Coupling of scales in a multiscale simulation using neural networks

Unger, Jörg F.; Könke, Carsten

doi:10.1016/j.compstruc.2008.05.004

Cited by 52 publications

(28 citation statements)

References 22 publications

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“…In [107], the constitutive relationship of the interface layer between reinforcement and concrete is approximated by neural networks, which are trained based on the numerical simulations on the mesoscale. The inclusion of the characteristic length as an additional parameter into the metamodel even allows to simulate softening [134] without a strong mesh sensitivity. However, a weak point of these metamodels is the curse of dimensionality, which means the higher the dimension of the input space the more training data are required in order to build a reliable model.…”

Section: Uncoupled Hierarchical Multiscale Modelsmentioning

confidence: 99%

Multiscale Modeling of Concrete

Unger

Eckardt

2011

Arch Computat Methods Eng

Self Cite

229

103

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In this paper, a mesoscale model of concrete is presented, which considers particles, matrix material and the interfacial transition zone (ITZ) as separate constituents. Particles are represented as ellipsoides, generated according to a prescribed grading curve and placed randomly into the specimen. Algorithms are proposed to generate realistic particle configurations efficiently. The nonlinear behavior is simulated with a cohesive interface model for the ITZ. For the matrix material, different damage/plasticity models are investigated. The simulation of localization requires to regularize the solution, which is performed by using integral type nonlocal models with strain or displacement averaging. Due to the complexity of a mesoscale model for a realistic structure, a multiscale method to couple the homogeneous macroscale with the heterogeneous mesoscale model in a concurrent embedded approach is proposed. This allows an adaptive transition from a full macroscale model to a multiscale model, where only the relevant parts are resolved on a finer scale. Special emphasis is placed on the investigation of different coupling schemes between the different scales, such as the mortar method and the arlequin method, and a discussion of their advantages and disadvantages within the current context. The applicability of the proposed methodology is illustrated for a variety of examples in tension and compression.

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Section: Uncoupled Hierarchical Multiscale Modelsmentioning

confidence: 99%

Multiscale Modeling of Concrete

Unger

Eckardt

2011

Arch Computat Methods Eng

Self Cite

229

103

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“…Depending on the type of training data in the offline stage, we classify these methods mainly into macroscopic and microscopic approaches. In macroscopic approaches, the stressstrain relations, or strain energy density functions, are directly fitted by regression methods, like deep neural network (DNN) [23,24,25,26] and Kriging methods [26,27]. Enabled by recent progresses in computer hardware systems, DNN becomes one of the most popular tools due to its large model generalities [28,29], and has also stimulated applications across different engineering disciplines [30,31,32,33].…”

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confidence: 99%

Exploring the 3D architectures of deep material network in data-driven multiscale mechanics

