Statistically isotropic random field models for mechanics of random solid and fluid media

Jetti, Yaswanth Sai

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https://hdl.handle.net/2142/130008 Copy

Description

Title

Statistically isotropic random field models for mechanics of random solid and fluid media

Author(s)

Jetti, Yaswanth Sai

Issue Date

2025-06-16

Director of Research (if dissertation) or Advisor (if thesis)

Ostoja-Starzewski, Martin

Doctoral Committee Chair(s)

Ostoja-Starzewski, Martin

Committee Member(s)

• Chamorro, Leonardo P
• Sowers, Richard B
• Luetkemeyer, Callan

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• stochastic mechanics
• fractals
• Hurst effects
• correlations
• statistically isotropic random fields
• tensor-valued random fields
• micromechanics
• rough surfaces
• turbulence spectra

Abstract

Many natural and engineered systems' mechanical and dynamical behavior is governed by multiscale randomness, manifesting across spatial and temporal domains through heterogeneous microstructures, surface roughness, and turbulent flows. Such systems exhibit both short-range (fractal) and long-range (Hurst) scaling behaviors that challenge conventional modeling approaches rooted in deterministic continuum mechanics. This dissertation develops a unified theoretical and computational framework for characterizing, modeling, and applying multiscale stochastic structures using statistically isotropic random fields. The research spans scalar, vector, and tensor-valued fields, with applications in rough surface mechanics, fluid turbulence, and micromechanical modeling of heterogeneous materials. This work introduces a novel parametric class of covariance functions capable of independently modeling fractal and Hurst effects. This class generalizes classical two-parameter models (e.g., Generalized Cauchy, Dagum) and introduces conditions that ensure the statistical decoupling of short-range and long-range scaling characteristics. Spectral analysis of this three-parameter model reveals how fractal dimension and Hurst parameter influence high and low-frequency regimes, providing interpretable connections to physical observables. The model is evaluated on multiscale experimental datasets, including rough surface profiles and turbulent velocity data, demonstrating its superior performance over traditional formulations. The implications of these random field models are investigated in solid mechanics through the study of contact behavior in non-self-affine rough surfaces. Surfaces generated using the proposed covariance class are subjected to frictionless, non-adhesive elastic contact analysis. The results reveal a strong dependence of contact area evolution on the fractal dimension and negligible sensitivity to the Hurst parameter, highlighting departures from predictions made by self-affine models and motivating further inquiry into covariance structure effects. The framework is then extended to turbulent flow modeling by incorporating an additional parameter and relating it to the integral length scale of the flow. This parameter is then utilized to explore the physical origins of a distinct spectral regime commonly observed in streamwise velocity spectra. A generalized mechanism based on statistical mixing of eddy clusters is proposed, linking this behavior to overlapping short- and long-range scaling within turbulent structures. To further generalize the framework, vector-valued random fields are studied under the constraints of statistical isotropy, homogeneity, and divergence-free (solenoidal) or curl-free (irrotational) properties. Mathematical relationships between such fields' longitudinal and lateral components are established using Abelian and Tauberian theorems, enabling consistent modeling of vector components with multiscale features. These results lay the foundation for constructing realistic turbulent velocity fields. In mechanics of materials, the dissertation investigates the scale dependence of apparent shear modulus fields derived from scalar random fields with specified fractal and Hurst characteristics. Simulations using a physics-based cellular automaton method reveal how these stochastic parameters govern convergence to representative volume element (RVE) behavior. However, a more general formulation is needed to model spatially resolved material properties for boundary-value problems. This approach leads to the development of tensor-valued random fields (TRFs) for stiffness and compliance properties at the mesoscale. A proposed construction methodology satisfies micromechanical consistency, captures anisotropic behavior, and preserves complete spatial correlation structure. Applied to a planar interpenetrating phase composite, the method produces non-Gaussian TRFs whose statistical properties vary with mesoscale size and microstructural randomness. These TRFs are then used to analyze crack tip stresses under remote anti-plane loading, and the critical influence of mesoscale variability on fracture behavior is illustrated.

Graduation Semester

2025-08

Type of Resource

Thesis

Handle URL

https://hdl.handle.net/2142/130008

Copyright and License Information

Copyright 2025 Yaswanth Sai Jetti

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