Concurrent Multiscale Model Research Articles

Fine Damage Identification Method of Transmission Tower Based on Concurrent Multi-Scale Modeling

In order to study the damage problem caused by the transmission tower fatigue cracks and bolt pretightening force loss ,this paper proposes a transmission tower damage identification method based on concurrent multi-scale model, namely establish solid model on nodes of fatigue crack and bolt looseness based on large scale model., subdividing elements size. Take a practical engineering 500kV transmission towers as an example to establish a concurrent multi-scale models. This paper simulates 8 kinds of conditions including bolt pretightening force loss and angle steel crack, research shows that the sum of wavelet packet energy curvature difference can effectively identify minute damage, and then get the function relation between damage level and damage index with no noise interference, also this provides a theoretical basis for it as actual damage monitoring indicators index.

Adaptive concurrent multiscale model for fracture and crack propagation in heterogeneous media

We introduce an adaptive concurrent multiscale methodology (ACM2) to handle situations in which both macroscopic and microscopic deformation fields strongly interact near the tip of a crack. The method is based on the balance between numerical and homogenization error; while the first type of error states that elements should be refined in regions of high deformation gradients, the second implies that element size may not be smaller than a threshold determined by the size of the unit cell representing the material’s microstructure. In this context, we build a finite element framework in which unit cells can be embedded in continuum region through appropriate macro–micro boundary coupling conditions. By combining the idea of adaptive refinement with the embedded unit cell technique, the methodology ensures that appropriate descriptions of the material are used adequately, regardless of the severity of deformations. We will then show that our computational technique, in conjunction with the extended finite element method, is ideal to study the strong interactions between a crack and the microstructure of heterogeneous media. In particular, it enables an explicit description of microstructural features near the crack tip, while a computationally inexpensive coarse scale continuum description is used in the rest of the domain. The paper presents several examples of crack propagation in materials with random microstructures and discuss the potential of the multiscale technique in relating microstructural details to material strength and toughness.

Concurrent multi-scale modelling and updating of long-span bridges using a multi-objective optimisation technique

This paper aims at developing an innovative technique of concurrent multi-objective optimisation for updating the multi-scale model of long-span bridges. A multi-scale model is established for the purpose of concurrently analysing the global response of the structure and nonlinear local damages in order to assess structural state and local damage evolution or deteriorating, respectively. A multi-objective optimisation technique is proposed in this work for concurrent multi-scale model updating, in which several key issues including the determination of the objective functions and constraint conditions, the multi-objective optimisation algorithm and how to find the optimal solution from many non-inferior solutions are studied. The proposed concurrent multi-objective optimisation technique is applied to update the initial multi-scale model of Runyang Suspension Bridge (RYSB) near Shanghai, and the updated model is validated by the data from the field tests conducted for obtaining the response in global (dynamic properties) and local levels.

Concurrent multifactor optimisation techniques for model updating of long-span bridges

This article aims at developing an innovative technique of concurrent multi-factor optimisation for updating the multi-scale model of civil infrastructure. A multi-scale model is established for the purpose of concurrently analysing the global response of the structure and non-linear damage of local details in order to meet the needs of evaluation on structural state as well as structural deteriorating. Traditional model updating methods cannot be applied directly to updating such type of models. The technique of concurrent multi-factor optimisation technique (CMFOT) developed in the article can update the multi-scale model by optimising simultaneously the different factors to affect on structural parameters. The key issues of the developed concurrent multifactor optimisation technique are discussed in details, and implementation of the model updating with CMFOT is presented by a case study of a welded steel truss with the available tested data. The multi-scale model of the truss is updated by using the proposed technique and other model updating methods in order to compare their difference. The proposed technique is also applied to updating the concurrent multi-scale model of a long-span suspension bridge, the Runyang Suspension Bridge (RYSB). The results show that CMFOT method is the improvement of traditional model updating methods. The main advantage of CMFOT is that the factors to be considered in CMFOT include not only those sensitive to the updated objective but also other factors sensitive to other objectives to be not updated currently. The computational efficiency of model updating by the CMFOT is higher than others when the correct sequence of multi factors updating is unknown. It is necessary to have sufficient measuring data from the field tests with careful arrangement of the measuring points for the purpose of the model updating with CMFOT for large civil infrastructure like RYSB.