Liu

2019

Journal of the Mechanics and Physics of Solids

146

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This paper extends the deep material network (DMN) proposed by Liu et al. (2019) [1] to tackle general 3-dimensional (3D) problems with arbitrary material and geometric nonlinearities. It discovers a new way of describing multiscale heterogeneous materials by a multi-layer network structure and mechanistic building blocks. The data-driven framework of DMN is discussed in detail about the offline training and online extrapolation stages. Analytical solutions of the 3D building block with a two-layer structure in both small-and finite-strain formulations are derived based on interfacial equilibrium conditions and kinematic constraints. With linear elastic data generated by direct numerical simulations on a representative volume element (RVE), the network can be effectively trained in the offline stage using stochastic gradient descent and advanced model compression algorithms. Efficiency and accuracy of DMN on addressing the long-standing 3D RVE challenges with complex morphologies and material laws are validated through numerical experiments, including 1) hyperelastic particle-reinforced rubber composite with Mullins effect; 2) polycrystalline materials with rate-dependent crystal plasticity; 3) carbon fiber reinforced polymer (CFRP) composites with fiber anisotropic elasticity and matrix plasticity. In particular, we demonstrate a threescale homogenization procedure of CFRP system by concatenating the microscale and mesoscale material networks. The complete learning and extrapolation procedures of DMN establish a reliable data-driven framework for multiscale material modeling and design.anisotropic responses, and may require burdensome calibration to find the model parameters. As a result, homogenization based on the concept of representative volume element (RVE) [11] has become an important approach to model multiscale materials [12]. Many analytical methods have been proposed, which adopt some micromechanics assumptions to simplify the full-field RVE problem, such as Hashin-Shtrikman bounds [13,14], the Mori-Tanaka method [15] and self-consistent methods [16]. Since most analytical methods are derived based on the solution for regular geometries and simple material models (e.g. Eshelby's solution for isotropic elastic materials [17]), it is usually difficult for them to consider complex microstructural morphologies, history-dependent materials and large deformations. Additionally, direct numerical simulation (DNS) tools, such as finite element [18], meshfree [19,20] and fast Fourier transform (FFT)-based micromechanics methods [21,22], are both flexible and accurate. However, a DNS model involves a detailed meshing of the RVE microstructures and requires tremendous computational cost, especially for 3D problems. Therefore, one of the fundamental issues in multiscale material modeling and design is how to find an accurate low-dimensional representation of the RVE for arbitrary morphologies and nonlinearities.In the past decade, a plethora of data-driven material modeling methods have been proposed based on exist...

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“…The rapidness of the FENN method highlights new perspectives concerning the multiscale analysis of biological tissues. Furthermore, NN approaches are beneficial for linking disparate dimensional scales, drastically reduce the computation time, incorporate the results of experimental and/or numerical calculations at low scales and to perform, if needed, inverse calculations to assess optimal inputs for given target outputs (Topping and Bahreininejad 1992;Jenkins 1997;Rafiq et al 2001;Unger and Konke 2008;Hambli et al 2006).…”

Section: Resultsmentioning

confidence: 99%

“…The output data are the updated bone properties and some trabecular bone factors. The NN approach is beneficial if the numerical analysis of the complex model is time consuming or unfeasible (Topping and Bahreininejad 1992;Jenkins 1997;Rafiq et al 2001;Unger and Konke 2008;Hambli et al 2006). Moreover, NN models can be applied for the integration of information extracted from experimental data and medical images.…”

Section: Introductionmentioning

confidence: 98%

Multiscale methodology for bone remodelling simulation using coupled finite element and neural network computation

Hambli

Katerchi

Benhamou

2010

Biomech Model Mechanobiol

112

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The aim of this paper is to develop a multiscale hierarchical hybrid model based on finite element analysis and neural network computation to link mesoscopic scale (trabecular network level) and macroscopic (whole bone level) to simulate the process of bone remodelling. As whole bone simulation, including the 3D reconstruction of trabecular level bone, is time consuming, finite element calculation is only performed at the macroscopic level, whilst trained neural networks are employed as numerical substitutes for the finite element code needed for the mesoscale prediction. The bone mechanical properties are updated at the macroscopic scale depending on the morphological and mechanical adaptation at the mesoscopic scale computed by the trained neural network. The digital image-based modelling technique using μ-CT and voxel finite element analysis is used to capture volume elements representative of 2 mm³ at the mesoscale level of the femoral head. The input data for the artificial neural network are a set of bone material parameters, boundary conditions and the applied stress. The output data are the updated bone properties and some trabecular bone factors. The current approach is the first model, to our knowledge, that incorporates both finite element analysis and neural network computation to rapidly simulate multilevel bone adaptation.

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Coupling of scales in a multiscale simulation using neural networks

Cited by 52 publications

References 22 publications

Multiscale Modeling of Concrete

Multiscale Modeling of Concrete

Exploring the 3D architectures of deep material network in data-driven multiscale mechanics

Multiscale methodology for bone remodelling simulation using coupled finite element and neural network computation

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