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Real-time validation of mechanical models coupling PGD and constitutive relation error

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Abstract

In this work, we introduce a general framework that enables to perform real-time validation of mechanical models. This framework is based on two main ingredients: (i) the constitutive relation error which constitutes a convenient and mechanically sound tool for model validation; (ii) a powerful method for model reduction, the proper generalized decomposition, which is used to compute a solution with separated representations and thus to run the validation process quickly. Performances of the proposed approach are illustrated on machining applications.

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Notes

  1. One can note that it is the discrete version of the error that corresponds to the CRE expressed in terms of strains.

  2. The interested reader can notice that the horizontal axis for \(\lambda _1\) and \(\lambda _2\) is reduced to start at zero, that is why we observe a scale from \(0\) to \(2.1\times 10^{7}\) instead of the true one from \(1.05\times 10^{7}\) to \(3.15\times 10^{7}\).

  3. One can note that this observation is not true at each order for \((\psi _n,\phi _n)\) (order 5 is more monotone than order 4). It is actually due to the complexity of the problem which involves 4D. In the specific simple case of the same problem but reduced to only 2D \(x\) and \(X\), variations of modes \((\psi _n,\phi _n)\) are quicker and quicker at each order.

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Authors and Affiliations

  1. LMT-Cachan (ENS Cachan/CNRS/Paris 6 University), 61 Avenue du Président Wilson, 94235 , Cachan Cedex, France

    Robin Bouclier, François Louf & Ludovic Chamoin

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  1. Robin Bouclier
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  2. François Louf
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  3. Ludovic Chamoin
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Correspondence to Ludovic Chamoin.

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Bouclier, R., Louf, F. & Chamoin, L. Real-time validation of mechanical models coupling PGD and constitutive relation error. Comput Mech 52, 861–883 (2013). https://doi.org/10.1007/s00466-013-0850-y

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