A new multiscale methodology for modeling of single and multi-body solid structures

Fixed Interfacial Multiscale Method (FIMM), a concurrent multiscale model is developed for mechanical analysis of solid nanostructures at the finite temperatures. A direct link between the nano field atoms and macro field nodes using the local atomic volume displacements associated with every macro field node in their common zone has been replaced with the previous methods. FIMM leaves negligible relative motion of atoms in every atomic volume by moving the interface into the macro part. A nano plate in extension and a nanorobotic manipulator have been simulated for comparison. The responses have been compared with the results of semi continuum approach, Molecular Dynamics (MDs), a developed simple Coarse Grained MD (CGMD) and two recently developed multiscale methods. Comparisons show that FIMM is at least 450% better than other methods in numerical cost, and it is also more accurate than other multiscale methods.

A scheme to combine molecular dynamics and dislocation dynamics

Many engineering challenges occur on multiple interacting length scales, e.g. during fracture atoms separate on the atomic scale while plasticity develops on the micrometer scale. To investigate the details of these events, a concurrent multiscale model is required which studies the problem at appropriate length- and time-scales: the atomistic scale and the dislocation dynamics scale. The AtoDis multiscale model is introduced, which combines atomistics and dislocation dynamicsinto a fully dynamic model that is able to simulate deformation mechanisms at finite temperature. The model uses point forces to ensure mechanical equilibrium and kinematic continuity at the interface. By resolving each interface atom analytically, and not numerically, the framework uses a coarse FEM mesh and intrinsically filters out atomistic vibrations. This multiscale model allows bi-directional dislocation transition at the interface of both models with no remnant atomic disorder. Thereby, the model is able to simulate a larger plastic zone than conventional molecular dynamics while reducing the need for constitutive dislocation dynamics equations. This contribution studies dislocation nucleation at finite temperature and investigates the absorption of dislocations into the crack wake.

Concurrent multi-scale crush simulations with a crystal plasticity model

The crush behavior of polycrystalline metallic square tubes under quasi-static axial loading condition is investigated through a mesoscale crystal plasticity model embedded in an explicit finite element simulation code as a concurrent multiscale model. The boundary value problem is defined at the local continuum scale whereas the material behavior is modeled at the mesoscale through crystal plasticity defined in a representative volume element. The anisotropic behavior of the tubes emerges from the texture induced by the large plastic deformations created during the manufacturing process. In this work, this effect is modeled by considering the texture generated by deforming a single element model with an embedded polycrystalline aggregate of face center cubic (FCC) crystals under basic loading paths, including uniaxial tension, uniaxial compression, and simple shear. This initial texture is then used at each integration point in the explicit crush simulations of a square tube model made of an FCC aluminum alloy. As energy absorption is dominated by the plastic collapse mechanisms at the corner elements, the influence of the initial texture and its evolution during crush are found to be significant.

Multi-scale fracture of random heterogeneous materials

This article presents new probabilistic models for generating microstructures and multi-scale fracture analysis of a random heterogeneous material. The microstructure model involves a level-cut, inhomogeneous, filtered Poisson field comprising a sum of deterministic kernel functions that are scaled by random variables and centred at Poisson points. The fracture model involves stochastic description of the particle volume fraction and locations and constituent material properties, two-scale algorithms including micro-scale and macro-scale analyses, and dimensional decomposition or Monte Carlo simulation for reliability analysis. Numerical results demonstrate that the random field model is capable of producing a wide variety of two- and three-dimensional microstructures containing particles of various sizes, shapes, densities, gradations and orientations. The results of fracture analysis indicate that the concurrent model developed is sufficiently accurate, gives probabilistic solutions very close to those generated from the micro-scale model and can reduce the computational effort of the latter model by more than a factor of two. In addition, the concurrent multi-scale model predicts crack trajectory as accurately as the micro-scale model. The stochastic models presented have the potential to fundamentally change the way advanced materials in high-technology applications, including the maritime industry, can be applied in the future.

