An efficient iterative inverse procedure is proposed for identification of distribution of loads that had led to a specific crack propagation path in a fractured component. This procedure determines the load applied to a part of the boundary based on the captured crack propagation path. The aim of this work, which is the first time to be presented, is important from the perspective of failure analysis

Through enrichment of the elastic potential by the second order gradient of deformation, gradient elasticity formulations are capable of taking nonlocal effects into account. Moreover, geometry‐induced singularities, which may appear when using classical elasticity formulations, disappear due to the higher regularity of the solution. In this contribution, a mixed finite element discretization for finite

Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational mechanics, including the inversion of borehole logging measurements for oil and gas applications. In this context, DL methods exhibit two key attractive features: a) once trained, they enable to solve an inverse problem

The natural fracture system plays an important role in the development of naturally fractured reservoirs. Traditionally, those reservoirs are simulated using dual‐porosity and dual‐permeability models. Conventional dual‐porosity models adopt over‐simplifications in terms of characterization of the fractured system. Generally, they focus on the hydraulic problem and do not consider the rock and fracture

This article proposes a new approach called revolutionary superposition layout (RSL) for obtaining optimum designs of nonconcurrent multiloads structures in general, and for connecting rod (CR) in particular. Since the compression and tension resulted from the combustion and exhaust strokes are nonconcurrent loads, the importance of this approach arises up. RSL depends on combining the optimum‐design

This paper propose a generalized shape optimization method for transient coupled acoustic‐mechanical interaction problems. The transient problem formulation allows to optimize for a broadband frequency content and the possibility to investigate transient phenomena such as pulse shaping. Throughout the work, the geometry is defined with the help of a nodal based design field, for which its zero level

We consider the numerical approximation of the flow‐coupled phase‐field model of two‐phase incompressible flows using the mass‐conserved Allen‐Cahn equation. Due to the highly nonlinear nature of the coupling, how to develop an accurate and practically efficient scheme has always been a challenging problem. To solve this challenge, we construct a novel effective fully decoupled scheme that is linear

Thermomechanical couplings are present in many materials and should therefore be considered in multiscale approaches. Specific cases of thermomechanical behavior are the isothermal and the adiabatic regime, in which the behavior of real materials differs. Based on the consistent asymptotic homogenization framework for thermomechanically coupled generalized standard materials, the present work is devoted

Whereas various simplistic microplane models of limited applicability, defined by stress‐strain curves on the microplane, can function as either explicit or implicit, the explicit‐to‐implicit conversion of realistic versatile microplane models for plain or fiber‐reinforced concrete, shale and composites has remained a challenge for quarter century. The reason is that these realistic models use microplane

Adaptive structures are characterized by their ability to adjust their geometrical and other properties to changing loads or requirements during service. This contribution deals with a method for the design of quasi‐static motions of structures between two prescribed geometrical configurations that are optimal with regard to a specified quality function while taking large deformations into account

This work presents a data‐driven magnetostatic finite‐element solver that is specifically well‐suited to cope with strongly nonlinear material responses. The data‐driven computing framework is essentially a multiobjective optimization procedure matching the material operation points as closely as possible to given material data while obeying Maxwell's equations. Here, the framework is extended with

The Material Point Method (MPM) is a hybrid particle‐mesh scheme conceptually placed between mesh‐based and mesh‐free methods, combining aspects of both and well suited to solving large deformation engineering problems involving historydependent material models. A unique drawback of the MPM is the cell crossing error whereby material points crossing grid cells suddenly produce spurious stress oscillations

In this paper, a novel adaptive mesh refinement scheme based on trimmed hexahedral meshes is proposed to simulate phase‐field fracture in brittle materials. A regular hexahedral background mesh is adaptively refined using a balanced octree algorithm to resolve the length scale in phase‐field fracture models. Adaptively refined TH meshes are created by cutting octree background meshes with the boundary

A novel reduced‐order modeling method with two‐step strategy is proposed for nonlinear buckling analysis of axially compressed thin‐walled cylinder. The nonlinear response analysis up until the buckling point is achieved quickly by solving the small‐scale reduced‐order model, accounting for the geometrically nonlinear behaviour. The buckling point is determined accurately using an efficient buckling

Driven by the promising applications of nano‐composites, the Steigmann‐Ogden (S‐O) interface stress model is used together with the classical Elasticity theory to model the effective mechanical properties of nano‐composites [32], considering both interface stretching and bending effects. However, no literature has been reported on analytical or numerical solutions for composites containing multiple

Scale separation is often assumed in most multiscale topology optimization frameworks. In this work, topology optimization of heterogeneous structures consisting of inseparable unit cells is studied. The cell morphology is given first and remains unchanged during the optimization process. A nonlocal numerical homogenization method is used to construct a mesoscopic constitutive relationship between

