Renyi entropy and fractional order mechanics for predicting complex mechanics of materials

Basanta Raj Pahari; William Oates

doi:10.1117/12.2613356

20 April 2022 Renyi entropy and fractional order mechanics for predicting complex mechanics of materials

Basanta Raj Pahari, William Oates

Author Affiliations +

Proceedings Volume 12044, Behavior and Mechanics of Multifunctional Materials XVI; 1204408 (2022) https://doi.org/10.1117/12.2613356
Event: SPIE Smart Structures + Nondestructive Evaluation, 2022, Long Beach, California, United States

Abstract

Recently we employed entropy dynamics, a statistical inference tool that facilitates quantifying posterior probabilities of likely particle positions, to create material models relating fractal polymers networks to their constitutive behaviors.1 This methodology is applicable to classical mechanics, electromagnetic field theory, and quantum mechanics, thus offering new opportunities to expand our understating of functional materials. The entropy dynamics approach usually starts by maximizing Shannon entropy of possible particle locations with added constraints to account for particle interactions or motion. Here, we take a broader approach and use the Renyi entropy, a generalization of the Shannon entropy, to build our constitutive models for multi-functional polymers. The Renyi entropy allows us to derive wide-ranging material constitutive models that consolidate other entropy approaches such as max-entropy, min-entropy, and collision entropy. Furthermore, we investigate material properties using fractional moment constraints instead of the widely used integer moment constraints. Finally, we show how our approach provides a way to building models relevant to a broad class of smart materials and structures.

Conference Presentation

Citation Download Citation

Basanta Raj Pahari and William Oates "Renyi entropy and fractional order mechanics for predicting complex mechanics of materials", Proc. SPIE 12044, Behavior and Mechanics of Multifunctional Materials XVI, 1204408 (20 April 2022); https://doi.org/10.1117/12.2613356

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

;

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE