We elaborated the concept of effective elasticity tensors based on the distance in the 21D space of these tensors.  

 

Our formulation is based on norms in that space, which allow us to quantify the concept of proximity between the measurements and models.

 

This concept diminishes restrictions of the Hookean idealization and extends its applicability to seismic data contaminated by experimental errors.

Danek T., Noseworthy, A., Slawinski, M.A.   (2018)   Effects of norms on general Hookean solids for their isotropic counterparts.   Dolomites Research Notes on Approximation.

Bos, L.P., Dalton, D.R., Slawinski, M.A. (2017)   On  commutativity and near commutativity of translational and rotational averages: Analytical proofs and numerical examination. arXiv: 1704.05541

 

Danek T., Noseworthy, A., Slawinski, M.A.   (2016)   On closest isotropic tensors and their norms.   arXiv: 1604.03833

 

Bos, L.P., Slawinski, M.A.   (2015)   2-norm effective isotropic Hookean solids.   Journal of Elasticity 120(1), 1–22

 

Danek, T., Slawinski, M.A.   (2015)   On choosing effective elasticity tensors using a Monte-Carlo method.   Acta Geophysica 63(1), 45–61

 

Danek, T., Kochetov, M., Slawinski, M.A.   (2015)   Effective elasticity tensors in context of random errors.   Journal of Elasticity 121(1), 55–67

 

Danek, T., Slawinski, M.A.   (2014)   On effective transversely isotropic elasticity tensors of Frobenius and L2 operator norms.   Dolomites Research Notes on Approximation 7

 

Danek, T., Kochetov, M., Slawinski, M.A.   (2013)   Uncertainty analysis of effective elasticity tensors using quaternion-based global optimization and Monte-Carlo method.   The Quarterly Journal of Mechanics and Applied Mathematics 66(2), 253–272

Diner, Ç., Kochetov, M., Slawinski, M.A.   (2011)   On choosing effective symmetry class for elasticity tensors.   The Quarterly Journal of Mechanics and Applied Mathematics 64(1), 57–74

 

Diner, Ç., Kochetov, M., Slawinski, M.A.   (2011)   Identifying symmetry classes of elasticity tensors using monoclinic distance function.   Journal of Elasticity 102(2), 175–190

 

Kochetov, M., Slawinski, M.A.   (2009)   Estimating effective elasticity tensors from Christoffel equations .   Geophysics 74(5), 67–73

 

Kochetov, M., Slawinski, M.A.   (2009)   On obtaining effective orthotropic elasticity tensors .   The Quarterly Journal of Mechanics and Applied Mathematics 62, 149–166

 

Bucataru, I., Slawinski, M.A.   (2009)   Invariant properties for finding distance in space of elasticity tensors .   Journal of Elasticity 94(2), 97–114

 

Kochetov, M., Slawinski, M.A.   (2009)   On obtaining effective transversely isotropic elasticity tensors .   Journal of Elasticity 94(1), 1–13

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