94 research outputs found
Efficient twoâscale simulations of microstructured materials using deep material networks
Deep material networks (DMN) are a promising piece of technology for accelerating concurrent multiscale simulations. DMNs are identified by linear elastic pre-computations on representative volume elements, and serve as high-fidelity surrogates for full-field simulations on microstructures with inelastic constituents. The offline training phase is independent of the online evaluation, such that a pre-trained DMN may be applied for varying material behavior of the constituents. In this contribution, we investigate a two-scale component simulation of industrial complexity accelerated by DMNs. To this end, a DMN is solved implicitly at every Gauss point to include the microstructure information into the macro simulation
A reduced order model for geometrically parameterized two-scale simulations of elasto-plastic microstructures under large deformations
In recent years, there has been a growing interest in understanding complex
microstructures and their effect on macroscopic properties. In general, it is
difficult to derive an effective constitutive law for such microstructures with
reasonable accuracy and meaningful parameters. One numerical approach to bridge
the scales is computational homogenization, in which a microscopic problem is
solved at every macroscopic point, essentially replacing the effective
constitutive model. Such approaches are, however, computationally expensive and
typically infeasible in multi-query contexts such as optimization and material
design. To render these analyses tractable, surrogate models that can
accurately approximate and accelerate the microscopic problem over a large
design space of shapes, material and loading parameters are required. In
previous works, such models were constructed in a data-driven manner using
methods such as Neural Networks (NN) or Gaussian Process Regression (GPR).
However, these approaches currently suffer from issues, such as need for large
amounts of training data, lack of physics, and considerable extrapolation
errors. In this work, we develop a reduced order model based on Proper
Orthogonal Decomposition (POD), Empirical Cubature Method (ECM) and a
geometrical transformation method with the following key features: (i) large
shape variations of the microstructure are captured, (ii) only relatively small
amounts of training data are necessary, and (iii) highly non-linear
history-dependent behaviors are treated. The proposed framework is tested and
examined in two numerical examples, involving two scales and large geometrical
variations. In both cases, high speed-ups and accuracies are achieved while
observing good extrapolation behavior
Deep material networks for efficient scale-bridging in thermomechanical simulations of solids
We investigate deep material networks (DMN). We lay the mathematical foundation of DMNs and present a novel DMN formulation, which is characterized by a reduced number of degrees of freedom. We present a efficient solution technique for nonlinear DMNs to accelerate complex two-scale simulations with minimal computational effort. A new interpolation technique is presented enabling the consideration of fluctuating microstructure characteristics in macroscopic simulations
Effective transient behaviour of heterogeneous media in diffusion problems with a large contrast in the phase diffusivities
This paper presents a homogenisation-based constitutive model to describe the
effective tran- sient diffusion behaviour in heterogeneous media in which there
is a large contrast between the phase diffusivities. In this case mobile
species can diffuse over long distances through the fast phase in the time
scale of diffusion in the slow phase. At macroscopic scale, contrasted phase
diffusivities lead to a memory effect that cannot be properly described by
classical Fick's second law. Here we obtain effective governing equations
through a two-scale approach for composite materials consisting of a fast
matrix and slow inclusions. The micro-macro transition is similar to
first-order computational homogenisation, and involves the solution of a
transient diffusion boundary-value problem in a Representative Volume Element
of the microstructure. Different from computational homogenisation, we propose
a semi-analytical mean-field estimate of the composite response based on the
exact solution for a single inclusion developed in our previous work [Brassart,
L., Stainier, L., 2018. Effective transient behaviour of inclusions in
diffusion problems. Z. Angew Math. Mech. 98, 981-998]. A key outcome of the
model is that the macroscopic concentration is not one-to-one related to the
macroscopic chemical potential, but obeys a local kinetic equation associated
with diffusion in the slow phase. The history-dependent macroscopic response
admits a representation based on internal variables, enabling efficient time
integration. We show that the local chemical kinetics can result in non-Fickian
behaviour in macroscale boundary-value problems.Comment: 36 pages, 14 figure
Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling
The computational homogenization of hyperelastic solids in the geometrically
nonlinear context has yet to be treated with sufficient efficiency in order to
allow for real-world applications in true multiscale settings. This problem is
addressed by a problem-specific surrogate model founded on a reduced basis
approximation of the deformation gradient on the microscale. The setup phase is
based upon a snapshot POD on deformation gradient fluctuations, in contrast to
the widespread displacement-based approach. In order to reduce the
computational offline costs, the space of relevant macroscopic stretch tensors
is sampled efficiently by employing the Hencky strain. Numerical results show
speed-up factors in the order of 5-100 and significantly improved robustness
while retaining good accuracy. An open-source demonstrator tool with 50 lines
of code emphasizes the simplicity and efficiency of the method.Comment: 28 page
Materialâinformed training of viscoelastic deep material networks
Deep material networks (DMN) are a data-driven homogenization approach that show great promise for accelerating concurrent two-scale simulations. As a salient feature, DMNs are solely identified by linear elastic precomputations on representative volume elements. After parameter identification, DMNs act as surrogates for full-field simulations of such volume elements with inelastic constituents.
In this work, we investigate how the training on linear elastic data, i.e., how the choice of the loss function and the sampling of the training data, affects the accuracy of DMNs for inelastic constituents. We investigate linear viscoelasticity and derive a material-informed sampling procedure for generating the training data and a loss function tailored to the problem at hand. These ideas improve the accuracy of an identified DMN and allow for significantly reducing the number of samples to be generated and labeled
An FEâDMN method for the multiscale analysis of short fiber reinforced plastic components
In this work, we propose a fully coupled multiscale strategy for components made from short fiber reinforced composites, where each Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN) which covers the different fiber orientation states varying within the component. These DMNs need to be identified by linear elastic precomputations on representative volume elements, and serve as high-fidelity surrogates for full-field simulations on microstructures with inelastic constituents.
We discuss how to extend direct DMNs to account for varying fiber orientation, and propose a simplified sampling strategy which significantly speeds up the training process. To enable concurrent multiscale simulations, evaluating the DMNs efficiently is crucial. We discuss dedicated techniques for exploiting sparsity and high-performance linear algebra modules, and demonstrate the power of the proposed approach on an injection molded quadcopter frame as a benchmark component. Indeed, the DMN is capable of accelerating two-scale simulations significantly, providing possible speed-ups of several magnitudes
An FE-DMN method for the multiscale analysis of thermomechanical composites
We extend the FE-DMN method to fully coupled thermomechanical two-scale simulations of composite materials. In particular, every Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN). Such a DMN serves as a high-fidelity surrogate model for full-field solutions on the microscopic scale of inelastic, non-isothermal constituents. Building on the homogenization framework of Chatzigeorgiou et al. (Int J Plast 81:18â39, 2016), we extend the framework of DMNs to thermomechanical composites by incorporating the two-way thermomechanical coupling, i.e., the coupling from the macroscopic onto the microscopic scale and vice versa, into the framework. We provide details on the efficient implementation of our approach as a user-material subroutine (UMAT). We validate our approach on the microscopic scale and show that DMNs predict the effective stress, the effective dissipation and the change of the macroscopic absolute temperature with high accuracy. After validation, we demonstrate the capabilities of our approach on a concurrent thermomechanical two-scale simulation on the macroscopic component scale
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