Advances in Discrete Dislocations Dynamics and Multiscale Modeling

Discrete dislocation dynamics is a numerical tool developed to model the plasticity of crystalline materials at an intermediate length scale, between the atomistic modeling and the crystal plasticity theory. In this review we show, using examples from the literature, how a discrete dislocation model can be used either in a hierarchical or a concurrent multiscale framework. In the last section of this review, we show through the uniaxial compression of microcrystal application, how a concurrent multiscale model involving a discrete dislocation framework can be used for predictive purposes.

Concurrent multi-scale modeling of civil infrastructures for analyses on structural deterioration—Part I: Modeling methodology and strategy

This paper aims to develop the methodology and strategy for concurrent finite element modeling of civil infrastructures at the different scale levels for the purposes of analyses of structural deteriorating. The modeling strategy and method were investigated to develop the concurrent multi-scale model of structural behavior (CMSM-of-SB) in which the global structural behavior and nonlinear damage features of local details in a large complicated structure could be concurrently analyzed in order to meet the needs of structural-state evaluation as well as structural deteriorating. In the proposed method, the “large-scale” modeling is adopted for the global structure with linear responses between stress and strain and the “small-scale” modeling is available for nonlinear damage analyses of the local welded details. A longitudinal truss in steel bridge decks was selected as a case to study how a CMSM-of-SB was developed. The reduced-scale specimen of the longitudinal truss was studied in the laboratory to measure its dynamic and static behavior in global truss and local welded details, while the multi-scale models using constraint equations and substructuring were developed for numerical simulation. The comparison of dynamic and static response between the calculated results by different models indicated that the proposed multi-scale model was found to be the most efficient and accurate. The verification of the model with results from the tested truss under the specific loading showed that, responses at the material scale in the vicinity of local details as well as structural global behaviors could be obtained and fit well with the measured results. The proposed concurrent multi-scale modeling strategy and implementation procedures were applied to Runyang cable-stayed bridge (RYCB) and the CMSM-of-SB of the bridge deck system was accordingly constructed as a practical application.

Concurrent multi-scale modeling of civil infrastructures for analyses on structural deteriorating—Part II: Model updating and verification

This paper is a continuation of the paper titled “Concurrent multi-scale modeling of civil infrastructure for analyses on structural deteriorating—Part I: Modeling methodology and strategy” with the emphasis on model updating and verification for the developed concurrent multi-scale model. The sensitivity-based parameter updating method was applied and some important issues such as selection of reference data and model parameters, and model updating procedures on the multi-scale model were investigated based on the sensitivity analysis of the selected model parameters. The experimental modal data as well as static response in terms of component nominal stresses and hot-spot stresses at the concerned locations were used for dynamic response- and static response-oriented model updating, respectively. The updated multi-scale model was further verified to act as the baseline model which is assumed to be finite-element model closest to the real situation of the structure available for the subsequent arbitrary numerical simulation. The comparison of dynamic and static responses between the calculated results by the final model and measured data indicated the updating and verification methods applied in this paper are reliable and accurate for the multi-scale model of frame-like structure. The general procedures of multi-scale model updating and verification were finally proposed for nonlinear physical-based modeling of large civil infrastructure, and it was applied to the model verification of a long-span bridge as an actual engineering practice of the proposed procedures.

A parametric study on probabilistic fracture of functionally graded composites by a concurrent multiscale method

This article reports the results of a parametric study on the fracture behavior of a crack in functionally graded materials. The study involves stochastic descriptions of particle and void numbers; location, size, and orientation characteristics; and constituent elastic properties; a concurrent multiscale model for calculating crack-driving forces; and Monte Carlo simulation for fracture reliability analysis. A level-cut, inhomogeneous, filtered Poisson field describes the statistically inhomogeneous microstructures of graded composites. Numerical results for an edge-cracked, graded specimen show that the particle shape and orientation for the same phase volume fractions have negligible effects on fracture reliability, even for graded materials with a high modular ratio. However, voids and the particle gradation parameter, if they exist or increase, can significantly raise the probability of fracture initiation. Limited crack-propagation simulations in graded composites containing brittle particles reveal that the fracture toughness of the matrix material can significantly influence the likelihood or the extent of crack growth.

