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The purpose of this paper is to use symmetry conditions for the reduction of computing times in problems involving finite element‐based multi‐scale constitutive models of nonlinear heterogeneous media.

Two types of representative volume element (RVE) symmetry often found in practice are considered: staggered‐translational and point symmetry. These are analyzed under three types RVE of kinematical constraints: periodic boundary fluctuations (typical of periodic media), linear boundary displacements (which gives an upper bound for the macroscopic stiffness) and the minimum kinematical constraint (corresponding to uniform boundary tractions and providing a lower bound for the macroscopic stiffness).

Numerical examples show that substantial savings in computing times are achieved by taking advantage of such symmetries. These are particularly pronounced in fully coupled two‐scale analyses, where the macroscopic equilibrium problem is solved simultaneously with a large number of microscopic equilibrium problems at Gauss‐point level. Speed‐up factors in excess of seven have been found in such cases, when both symmetry conditions considered are present at the same time.

This paper extends the original considerations of Ohno et al. to account for other RVE kinematical constraints, namely, the linear boundary displacement and the minimum kinematical constraint (or uniform boundary traction model). Provides a more precise assessment of the impact of the use of such symmetries on computing times by means of numerical examples. In addition, for completeness, the direct enforcement of such constraints within a Newton‐based finite element solution procedure for the RVE equilibrium problem is detailed in the paper.

Hybrid simulation, which is a general technique for obtaining the seismic response of an entire structure, is an improvement of the traditional seismic test technique. In order to improve the analysis accuracy of the numerical substructure in hybrid simulation, the purpose of this paper is to propose an innovative hybrid simulation technique. The technique combines the multi-scale finite element (MFE) analysis method and hybrid simulation method with the objective of achieving the balance between the accuracy and efficiency for the numerical substructure simulation.

To achieve this goal, a hybrid simulation system is established based on the MTS servo control system to develop a hybrid analysis model using an MFE model. Moreover, in order to verify the efficiency of the technique, the hybrid simulation of a three-storey benchmark structure is conducted. In this simulation, a ductile column—represented by a half-scale scale specimen—is selected as the experimental element, meanwhile the rest of the frame is modelled as microscopic and macroscopic elements in the Abaqus software simultaneously. Finally, to demonstrate the stability and accuracy of the proposed technique, the seismic response of the target structure obtained via hybrid simulation using the MFE model is compared with that of the numerical simulation.

First, the use of the hybrid simulation with the MFE model yields results similar to those obtained by the fine finite element (FE) model using solid elements without adding excessive computing burden, thus advancing the application of the hybrid simulation in large complex structures. Moreover, the proposed hybrid simulation is found to be more versatile in structural seismic analysis than other techniques. Second, the hybrid simulation system developed in this paper can perform hybrid simulation with the MFE model as well as handle the integration and coupling of the experimental elements with the numerical substructure, which consists of the macro- and micro-level elements. Third, conducting the hybrid simulation by applying earthquake motion to simulate seismic structural behaviour is feasible by using Abaqus to model the numerical substructure and harmonise the boundary connections between three different scale elements.

In terms of the implementation of the hybrid simulation with the MFE model, this work is helpful to advance the hybrid simulation method in the structural experiment field. Nevertheless, there is still a need to refine and enhance the current technique, especially when the hybrid simulation is used in real complex engineering structures, having numerous micro-level elements. A large number of these elements may render the relevant hybrid simulations unattainable because the time consumed in the numeral calculations can become excessive, making the testing of the loading system almost difficult to run smoothly.

The MFE model is implemented in hybrid simulation, enabling to overcome the problems related to the testing accuracy caused by the numerical substructure simplifications using only macro-level elements.

This paper is the first to recognise the advantage of the MFE analysis method in hybrid simulation and propose an innovative hybrid simulation technique, combining the MFE analysis method with hybrid simulation method to strike a delicate balance between the accuracy and efficiency of the numerical substructure simulation in hybrid simulation. With the help of the coordinated analysis of FEs at different scales, not only the accuracy and reliability of the overall seismic analysis of the structure is improved, but the computational cost can be restrained to ensure the efficiency of hybrid simulation.

The purpose of this paper is to capture the actual structural behavior of the longest timber footbridge in Spain by means of a multi-scale model updating approach in conjunction with ambient vibration tests.

