This paper presents a finite element methodology for modelling solid media with any number of straight or curved reinforcing bars (rebars). The formulation can handle rebars arbitrarily located within a 2D or 3D finite element mesh without the need for nodal compatibility. A new continuous rod–solid interface (or joint) element is developed to connect bulk elements to the rebars, including a method

In this paper, a new method is presented to concurrently determine the structural layout and joint interface during the multi-material topology optimization (MMTO) process. Although the development of additive manufacturing techniques allows the fabrication of multi-material structures for soft materials with graded properties, joint materials for joining metals or composites are still needed. This

Topology optimization techniques are typically performed on a design domain with pre-determined support conditions to generate efficient structures. Allowing the optimizer to simultaneously design supports and topology offers new design possibilities to achieve improved structural performance and reduce the cost of supports. However, existing simultaneous optimization techniques are limited, with most

This paper aims to develop a moving-mesh type Finite Element Method for the computation of the transient unconfined seepage flow through the porous medium. The proposed method is based on the time discontinuous Galerkin Space-Time Finite Element Method (ST/FEM). It solves the seepage problem in the saturated region. The primary unknown in ST/FEM is piezometric pressure. Fluid velocities are derived

A novel finite element-based simulation method is proposed for fused deposition modeling in two dimensions. The method assumes full coupling between the mechanical and thermal response under the assumptions of infinitesimal deformation and finite temperature variation. To account for continuous temperature-induced changes in the geometry, new elements are deposited on the current configuration, while

The behavior of dry fibers is a key component in modeling composite materials. However, it can become very expensive in computation time to model each individual filament. We propose here a new multi-scale method featuring beam elements embedded in truss elements. Truss elements are used to model contact responses and traction while beams elements are used to characterize flexion. This approach is

Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among them is not always a trivial task. This work presents a comparison of the performance of a priori and a posteriori proper generalised decomposition (PGD) algorithms

This article presents a method for generalized shape optimization of time-harmonic vibroacoustic problems. The modeling approach utilizes an immersed boundary cut element method in conjunction with a level set representation of the geometry. The cut element method utilizes a fixed background mesh, a dimensionless contrast parameter and an integration scheme to realize complex geometries and obtain

Design optimization of geometrically nonlinear structures is well known as a computationally expensive problem by using incremental-iterative solution techniques. To handle the problem effectively the optimization algorithm needs to ensure that the trade-off between the computational time and the quality of the solution is found. In this study, a deep neural network (DNN)-based surrogate model which

In the field of structural dynamics, it can be particularly interesting to consider a different time integrator and time scale in a different part of a problem (i.e. in the case of multi-physics problems, non smooth contact mechanics, seismic engineering with impacts, soil-structure interaction problems, or multiscale models using macro-element systems with a dynamic internal equilibrium). This paper

An extension to the interface finite element with eMbedded Profile for Joint Roughness (MPJR interface finite element) is herein proposed for solving the frictional contact problem between a rigid indenter of any complex shape and an elastic body under generic oblique load histories. The actual shape of the indenter is accounted for as a correction of the gap function. A regularised version of the

This paper proposes a level set-based topology optimization method for acoustic metasurfaces consisting of multiple types of unit cells. As a type of acoustic metasurface, we focus on a two-layered metasurface, where each layer contains various types of unit cell designs. To handle this metasurface, we first propose a two-scale homogenization method based on previous studies targeting metasurfaces

In this paper, an enhanced solid finite element formulation for rotor dynamics analysis is presented. The element kinematics is first defined with a Total Lagrangian formulation in order to account for possible centrifugal stiffening effect and its associated pre-stress deformation. The novelty of the three-dimensional element proposed in this study is then to correctly consider the effect of inertia

Accurate simulation of bolted joints is not always consistent with industrial requirements, since numerous nonlinearities in the vicinity of the bolt can lead to overly expensive calculations. For this reason, commercial finite element (FE) codes preferentially use substitutes for bolts, such as simplified models or connectors. In this paper, a nonlinear FE connector with its identification methodology

In this paper, different degenerated shell approaches in conjunction with a layer-wise (LW) model for composite structures are investigated using Finite Element method. The first one involves a classical LW model. The second one is based on a variable separation method, the Proper Generalized Decomposition (PGD), in which the displacement field is approximated as a sum of separated functions of the