This article addresses the efficient finite element solution of exterior acoustic problems with truncated computational domains surrounded by perfectly matched layers (PMLs). The PML is a popular nonreflecting technique that combines accuracy, computational efficiency, and geometric flexibility. Unfortunately, the effective implementation of the PML for convex domains of general shape is tricky because

Finite elements with Allman’s rotations provide good computational efficiency for explicit codes exhibiting less locking than linear elements and lower computational cost than quadratic finite elements. One way to further raise their efficiency is to increase the feasible time step or increase the accuracy of the lowest eigenfrequencies via reciprocal mass matrices. This paper presents a formulation

The present study proposes a method of robust topology optimization assuming uncertainties in the magnitude and direction of loads applied to a geometrically nonlinear structure. The objective function is the sum of the expected value and the standard deviation of end‐compliance of a structure with a compressible Neo‐Hookean hyperelasticity. In this study, quadratic approximation of the end‐compliance

A higher‐order fictitious domain method (FDM) for Reissner–Mindlin shells is proposed which uses a three‐dimensional background mesh for the discretization. The midsurface of the shell is immersed into the higher‐order background mesh and the geometry is implied by level‐set functions. The mechanical model is based on the tangential differential calculus which extends the classical models based on

For some polycrystalline materials such as austenitic stainless steel, magnesium, TATB, and HMX, twinning is a crucial deformation mechanism when the dislocation slip alone is not enough to accommodate the applied strain. To predict this coupling effect between crystal plasticity and deformation twinning, we introduce a mathematical model and the corresponding monolithic and operator splitting solvers

The generic problem in supervised machine learning is to learn a function f from a collection of samples, with the objective of predicting the value taken by f for any given input. In effect, the learning procedure consists in constructing an explicit function that approximates f in some sense. In this article is introduced a Fourier‐based machine learning method which could be an alternative or a

This article proposes a decoupling scheme for two‐scale analysis of fiber‐reinforced plastics (FRP) exhibiting finite thermoviscoelasticity in consideration of the dependences of resin's mechanical and nonmechanical deformation characteristics on the degree of cure (DOC) and ambient temperature. To characterize the macroscopic material behavior, numerical material tests are carried out on a unit cell

A root‐finding absorbing boundary condition (RFABC) for scalar‐wave propagation problems in infinite anisotropic media was developed. Although the phase velocity and the group velocity in isotropic media have the same sign, the sign of the latter can differ from that of the former in anisotropic media. Therefore, a RFABC for anisotropic scalar waves consistent with the group velocity of the considered

Materials accumulate energy around voids and defects under external loading, causing the formation of micro‐cracks. With increasing or repeated loads, those micro‐cracks eventually coalesce to form macro‐cracks, which in a brittle material can cause catastrophic failure without apparent permanent deformation. At the continuum level, a stochastic phase‐field model is employed to simulate failure through

We present a consistent approach that allows to solve challenging general nonlinear fluid‐structure‐contact interaction (FSCI) problems. The underlying formulation includes both “no‐slip” fluid‐structure interaction as well as frictionless contact between multiple elastic bodies. The respective interface conditions in normal and tangential orientation and especially the role of the fluid stress within

A time step must be selected for any explicit discrete element method (DEM) simulation. This time step must be small enough to ensure a stable simulation but should not be overly conservative for computational efficiency. There are established methods to estimate critical time steps for simulations of spherical particles. However, there is a comparable lack of guidance on choosing time steps for DEM

The wetting of deformable elastic structures has been recently shown to comprise a rich variety of new physical phenomena (stick‐slip motion, durotaxis, Shuttleworth effect, etc.) whose fundamental understanding demands for numerical simulation tools. In this article, we develop a novel unified model and numerical method for this problem. As special features, the method includes exact incompressibility

The research challenges in numerical methods in engineering are in constant evolution. The two driving forces for this evolution are the development of novel methods and algorithms and the investigation of new fields of application where numerical modelling opens unexplored perspectives to experimentalists and practitioners. We took occasion of Prof. Antonio Huerta's sixtieth birthday to ponder the

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

A domain decomposition approach for high‐dimensional random PDEs exploiting the localization of random parameters is presented. To obtain high efficiency, surrogate models in multi‐element representations in the parameter space are constructed locally when possible. The method makes use of a stochastic Galerkin FETI‐DP formulation of the underlying problem with localized representations of involved

One of the most appealing techniques in local refinement for isogeometric analysis (IGA) is hierarchical B‐splines which can be improved by resorting to truncation mechanism called truncated hierarchical B‐splines. Although it has a simple concept, it involves implementing the hierarchical definition of shape functions to existing codes. In this contribution, we present a simple method defined by knot