Stochastic multiscale models for fracture analysis of functionally graded materials

This article presents three multiscale models, including sequential, invasive, and concurrent models, for fracture analysis of a crack in a two-phase, functionally graded composite. The models involve stochastic description of the particle volume fractions, particle locations, and constituent material properties; a two-scale algorithm including microscale and macroscale analyses for determining crack-driving forces; and two stochastic methods for fracture reliability analysis. The particle volume fractions, defined by a generic inhomogeneous random field, are related to the intensity function of an inhomogeneous Poisson field, which describes the statistically inhomogeneous microstructure of a functionally graded composite. Two stochastic methods, the dimensional decomposition method and direct Monte Carlo simulation, have been employed for obtaining the probabilistic characteristics of crack-driving forces and reliability analysis. Numerical results indicate that the sequential and invasive multiscale models are the most computationally inexpensive models available, but they may not produce acceptable probabilistic characteristics of stress-intensity factors or accurate probability of fracture initiation. The concurrent multiscale model is sufficiently accurate, gives probabilistic solutions very close to those generated from the microscale model, and can reduce the computational effort of the latter model by more than a factor of two. In addition, the concurrent multiscale model predicts crack trajectory as accurately as the microscale model.

A domain partitioning based pre-processor for multi-scale modelling of cast aluminium alloys

In this paper, a microstructural morphology based domain partitioning MDP methodology is developed for materials with non-uniform heterogeneous microstructure. The comprehensive set of methods is intended to provide a concurrent multi-scale analysis model with an initial computational domain that delineates regions of statistical homogeneity and inhomogeneity. The MDP methodology is intended to be a pre-processor to multi-scale analysis of mechanical behaviour and damage of heterogeneous materials, e.g. cast aluminium alloys. It introduces a systematic three-step process that is based on geometric features of morphology. The first step simulates high resolution microstructural information from low resolution micrographs of the material and a limited number of high resolution optical or scanning electron microscopy micrographs. The second step is quantitative characterization of the high resolution images to create effective metrics that can relate microstructural descriptors to material behaviour. The third step invokes a partitioning method to demarcate regions belonging to different length scales in a concurrent multi-scale model. Partitioning criteria for domain partitioning are defined in terms of microstructural descriptors and their functions. The effectiveness of these metrics in differentiating microstructures of a 319-type cast aluminium alloy with different secondary dendrite arm spacings SDAS is demonstrated. The MDP method establishes intrinsic material length scales for the different SDAS, namely, 23, 70 and 100 µm, and consequently subdivides the computational domain for concurrently coupling macro- and micromechanical analyses in the multi-scale model.

Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature

Coarse-grained molecular dynamics (CGMD) is a technique developed as a concurrent multiscale model that couples conventional molecular dynamics (MD) to a more coarse-grained description of the periphery. The coarse-grained regions are modeled on a mesh in a formulation that generalizes conventional finite element modeling (FEM) of continuum elasticity. CGMD is derived solely from the MD model, however, and has no continuum parameters. As a result, it provides a coupling that is smooth and provides control of errors that arise at the coupling between the atomistic and coarse-grained regions. In this article, we elaborate on the formulation of CGMD, describing in detail how CGMD is applied to anharmonic solids and finite temperature simulations. As tests of CGMD, we present in detail the calculation of the phonon spectra for solid argon and tantalum in 3D, demonstrating how CGMD provides a better description of the elastic waves than that provided by FEM. We also present elastic wave scattering calculations that show the elastic wave scattering is more benign in CGMD than FEM. We also discuss the dependence of scattering on the properties of the mesh. We introduce a rigid approximation to CGMD that eliminates internal relaxation, similar to the Quasicontinuum technique, and compare it to the full CGMD.

Concurrent multiscale model of an atomic crystal coupled with elastic continua

A methodology based on a Green's function formalism, which enables the coupling between atomic and continuous systems, is employed to evaluate the dynamical properties of concurrent elastic multiscale models. Boundary conditions satisfying the continuity of displacement and stress across interfaces between a harmonic crystal and continua are insufficient to establish seamless coupling at high frequency. The elastic mismatch in coupled discrete/continuous models is inherently linked to the difference in dispersion of the constitutive media.