Almost all the mesh-free methods are restricted to 2-D problems owing to the difficulty in generating 3-D grids. One effective way to overcome this limitation is to utilize the concept of hierarchical modeling for elastic structures. It was introduced originally for the dimensionally-reduced analysis of 3-D structures, but it can be used for the reverse purpose. By assuming the displacement field in

To improve the impact resistance of reinforced concrete structures, a detailed understanding of the dynamic response is required. This study investigates this impact resistance using experiments in combination with 3D non-linear finite element (FE) simulations. The experiments made use of high-speed photography and digital image correlation (DIC), while a damage-plasticity constitutive model for concrete

Cellular ceramic materials possess many favorable properties that allow to develop efficient modern-day high-temperature thermal energy conversion systems and processes. The energy conversion within these porous media is governed by tightly coupled conduction–radiation physics. To efficiently design and optimize these systems, a comprehensive understanding of the conduction–radiation behavior within

This paper introduces the inverse finite element method using simple brick elements that can be used for shell analysis. The proposed element is the inverse counterpart of an existing Lagrangean-based “direct” trilinear hexahedral finite element that uses the approaches of reduced integration, assumed natural strains and enhanced assumed strain to prevent locking defects in shell modeling. Like the

The wave finite element method has been developed for waveguides and periodic structures with advantages in the calculation time. However, this method cannot be applied easily if the structure is subjected to complex or density loads and this is the aim of this article. Based on the finite element method, the dynamic equation of one period of the structure is rewritten to obtain a relation between

A mesh adaption approach for strongly coupled problems is proposed, based on a variational principle. The adaption technique relies on optimality properties of an energy-like potential and is hence free from error estimates and the associated computational cost. According to the saddle point nature of this variational principle, a staggered solution approach appears more natural and leads to separate

One of the main issues when dealing with the numerical optimization of mechanical structures is the balance between computation time and model accuracy. The work presented herein aims at accelerating global optimization by using the framework of Bayesian optimization on a quantity of interest together with multiple levels of fidelity. These multi-fidelity data are generated from a model-order reduction

In this work, we introduce a novel hp-adaptive strategy. The main goal is to minimize the complexity and implementational efforts hence increasing the robustness of the algorithm while keeping close to optimal numerical results. We employ a multi-level hierarchical data structure imposing Dirichlet nodes to manage the so-called hanging nodes. The hp-adaptive strategy is based on performing quasi-optimal

A background to the constitutive modeling of elastic-inelastic material response is provided to highlight the uniqueness of the Eulerian formulation of general nonlinear fully anisotropic thermoelastic-inelastic materials proposed in Rubin (1994) [1]. This model introduced Eulerian evolution equations for a triad of microstructural vectors that characterize elastic deformations and anisotropic orientations

Ground-borne vibrations are disturbing to human beings. In order to model and reduce these vibrations, the calculation of the harmonic Green's-functions of the soil is highly required since the most effective numerical solution to predict ground-borne vibration is to couple the finite-element and the boundary-element methods. In this work, we elaborate a direct space-frequency formulation that is especially

The extended finite element method (XFEM) and the level set method (LSM) are applied to simulate the solidification phenomenon and the behavior of the liquid-solid phase transition. The temperature-based energy equation is loosely-coupled with the incompressible Navier-Stokes (INS) equations and solved by XFEM using the Stefan condition to express the energy conservation law for phase change. The INS

Improving gas turbine performance depends almost exclusively on the maximum temperature of the combustion gases. This temperature is limited by the thermomechanical strength of the turbine vanes. In this work, a Chimera approach for overlapping grids in the finite element method (FEM) context is proposed to optimize the arrangement of several cooling passages within the vane to minimize its average

The cracking elements method (CEM) is a novel Galerkin-based numerical approach for simulating cracking and fracturing processes. It is a crack-opening approach that avoids precise descriptions of the mechanical states of crack tips and captures the initiations and propagations of multiple cracks without nodal enrichment or crack tracking. The CEM requires element types with nonlinear interpolation

We propose an adaptive curved virtual element method (ACVEM) which is able to combine an exact representation of the involved computational geometry and a dynamic tuning of the optimal mesh resolution through a robust and efficient residual-based a-posteriori error estimator. A theoretical analysis on the reliability of the estimator and a gallery of numerical tests supports the efficacy of the proposed

A new numerical method is presented for evaluating the effective properties of heterogeneous viscoelastic materials, and an efficient and high-fidelity Direct Numerical Simulation (DNS) is addressed by integrating the advantages of the quadtree Scaled Boundary Finite Element Method (SBFEM) and a temporally recursive adaptive algorithm. The quadtree technique that can be directly implemented with input

