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Non‐Gaussian positive‐definite matrix‐valued random fields with constrained eigenvalues: Application to random elasticity tensors with uncertain material symmetries
13 references·8 citing·36 second hop
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure609 cited
  • 2000A nonparametric model of random uncertainties for reduced matrix models in structural dynamics475 cited
  • 2007Microstructural Randomness and Scaling in Mechanics of Materials380 cited
  • 2005Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators183 cited
  • 2005Maximum likelihood estimation of stochastic chaos representations from experimental data146 cited
  • 2008Statistical volume element method for predicting microstructure–constitutive property relations133 cited
  • 2009Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions93 cited
  • 2010Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data87 cited
  • 2008Asymptotic Sampling Distribution for Polynomial Chaos Representation from Data: A Maximum Entropy and Fisher Information Approach80 cited
  • 2008Nonparametric stochastic modeling of linear systems with prescribed variance of several natural frequencies78 cited
  • 2009A Bounded Random Matrix Approach for Stochastic Upscaling63 cited
  • 2010Modeling of random anisotropic elastic media and impact on wave propagation

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46 cited

Cited by

  • 2014Itô SDE--based Generator for a Class of Non-Gaussian Vector-valued Random Fields in Uncertainty Quantification21 cited
  • 2020Modeling non-Gaussian random fields of material properties in multiscale mechanics of materials19 cited
  • 2011Probabilistic modeling of apparent tensors in elastostatics: A MaxEnt approach under material symmetry and stochastic boundedness constraints18 cited
  • 2015STOCHASTIC REPRESENTATIONS AND STATISTICAL INVERSE IDENTIFICATION FOR UNCERTAINTY QUANTIFICATION IN COMPUTATIONAL MECHANICS17 cited
  • 2014Variational Theory and Computations in Stochastic Plasticity16 cited
  • 2024Stochastic modelling of symmetric positive definite material tensors12 cited
  • 2012Variational formulations and functional approximation algorithms in stochastic plasticity of materials11 cited
  • 2015New Metrics for Validation of Data-Driven Random Process Models in Uncertainty Quantification10 cited