The present paper is dedicated to the modeling of the non-linear behavior of reinforced concrete structures subject to transverse shear or torsion under monotonic and cyclic loading. The fiber beam element approach has been proved to be an interesting modeling strategy, but needs to be improved for shear effects. This can be achieved by enhancing the cross-section kinematics with a warping displacement

An immersed boundary shell element formulation based on Kirchhoff-Love shell theory is presented here that uses a background mesh consisting of uniform 3D B-spline elements within which the geometry and the boundaries are embedded. In this theory, rotation is assumed to be identical to slope which introduces second derivatives of deflection in the weak form. As a result, elements that provide tangent

The dissipated strain energy, representing a monotonically increasing state variable in nonlinear fracture mechanics, can be used to develop an arc-length constraint equation for tracking the energy dissipation path instead of the elastic unloading path of the response of a structure. This was the motivation for the development of a dissipation-based arc-length method, followed by its implementation

A high fidelity fluid-structure interaction simulation may require many days to run, on hundreds of cores. This poses a serious burden, both in terms of time and economic considerations, when repetitions of such simulations may be required (e.g. for the purpose of design optimization). In this paper we present strategies based on (constrained) Bayesian optimization (BO) to alleviate this burden. BO

In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well and states new issues, here tackled, concerning good quality mesh elements and reliability of the simulations. In this paper we numerically investigate optimality

Uncertainty quantification (UQ) within topology optimization (TO) is a growing trend, with designers recognizing that deterministic analysis does not reflect the natural variabilities found in real-world structural performance. Thus far the majority of works have dealt with uncertain loading and material properties; however, minimal research has considered uncertain boundary conditions (BCs), which

Uncertainty Quantification (UQ) is a key discipline for computational modeling of complex systems, enhancing reliability of engineering simulations. In crashworthiness, having an accurate assessment of the behavior of the model uncertainty allows reducing the number of prototypes and associated costs. Carrying out UQ in this framework is especially challenging because it requires highly expensive simulations

The limitations of the dynamic theories for the thin layered elastic structures, which very often have different physical and geometrical contrast properties of the layers in today's high-tech applications, bring a number of challenges in the numerical computation of the dynamic response. This is a strong motivation to develop a suitable computational methodology for accurate evaluation and implementation

In this paper, the construction of Ck basis functions is proposed for paraxial d-dimensional rectangular meshes with arbitrary hanging nodes and arbitrary polynomial degree distributions. The construction is based on the large-support approach introduced in [1] for C0 basis functions in 2D and uses hierarchical tensor-product shape functions which combine Hermite shape functions with Gegenbauer polynomials

This work exploits the high accuracy of the mixed 3−field u/e/p formulation to address materially non-linear inelastic problems including isochoric deformations. Motivated by the strain-driven format of several constitutive equations used in FEA, the mixed u/s/p formulation is reinterpreted, selecting the deviatoric strains as primary variables, together with the displacements and the pressure field

In this paper, we have modified the stress integration scheme proposed by Choi and Yoon [1]; which is based on the numerical approximation of the yield function gradients, to implement in the finite element code ABAQUS three elastic isotropic, plastic anisotropic constitutive models with yielding described by Yld2004-18p [2], CPB06ex2 [3] and Yld2011-27p [4] criteria, respectively. We have developed

Abstract For finite strain plasticity, we use the multiplicative decomposition of the deformation gradient to obtain a differential-algebraic system (DAE) in the semi-explicit form and solve it by a half-explicit algorithm. The terminology HERK is synonym of Half-Explicit Runge-Kutta method for DAE. The source is here the right Cauchy-Green tensor and an exact Jacobian of the second Piola-Kirchhoff

This paper presents a new parallel mesh generation method leading to subdomains of shape well-suited to Schur based domain decomposition methods such as the FETI and BDD solvers. Starting from a coarse mesh, subdomains meshes are created in parallel through hierarchical mesh refinement and morphing techniques. The proposed methodology aims at limiting the occurrence of known pathological situations