In case of very thin surface coatings, the coating layer is often ignored in a large-scale Finite Element Analysis. This is mainly due to extensive numerical cost required to capture the correct mechanical behaviour of the layer, especially if the coating is significantly softer than the substrate. To overcome the excessive computational cost, due to the full discretization of the thin layer, in large-scale

Experimental and numerical study regarding fracture in laser-processed steel components is addressed in the present work. Samples of stainless steel (SS) 316L were obtained by an additive manufacturing process, the directed energy deposition (DED), using different deposition orientations, and tested experimentally until fracture. Microstructural investigations, prior and after fracture, were performed

Although the Hughes-Winget rotation tensor is not strongly objective when stretching occurs during a time step it is very accurate when the incremental stretching during the time step is small, a condition that is almost always met in practice. Two types of evolution equations based on the Jaumann derivative are examined which show that the main source of error in the numerical algorithms is due to

The paper explores the ability of an explicit time integration procedure to simulate the dynamics of shear rupture between unbounded elastic blocks on frictional interface, modeled with the finite element method. The behaviour of the interface is governed by Rate and State (RS) friction laws, proposed to describe the rate dependent phenomena observed in experiments on rocks and many other materials

With the goal of improving upon the accuracy of D. Arnold's MINI element for finite strain plasticity, and more precisely calculate the elastic/plastic interface, we extend this element formulation to include, as nodal degrees-of-freedom, a function of the second invariant of the deviatoric stress, J2. A finite-strain J2 − u − p mixed formulation of the classical low-order tetrahedron element is introduced

This paper studies elasto-plastic large deformation behaviour of thin shell structures using the isogeometric computational approach with the main focus on the efficiency in modelling the multi-patches and arbitrary material formulation. In terms of modelling, we employ the bending strip method to connect the patches in the structure. The incorporation of bending strips allows to eliminate the strict

An approach to improve the membrane behaviour of the four-node shell element with 24 degrees of freedom DKMQ24 proposed by Katili et al. (2015) is presented. This improvement is based on a different approximation of drilling rotations, based on Allman's shape functions. Further, the element formulation is enhanced by the use of selective reduced integration of shear terms and by the proportional scaling

Simulation of restrained ring shrinkage and cracking of cementitious materials in a multiphysics simulation framework (MOOSE) is discussed in this paper. The 3D numerical model analyzes residual stress development and crack initiation/propagation in cement pastes by applying an eigenstrain which varies over the depth of the specimen based on the relative humidity of the pores as moisture diffuses from

Topology optimization techniques have been widely used in structural design. Conventional optimization techniques usually are aimed at achieving the globally optimal solution which maximizes the structural performance. In practical applications, however, designers usually desire to have multiple design options, as the single optimal design often limits their artistic intuitions and sometimes violates

A numerical model to take into account the effect of the stress state on the bond behavior between steel and concrete in reinforced concrete structures is proposed. It is based on a zero thickness element, adapted to large-scale simulations and the use of 1D elements for steel bars. The proposed model also assumes the definition of a bond stress – slip law which includes the confining pressure around

Higher order finite element (FE) methods provide significant advantages in a number of applications such as wave propagation, where high order shape functions help to mitigate pollution (dispersion) error. However, classical assembly of higher order systems is computationally burdensome, requiring the evaluation of many point quadrature schemes. When the Discontinuous Petrov-Galerkin (DPG) FE methodology

In this paper, we extend the concept of MINI element over triangles to star convex arbitrary polytopes. This is achieved by employing the volume averaged nodal projection (VANP) method over polytopes in combination with the strain smoothing technique. Within this framework, the dilatation strain is projected onto the linear approximation space, thus resulting in a purely displacement based formulation

In this paper, a novel data-driven nonlinear solver (DDNS) for solid mechanics using time series forecasting is first proposed. The key concept behind this work is to modify the starting point of iterations of the modified Riks method (M-R). The modified Riks method starts iterations at the previously converged solution point while the proposed method starts at a predicted point which is very close

For large-scale equipment, e.g. aerospace and architecture industry, it is valuable to guarantee that one structure could survive partial damages. Due to the location of the damage is unknown in prior, results in a high number of failure scenarios to be calculated when considering fail-safe requirement in topology optimization. In this article, we propose an efficient continuum topology optimization

Reliable numerical modeling of asphalt concrete (AC) is a complex problem due to a non periodic random structure of this material and a nonlinear behavior of its interacting constituents. Phenomena observed at the lower resolution highly influence the overall response of pavement layers made of asphalt concrete. In this paper, we focus on the selected aspects of its efficient numerical modeling using