In a first stage, a numerical pre-test analysis of the full bridge is performed, using standard beam-type finite elements with isotropic material properties. This approach offers a first structural model in which optimal sensor placement (OSP) methodologies are applied to improve the system identification process. In particular, the effective independence (EFI) method is used to determine the optimal locations of a set of sensors. Ambient vibration tests are conducted to determine experimentally the modal characteristics of the structure. The identified modal parameters are compared with those values obtained from this preliminary model. To improve the accuracy of the numerical predictions, the material response is modeled by means of a homogenization-based multi-scale computational approach. In a second stage, the structure is modeled by means of three-dimensional solid elements with the above material definition, capturing realistically the full orthotropic mechanical properties of wood. A genetic algorithm (GA) technique is adopted to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.

An overall good agreement is found between the results of the updated numerical simulations and the corresponding experimental measurements. The longitudinal and transverse Young's moduli, sliding and rolling shear moduli, density and natural frequencies are computed by the present approach. The obtained results reveal the potential predictive capabilities of the present GA/multi-scale/experimental approach to capture accurately the actual behavior of complex materials and structures.

The uniqueness and importance of this structure leads to an intensive study of its structural behavior. Ambient vibration tests are carried out under environmental excitation. Extraction of modal parameters is obtained from output-only experimental data. The EFI methodology is applied for the OSP on a large-scale structure. Information coming from several length scales, from sub-micrometer dimensions to macroscopic scales, is included in the material definition. The strong differences found between the stiffness along the longitudinal and transverse directions of wood lumbers are incorporated in the structural model. A multi-scale model updating approach is carried out by means of a GA technique to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.

The purpose of this paper is to investigate the influence of geometrical microstructure of items obtained by applying a three-dimensional (3D) printing technology on their mechanical strength.

Three-dimensional printed items (3DPI) are composite structures of complex internal constitution. The buildup of the finite element (FE) computational models of 3DPI is based on a multi-scale approach. At the micro-scale, the FE models of representative volume elements corresponding to different additive layer heights and different thicknesses of extruded fibers are investigated to obtain the equivalent non-linear nominal stress–strain curves. The obtained results are used for the creation of macro-scale FE models, which enable to simulate the overall structural response of 3D printed samples subjected to tensile and bending loads.

The validation of the models was performed by comparing the computed results against the experimental ones, where satisfactory agreement has been demonstrated within a marked range of thicknesses of additive layers. Certain inadequacies between computed against experimental results were observed in cases of thinnest and thickest additive layers. The principle explanation of the reasons of inadequacies takes into account the poorer quality of mutual adhesion in case of very thin extruded fibers and too-early solidification effect.

Flexural and tensile experiments are simulated by FE models that are created with consideration to microstructure of 3D printed samples.

The purpose of this paper is to predict the yield locus of porous ductile materials, evaluate the impact of void geometry and compare the computational results with existing analytical models.

A computational homogenization strategy for the definition of the elasto-plastic transition is proposed. Representative volume elements (RVEs) containing single-centred ellipsoidal voids are analysed using three-dimensional finite element models under the geometrically non-linear hypothesis of finite strains. Yield curves are obtained by means of systematic analysis of RVEs considering different kinematical models: linear boundary displacements (upper bound), boundary displacement fluctuation periodicity and uniform boundary traction (lower bound).

The influence of void geometry is captured and the reduction in the material strength is observed. Analytical models usually overestimate the impact of void geometry on the yield locus.

This paper proposes an alternative criterion for porous ductile materials and assesses the accuracy of analytical models through the simulation of three-dimensional finite element models under geometrically non-linear hypothesis.

The purpose of this paper is to consider the computational tools for solving a strongly coupled multi‐scale problem in the context of inelastic structural mechanics.

In trying to maintain the highest level of generality, the finite element method is employed for representing the microstructure at this fine scale and computing the solution. The main focus of this work is the implementation procedure which crucially relies on a novel software product developed by the first author in terms of component template library (CTL).

The paper confirms that one can produce very powerful computational tools by software coupling technology described herein, which allows the class of complex problems one can successfully tackle nowadays to be extended significantly.

This paper elaborates upon a new multi‐scale solution strategy suitable for highly non‐linear inelastic problems.

The purpose of this study is to present a multi-scale analysis methodology for calculating the effective stiffnesses and the micro stresses of helically wound structures efficiently and accurately. The helically wound structure is widely applied in ocean and civil engineering as load-bearing structures with high flexibility, such as wire ropes, umbilical cables and flexible risers. Their structures are usually composed of a number of twisted subcomponents with relatively large slender ratio and have the one-dimensional periodic characteristic in the axial direction. As the huge difference between the axial length and the cross-section size of this type of structures, the finite element modeling and theoretical analysis based on some assumption are usually unavailable leading to the reduction of computability; even the optimization design becomes infeasible.