Herein, we present a novel method for searching anti-resonance frequencies, using an eigenvalue analysis that does not need to search every dip of amplitude in the frequency response function. The eigenvalue equation is derived by utilizing the fact that the solutions of a forced vibration equation are equal to zero at anti-resonance frequencies. The characteristics of the eigenvalue problem are analyzed

We propose a geometrically nonlinear extended isogeometric analysis approach for cohesive fracture. A shifting technique is used to enforce compatibility in the direction perpendicular to the crack path, while a blending technique has been adopted to remove the effect of the discontinuity in the extension of the cohesive crack. Bézier extraction is employed to cast the formulation in a finite element

The simulation of complex material failure processes requires a precise differentiation of the involved failure mechanisms like fracture or plasticity. This is commonly achieved by using a so-called multisurface failure criterion, where each failure surface is related to a certain failure mechanism. In the case of plasticity, failure surfaces define the elastic domain of the material and any stress

This paper evaluates the performances of second-order finite elements for nodal lumped-mass explicit methods in nonlinear solid dynamics, with a particular emphasis on 10-node “serendipity” and 15-node “Lagrange” tetrahedral elements. Historically, many nonlinear explicit finite element codes have exclusively used first-order elements, until a fairly recent flurry of activity that has resulted in higher-order

This paper presents a trans-scale finite element model based on hydraulic-thermal-mechanical coupling equations of porous medium to simulate the behavior of concrete during freezing and thawing. Unlike previous models that regard concrete as homogeneous material, this paper aims to establish a macro-size concrete model with detailed micro-structure, the aggregates (mm) and air voids (μm) are randomly

We propose a new approach to the prediction of multiaxial fatigue with proportional and non-proportional loading based on a recently developed three-dimensional small-strain microplasticity-based constitutive theory. The core idea of the theory is to incorporate pre-full-yield microplastic deformations in a computationally efficient way. Fatigue life is then correlated to the accumulated (micro)plastic

A crystal plasticity based finite element (CPFE) framework is developed for performing representative volume element (RVE) calculations on two-phase materials. The present paper investigates the mechanical response and the evolution of microstructure of dual-phase (DP) steels under uniaxial tensile loading, with a special focus on void nucleation. The spatial distribution and morphology of the ferrite

Abstract A flapping motion is an important fluid–structure interaction (FSI) phenomenon. Although it has been extensively studied, there are still many unknowns. Because there are numerous parameters in the kinematics and morphology for flapping motions, it is difficult to experimentally determine parameter values that enhance flapping aerodynamics because of the associated time, cost, and space constraints

A comprehensive theoretical and experimental investigation is presented of the behavior of polyurea composites subjected to high strain-rate impact loading. The composites under consideration consist of an assembly of steel sections and inserts manufactured from layers of polyurea or polyurea augmented with aluminum layers (AL). A finite element model (FEM) is developed to predict the dynamics of this

Abstract This paper proposes a semi-analytical interval method for static response bounds analysis of structures subjected to spatially uncertain loads. In the investigated problem, the external loads applied to the structure are spatially uncertain but bounded, which are quantified by an interval field model using upper and lower bounds. By introducing the interval field and its series expansion form

Abstract The non-ordinary state-based peridynamics (NSPD) is a promising method for fracture analysis, and it can incorporate the constitutive relationship of classical continuum mechanics in peridynamics. However, the high computational cost is one of the main reasons limiting its usage. To improve computational efficiency of NSPD, a stability-enhanced peridynamic (PD) element is proposed to couple

Abstract This paper presents the development of an ABAQUS™ plug-in for estimation of the effective properties of heterogeneous three-dimensional periodic media using the asymptotic homogenization method (AHM). The developed plug-in is user-friendly and requires only basic skills in ABAQUS™. All aspects of the plug-in development are presented, including the solutions found to implement this approach

Abstract 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

Abstract 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

Abstract The current work proposes a novel approach for the implementation of periodic representative volume element (RVE) based multiscale modeling using the finite element method. The approach is based on a rigorous mechanics foundation that implements appropriate boundary conditions for the RVE analysis and simplifies the homogenization technique. Stress components are relaxed in the chosen periodic

Abstract 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

Abstract 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

Abstract 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

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 quasi-optimal 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 unrefinements

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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