New elements are proposed in the present work based on the harmonic coordinates in which the shape functions satisfy the Laplace equation. The harmonic functions have some appealing characteristics that made it possible to define elements with arbitrary shape functions on the element boundaries and arbitrary node arrangement. In the present work, without loss of generality, we formulate a set of quadrilateral

This paper presents a finite element formulation of curved thin beams, useful for modelling structures made of filiform elements. The proposed element is intended to model structures formed by several wires, subjected to very large bending displacements so that their final shapes can be completely different from the original ones. The model is based on the description of the planar wire geometry through

All crack models developed to date can be classified into discrete- and continuum-based approaches. While discrete models are advantageously capable of capturing the kinetics of fractures, continuum-based approaches still pique considerable interest due to their straightforward implementation within the finite element method (FEM) framework. The cracking element method (CEM), a recently developed numerical

This paper proposes a Computational Fluid Dynamics (CFD) framework with the aim of combining consistency and efficiency for the numerical simulation of high Reynolds number flows encountered in engineering applications for aerodynamics. The novelty of the framework is the combination of a Reynolds-Averaged Navier–Stokes (RANS) model with an anisotropic mesh adaptation strategy handling arbitrary immersed

In this work, we propose a position-based finite element formulation for incompressible Newtonian flows under total Lagrangian description. Such formulation is different from the traditional finite element approach used in fluid dynamics by using current nodal positions as main variable instead of nodal velocities. The variational form of the governing equations is derived by applying the stationary

In the present study, the ability of the classical solid-shell element to satisfy the membrane patch test is examined. Theoretical and numerical investigations showed that the classical solid-shell element fails to satisfy the membrane patch test when the elements' referential covariant base vectors in the thickness directions are coordinate-dependent. This deficiency has motivated the development

Direct Energy Deposition (DED) is being widely used to repair damaged components to increase service life and economical operation. Process parameters including laser power, traverse speed and the mass flowrate of the feedstock material may be adapted in-situ. This allows bespoke repair strategies to be devised to match the variability in the condition of the parts supplied that require repair; however

The calculation of wave radiation in exterior domains by finite element methods can lead to large computations even if we consider linear problems in the frequency domain as in this article. Here, we study two-dimensional acoustics described by the Helmholtz equation. A large part of the exterior domain is meshed and this computational domain is truncated at some distance where local or global boundary

The subject paper purportedly proposes a novel enriched finite element method for modeling problems with strong discontinuities such as those encountered in fracture mechanics. The purpose of this document is to demonstrate that the method in the subject paper (Non-nodal eXtended Finite Element Method, NXFEM) is conceptually identical to the Discontinuity-Enriched Finite Element Method (DE-FEM) [Int

To predict the vibroacoustic performance of complex thin-walled structures, an analysis using a finite element model considering structure–acoustic interaction is often required. The acoustic response of such models can be time-consuming to compute and sensitive to minor design changes. These models can be too computationally intense since fast design optimizations must be performed. Moreover, knowledge

Among metal additive manufacturing technologies, powder-bed fusion features very thin layers and rapid solidification rates, leading to long build jobs and a highly localized process. Many efforts are being devoted to accelerate simulation times for practical industrial applications. The new approach suggested here, the virtual domain approximation, is a physics-based rationale for spatial reduction

An implementation of the coupled criterion (CC) for crack initiation simulation in the commercial finite element (FE) code Abaqus/Standard is proposed. This finite fracture mechanics approach allows crack initiation to be modeled by fulfilling simultaneously a stress and an energy conditions, which results in the determination of the loading level and crack length at initiation. Two procedures are

This paper deals with the development of a non-linear finite element model for reinforced concrete members under torsion. Using multi-fiber approach and displacement-based formulation, an enhanced multi-fiber 3D beam is proposed for predicting the behavior of reinforced concrete elements under torsion. The sectional analysis under elastic torsion is considered following Saint-Venant torsional theory

The bi-material interface arc crack has been the focus of interest in the composite community, where it is usually referred to as the fiber-matrix interface crack. In this work, we investigate the convergence properties of the Virtual Crack Closure Technique (VCCT) when applied to the evaluation of the Mode I, Mode II and total Energy Release Rate of the fiber-matrix interface crack in the context

Nodally integrated elements exhibit spurious modes in dynamic analyses (such as in modal analysis). Previously published methods involved a heuristic stabilization factor, which may not work for a large range of problems, and a uniform amount of stabilization was used over all the finite elements in the mesh. The method proposed here makes use of energy-sampling stabilization. The stabilization factor

