrated in small and large deformation analyses of hyperelastic materials in this study. Formulation of the proposed shell element is based on