Ostoja-Starzewski presents USACM webinar on his recent research

Earlier this month, MechSE Professor Martin Ostoja-Starzewski presented a webinar on the topic of “Tensor Random Fields in Mechanics” in the TTA-UQ and Probabilistic Modeling series.

These webinars are organized by the Uncertainty Quantification and Probabilistic Modeling Technical Thrust Area of the U.S. Association of Computational Mechanics (USACM).

Ostoja-Starzewski’s webinar focused on how the mechanics and physics of random media suggest that stochastic PDEs and stochastic finite element (SFE) methods require mesoscale tensor-valued random fields (TRFs) of constitutive laws with locally anisotropic fluctuations. Such models are also useful when there is interest in fields of dependent quantities (velocity, strain, stress, etc.) that need to be constrained by the balance laws (of mass, momentum, etc.). Examples include irrotational and solenoidal TRFs.

In his presentation, he reviewed the canonical forms of general correlation structures of statistically stationary and isotropic TRFs of ranks 1,…,4 in 3D. Besides “conventional” correlations, his research group’s approach can be used to construct TRFs with fractal and Hurst (long-range memory) characteristics. This research extends his earlier work on scalar-valued RFs (including random processes) in vibration problems, rods and beams with random properties under random loadings, elastodynamics, wavefronts, fracture, homogenization of random media, and contact mechanics.

Ostoja-Starzewski’s presentation was centered around several of his recent publications:

1. ​A. Malyarenko and M. Ostoja-Starzewski, Tensor-Valued Random Fields for Continuum Physics, Cambridge University Press, 2019. 
2. ​A. Malyarenko, M. Ostoja-Starzewski, and A. Amiri-Hezaveh, Random Fields of Piezoelectricity and Piezomagnetism, Springer, 2020.