In this paper and in the framework of the Asymptotic Numerical Method (ANM), we investigate numerically improved vectorial Padé Approximants. The ANM is a branch-by-branch continuation algorithm, each branch is represented by a vectorial Taylor series with respect to a path parameter. In the ANM, the vectorial Padé approximants have been introduced to increase the validity range of vectorial Taylor

This paper introduces a novel hybrid finite element (FE) formulation of shell element to enable assembly process simulation of compliant sheet-metal parts with higher efficiency and flexibility. Efficiency was achieved by developing both new hybrid quadrilateral and triangular elements. Quadrilateral element (QUAD+) was formulated by combining area geometric quadrilateral 6 (AGQ6) nodes and mixed interpolated

Physical accuracy of discretization methods for frictional contact mechanics originates from precise representation of discontinuous frictional and normal interaction laws, appropriate time-integration for velocity and acceleration (which is unbounded at impacting points) and also contact discretization techniques. In terms of discontinuous behavior in the presence of inertia, two themes are of concern:

A multiscale space/time computational framework for high cycle fatigue (HCF) life predictions is established by integrating the extended space-time finite element method (XTFEM) with a multiscale progressive damage model. While the robustness of the multiscale space/time method has been previously demonstrated, the associated high computational cost remains a critical barrier for practical applications

Multi-ionic reactive transport modeling can provide a better understanding of localized corrosion in iron and steel alloys. However, one-step numerical methods used to solve reactive transport equations in a fully-coupled manner may suffer from poor conditioning and numerical convergences issues. In this paper, a sequential non-iterative approach (SNIA) is developed to enable robust numerical simulation

This paper describes an inverse shape design method for thermoelastic bodies. With a known equilibrium shape as input, the focus of this paper is the determination of the corresponding initial shape of a body undergoing thermal expansion or contraction, as well as nonlinear elastic deformations. A distinguishing feature of the described method lies in its capability to approximately prescribe an initial

Variational space-time formulations for partial differential equations have been of great interest in the last decades, among other things, because they allow to develop mesh-adaptive algorithms. Since it is known that implicit time marching schemes have variational structure, they are often employed for adaptivity. Previously, Galerkin formulations of explicit methods were introduced for ordinary

In this article, a new algorithm is developed for predicting crack initiation and growth direction in 3D solid concrete. The algorithm combines the anisotropic damage-plasticity model used for simulation of concrete material degradation (crack) and irreversible plastic deformation and the eXtended Finite Element Method (X-FEM). The Voyiadjis local anisotropic damage-plasticity model is expressed in

We present a deep learning method to investigate the effect of flexoelectricity in nanostructures. For this purpose, deep neural network (DNN) algorithm is employed to map the relation between the inputs and the material response of interest. The DNN model is trained and tested making use of database that has been established by solving the governing equations of flexoelectricity using a NURBS-based

For the accurate imposition of surface loads using the Finite Element Method normally the load is discretized at the surface facets. Therefore appropriate surface shape functions are needed. If the surface contains kinks, which occurs often in contact cases, the imposition is more complicated. In order to simplify the imposition of surface loads, an alternative approach is presented. This formulation

With the increasing popularity of nanocomposites appears the necessity of the development of efficient modelization procedures. In particular, numerical strategies have to be developed to reproduce and predict the size effect observed on such materials. Usually, the size effect is taken into account by introducing a surface elasticity at the interface between the nano-inclusions and the matrix. Whereas

A finite-strain tetrahedron with continuous stresses is proposed and analyzed. The complete stress tensor is now a nodal tensor degree-of-freedom, in addition to displacement. Specifically, stress conjugate to the relative Green-Lagrange strain is used within the framework of the Hellinger-Reissner variational principle. This is an extension of the Dunham and Pister element to arbitrary constitutive

In the present article, we propose a fully coupled thermo-elasto-plastic-damage theory, which includes both kinematic and isotropic hardening, and also accounts for hydrogen diffusion in metals. This theory is based on the thermodynamics of irreversible processes under small deformation hypothesis and suppose that hydrogen diffuses in both normal interstitial lattice sites and trapping sites. This

This paper deals with problems emerging in a non-linear analysis of systems modelled by the strain softening material. Apart from sharp turns on the load-displacement diagram that characterize such numerical models, snap-back, artificial unloading and possibility of bifurcation occurrence are often encountered. These aspects challenge a non-linear system solver, in a sense of finding the appropriate

It is well known that the mechanical properties of extrusion blow molded plastic bottles are influenced by the process conditions, which leads to local orthotropic process-dependent material parameters. In this study, these parameters as well as local orientation effects are for the first time considered in the structural analysis of extrusion blow molded products. Furthermore, an integrative simulation