Recently established Harris Hawks Optimization (HHO) has natural behavior for finding an optimum solution in global search space without getting trapped in previous convergence. However, the exploitation phase of the current Harris Hawks Optimizer algorithm is poor. In the present research, an improved version of the Harris Hawks Optimization algorithm, which combines Harris Hawks Optimizer with Canis

This paper focuses mainly on the development of explicit integration algorithms for structural dynamics. Some known single‐step explicit schemes are firstly reviewed and their algorithmic parameters are uniformly given as a function of ρb, denoting spectral radius at the bifurcation point. The simple review reveals that there are still some problems to be addressed. Then, a simple but general explicit

The present article develops two formulations of zero‐thickness mortar/interface finite elements for unmatched meshes, which are implemented in a unified theoretical framework. The first one is displacement‐based and may be considered a natural extension of the traditional zero‐thickness interface element to the case of unmatched meshes on each side of the discontinuity. The other one is hybrid, with

In this article, a novel mesh‐free, moving Kriging (MK) based collocation scheme for the numerical solution of partial differential equations (PDEs) is introduced. In contrast to methods that are based on a Galerkin weak form of the governing PDEs, the MK collocation (MKC) approach, which is strong form based, is truly mesh‐free in the sense that no background mesh is required for numerical integration

We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi‐discrete approximation and derive optimal error estimates under h‐ and p‐refinement in both the energy and the L2 norms. The performance of the proposed virtual element method is assessed on a set of different computational meshes

A finite element formulation is presented for a direct approach to model elastoplastic deformation in slender bodies using the special Cosserat rod theory. The direct theory has additional plastic strain and hardening variables, which are functions of just the rod's arc‐length, to account for plastic deformation of the rod. Furthermore, the theory assumes the existence of an effective yield function

A condensed algorithm for adaptive component mode synthesis is proposed to compute the dynamics of viscoelastic flexible multibody systems efficiently and accurately. As studied, the continuous use of modes derived from the initial configuration will lead to poor convergence when dealing with geometric nonlinearity caused by large deformations and overall rotations. The modal reduction at a series

When linear inclusions are embedded into a matrix, a perturbation is introduced in the boundary value problem written at the macroscale. Such inhomogeneity can provoke sharp gradients in the solution and a correct evaluation of the interface stress state reveals necessary when localized material degradations can lead to global failure mechanisms. In order to account for such refined description in

In this article, 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

Indirect Trefftz method is proposed for solving two‐dimensional boundary value problems of the strain gradient elasticity theory (SGET). A system of trial functions satisfying the fourth‐order equilibrium equations of SGET are developed based on the generalized Papkovich‐Neuber potentials. The classical part of the displacement solution is represented through the T‐complete system of functions satisfying

The use of pressure‐dependent plasticity models with a non‐associated flow rule causes a loss of the well‐posedness for sufficiently low hardening rates. Apart from a mesh dependence, this can result in poor convergence, or even divergence of the iterative procedure employed to find an equilibrium configuration. This can be aggravated when other nonlinear, dissipative mechanisms are introduced, for

Adaptive algorithms for computing the reduced‐order model of time‐delay systems (TDSs) are proposed in this work. The algorithms are based on interpolating the transfer function at multiple expansion points and greedy iterations for selecting the expansion points. The ℒ ∞ ‐error of the reduced transfer function is used as the criterion for choosing the next new expansion point. One heuristic greedy

When designing a structure or engineering a component, it is crucial to use methods that provide fast and reliable solutions, so that a large number of design options can be assessed. In this context, the proper generalized decomposition (PGD) can be a powerful tool, as it provides solutions to parametric problems, without being affected by the “curse of dimensionality.” Assessing the accuracy of the

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 article, a novel pseudo‐cost domain

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 three‐dimensional bodies by integrating statistic information from experiments, including particle size and shape, and powder

We investigate the temporal accuracy of two generalized‐ α schemes for the incompressible Navier‐Stokes equations. In a widely‐adopted approach, the pressure is collocated at the time step tn + 1 while the remainder of the Navier‐Stokes equations is discretized following the generalized‐ α scheme. That scheme has been claimed to be second‐order accurate in time. We developed a suite of numerical code

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, which forms a stable force state formulation corresponding to the non‐uniform deformation. The proposed controlling scheme does not include

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, that is, their inability to accurately handle the locality of the stress constraints. This article presents a three‐dimensional design methodology that

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 mesh‐based 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

The peridynamic equation consists in an integro‐differential equation of the second order in time which has been proposed for modeling fractures and damages in the context of nonlocal continuum mechanics. In this article, we study numerical methods for the one‐dimension nonlinear peridynamic problems. In particular we consider spectral Fourier techniques for the spatial domain while we will use the

This article 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‐block‐wise 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 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

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, and period elongation are theoretically and numerically solved. The influence of two algorithmic parameters on basic properties of the proposed method is studied to obtain optimal parameters

The primary objective of this study is threefold: (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

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

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

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