Based on the asymptotic homogenization theory, the one-dimensional periodic helically wound structure is equivalent to the one-dimensional homogeneous beam. A novel implementation of the homogenization is derived for the analysis of the effective mechanical properties of the helically wound structure, and the tensile, bending, torsional and coupling stiffness properties of the effective beam model are obtained. On this basis, a downscaling analysis formation for the micro-component stress in the one-dimensional periodic wound structure is constructed. The stress of micro-components in the specified geometry position of the helically wound structure is obtained basing on the asymptotic homogenization theory simultaneously.

By comparing with the result from finite element established accurately, the established multi-scale calculation method of the one-dimensional periodic helically wound structure is verified. The influence of size effects on the macro effective performance and the micro-component stress is discussed.

This paper will provide the theoretical basis for the efficient elastoplastic analysis of the helically wound structure, even the fatigue analysis. In addition, it is necessary to point out that the axial length of the helically wound structure in the general engineering problems that such as deep-sea risers and submarine cables.

To provide a computational strategy for highly accurate analyses of non‐linear inelastic behaviour for heterogeneous structures in civil and mechanical engineering applications

Adapts recent developments on mathematical formulations of multi‐scale problems to the recently developed component technology based on C++ generic templates programming.

Provides the understanding how theoretical hypotheses, concerning essentially the multi‐scale interface conditions, affect the computational precision of the strategy.

The present approach allows a very precise modelling of multi‐scale aspects in structural mechanics problems and can play an essential tool in searching for an optimal structural design.

Provides all the ingredients for constructing an efficient multi‐scale computational framework, from the theoretical formulation to the implementation for parallel computing. It is addressed to researchers and engineers analysing composite structures under extreme loading.

The purpose of this paper is to assess the Gurson yield criterion for porous ductile metals.

A finite element procedure is used within a purely kinematical multi‐scale constitutive modelling framework to determine estimates of extremal overall yield surfaces. The RVEs analysed consist of an elastic‐perfectly plastic von Mises type matrix under plane strain conditions containing a single centered circular hole. Macroscopic yield surface estimates are obtained under three different RVE kinematical assumptions: linear boundary displacements (an upper bound); periodic boundary displacement fluctuations (corresponding to periodically perforated media); and, minimum constraint or uniform boundary traction (a lower bound).

The Gurson criterion predictions fall within the bounds obtained under relatively high void ratios – when the bounds lie farther apart. Under lower void ratios, when the bounds lie close together, the Gurson predictions of yield strength lie slightly above the computed upper bounds in regions of intermediate to high stress triaxiality. A modification to the original Gurson yield function is proposed that can capture the computed estimates under the three RVE kinematical constraints considered.

Assesses the accuracy of the Gurson criterion by means of a fully computational multi‐scale approach to constitutive modelling. Provides an alternative criterion for porous plastic media which encompasses the common microscopic kinematical constraints adopted in this context.

The great magnitude differences between the integral tunnel and its structure details make it impossible to numerically model and analyze the global and local seismic behavior of large-scale shield tunnels using a unified spatial scale, even with the help of supercomputers. The paper aims to present a combined equivalent & multi-scale simulation method, by which the tunnel's major mechanical properties under seismic loads can be represented by the equivalent model, and the seismic responses of the interested details can be studied efficiently by the coupled multi-scale model.

The nominal orthotropic material constants of the equivalent tunnel model are inversely determined by fitting the modal characteristics of the equivalent model with the corresponding segmental lining model. The critical sections are selected by comprehensive analyzing of the integral compression/extension and bending loads in the equivalent lining under the seismic shaking and the coupled multi-scale model containing the details of interest is solved by the mixed time explicit integration algorithm.

The combined equivalent & multi-scale simulation method is an effective and efficient way for seismic analyses of large-scale tunnels. The response of each flexible joint is related to its polar location on the lining ring, and the mixed time integration method can speed-up the calculation process for hybrid FE model with great differences in element sizes.

The orthotropic equivalent assumption is, to the best of the authors’ knowledge, for the first time, used in the 3D simulation of the shield tunnel lining, representing the rigidity discrepancies caused by the structural property.