Next Article in Journal
Asymptotic Separation of Solutions to Fractional Stochastic Multi-Term Differential Equations
Next Article in Special Issue
Fox H-Functions in Self-Consistent Description of a Free-Electron Laser
Previous Article in Journal
Random Times for Markov Processes with Killing
Previous Article in Special Issue
An Entropy Paradox Free Fractional Diffusion Equation
Article

Scaling in Anti-Plane Elasticity on Random Shear Modulus Fields with Fractal and Hurst Effects

1
Department of Mechanical Science & Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
2
Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
3
Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Carlo Cattani
Fractal Fract. 2021, 5(4), 255; https://doi.org/10.3390/fractalfract5040255
Received: 28 October 2021 / Revised: 28 November 2021 / Accepted: 30 November 2021 / Published: 4 December 2021
(This article belongs to the Special Issue 2021 Feature Papers by Fractal Fract's Editorial Board Members)
The scale dependence of the effective anti-plane shear modulus response in microstructures with statistical ergodicity and spatial wide-sense stationarity is investigated. In particular, Cauchy and Dagum autocorrelation functions which can decouple the fractal and the Hurst effects are used to describe the random shear modulus fields. The resulting stochastic boundary value problems (BVPs) are set up in line with the Hill–Mandel condition of elastostatics for different sizes of statistical volume elements (SVEs). These BVPs are solved using a physics-based cellular automaton (CA) method that is applicable for anti-plane elasticity to study the scaling of SVEs towards a representative volume element (RVE). This progression from SVE to RVE is described through a scaling function, which is best approximated by the same form as the Cauchy and Dagum autocorrelation functions. The scaling function is obtained by fitting the scaling data from simulations conducted over a large number of random field realizations. The numerical simulation results show that the scaling function is strongly dependent on the fractal dimension D, the Hurst parameter H, and the mesoscale δ, and is weakly dependent on the autocorrelation function. Specifically, it is found that a larger D and a smaller H results in a higher rate of convergence towards an RVE with respect to δ. View Full-Text
Keywords: homogenization; scaling; effective response; cellular automata homogenization; scaling; effective response; cellular automata
Show Figures

Figure 1

MDPI and ACS Style

Jetti, Y.S.; Ostoja-Starzewski, M. Scaling in Anti-Plane Elasticity on Random Shear Modulus Fields with Fractal and Hurst Effects. Fractal Fract. 2021, 5, 255. https://doi.org/10.3390/fractalfract5040255

AMA Style

Jetti YS, Ostoja-Starzewski M. Scaling in Anti-Plane Elasticity on Random Shear Modulus Fields with Fractal and Hurst Effects. Fractal and Fractional. 2021; 5(4):255. https://doi.org/10.3390/fractalfract5040255

Chicago/Turabian Style

Jetti, Yaswanth S., and Martin Ostoja-Starzewski. 2021. "Scaling in Anti-Plane Elasticity on Random Shear Modulus Fields with Fractal and Hurst Effects" Fractal and Fractional 5, no. 4: 255. https://doi.org/10.3390/fractalfract5040255

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop