Mixed-integer programming formulation of a data-driven solver in computational elasticity

Kanno, Yoshihiro

doi:10.1007/s11590-019-01409-w

Cited by 38 publications

(37 citation statements)

References 11 publications

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“…27(a) porosity values are very close to each other while permeability values differ considerably and so, after some fixed-point iterations, there is a possibility for the solver to be trapped between several choices each selected from a different data set. It is well-known that heuristic approaches, e.g., fixed-point iteration used in our research, may not find the global optima for combinatorial optimization problems [116,117], i.e., trapped between some local minima. As suggested in [116] an alternative optimization problem can be formulated by a relaxation method which makes the optimization problem convex, and consequently, a global optimum is guaranteed.…”

Section: Multifidelity Simulations Of Berea Sandstone Datamentioning

confidence: 99%

A kd-tree-accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

Bahmani

Sun

2021

Computer Methods in Applied Mechanics and Engineering

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We present a hybrid model/model-free data-driven approach to solve poroelasticity problems. Extending the data-driven modeling framework originated from Kirchdoerfer and Ortiz (2016), we introduce one model-free and two hybrid modelbased/data-driven formulations capable of simulating the coupled diffusion-deformation of fluid-infiltrating porous media with different amounts of available data. To improve the efficiency of the model-free data search, we introduce a distance-minimized algorithm accelerated by a k-dimensional tree search. To handle the different fidelities of the solid elasticity and fluid hydraulic constitutive responses, we introduce a hybridized model in which either the solid and the fluid solver can switch from a model-based to a model-free approach depending on the availability and the properties of the data. Numerical experiments are designed to verify the implementation and compare the performance of the proposed model to other alternatives. c

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Section: Multifidelity Simulations Of Berea Sandstone Datamentioning

confidence: 99%

A kd-tree-accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

Bahmani

Sun

2021

Computer Methods in Applied Mechanics and Engineering

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“…A class of Data-Driven problems consists of finding the compatible and equilibrated internal state z ∈ E that minimizes the distance to the global material data set D = D 1 × · · · × D M . To this end, we metrize the local phase spaces Z e by means of norms of the form (5) |z e | e = C e e · e + C −1 e σ e · σ e 1/2 , for some symmetric and positive-definite matrices {C e } M e=1 , with corresponding distance (6) d e (z e , y e ) = |z e − y e | e , for y e , z e ∈ Z e . The local norms induce a metrization of the global phase Z by means of the global norm i. e., we wish to find the point y ∈ D in the material data set that is closest to the constraint set E of compatible and equilibrated internal states or, equivalently, we wish to find the compatible and equilibrated internal state z ∈ E that is closest to the material data set D.…”

Section: Materials Data Distance Minimisation Paradigmmentioning

confidence: 99%

“…and z 0 ∈ Z arbitrary, where P D denotes the closest point projection of a point in Z onto D. Iteration (13) first finds the closest point P D z j to z j on the material data set D and then projects the result back to the constraint set E. The iteration is repeated until P D z j+1 = P D z j , i. e., until the data association to points in the material data set remains unchanged. Note that more sophisticated algorithms can be considered to solve this combinatorial optimization problem [6]. Equations (11) define two standard linear elasticity problems, which can be interpreted as follows.…”

Section: Data-driven Simulation Algorithmmentioning

confidence: 99%

Model-free data-driven methods in mechanics: material data identification and solvers

2019

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This paper presents an integrated model-free data-driven approach to solid mechanics, allowing to perform numerical simulations on structures on the basis of measures of displacement fields on representative samples, without postulating a specific constitutive model. A material data identification procedure, allowing to infer strain-stress pairs from displacement fields and boundary conditions, is used to build a material database from a set of mutiaxial tests on a nonconventional sample. This database is in turn used by a data-driven solver, based on an algorithm minimizing the distance between manifolds of compatible and balanced mechanical states and the given database, to predict the response of structures of the same material, with arbitrary geometry and boundary conditions. Examples illustrate this modelling cycle and demonstrate how the datadriven identification method allows importance sampling of the material state space, yielding faster convergence of simulation results with increasing database size, when compared to synthetic material databases with regular sampling patterns.

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“…the strain-stress couples to calculate (in each finite element of the mesh for instance) and the material states database, under the constraints of satisfying both equilibrium equations and compatibility conditions. Slightly different formulations of this solver have been proposed [20,21].…”

Section: Introductionmentioning

confidence: 99%

Measuring stress field without constitutive equation

Dalemat

Coret

Leygue

et al. 2019

Mechanics of Materials

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The present paper proposes a coupled experimental-numerical protocol to measure heterogeneous stress fields in a model-free framework. This work contributes to developing the emerging realm of mechanics without constitutive equation. In fact, until now these types of simulations have been missing database of real and rich material behaviour. The technique consists in coupling Digital Image Correlation (DIC) measurements and the Data Driven Identification (DDI) algorithm, recently developed by Leygue et al.(Databased derivation of material response. Computer Methods in Applied Mechanics and Engineering 331, 184-196 (2018)). This algorithm identifies the mechanical response of a material, i.e. stress-strain data, without postulating any constitutive equation, but with the help of a large database of displacement fields and loading conditions. The only governing equation used in this algorithm is the mechanical equilibrium. The bias induced by the choice and the calibration of a constitutive model is thus removed. In the abovementioned paper, the relevance of the method has been demonstrated with synthetic data issued from finite element computations. Here, its efficiency is assessed with "real" experimental data. A multi-perforated elastomer membrane is uniaxially stretched in large strain. Practical challenges are addressed when using the DDI algorithm, especially those due to unmeasured data during experiments. Easy-to-implement solutions are proposed and the DDI technique is successfully applied: heterogeneous stress fields are computed from real data. Considering that the material is elastic, its strain energy density is then measured. Good agreement with standard uniaxial tensile experimental results validates the approach on real data. Highlights-Data Driven Identification technique is applied to measured displacements and forces-Experimental stress field is determined without presupposing constitutive equation-Practical solutions to use Digital Image Correlation raw data are provided-The technique is applied to a perforated elastomer sheet under large strain 1

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Mixed-integer programming formulation of a data-driven solver in computational elasticity

Cited by 38 publications

References 11 publications

A kd-tree-accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

A kd-tree-accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

Model-free data-driven methods in mechanics: material data identification and solvers

Measuring stress field without constitutive equation

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