## Combined Gradient – Stochastic Models for Composites [K]

**Avraam
Konstantinidis**^{1}; Elias
Aifantis^{1};

^{1}ARISTOTLE UNIVERSITY OF THESSALONIKI, Thessaloniki, Greece;

**Type of Paper:** Keynote

**Id Paper:** 376

**Topic:** 64## Abstract:

The deterministic internal length gradient (ILG) mechanics framework for elasticity and plasticity is extended to account for internal stress fluctuations due to stochastic effects associated with deformation-induced microstructures. Various existing approaches are first briefly reviewed and then an integrated discussion is provided. The role of probability density functions (PDFs) is examined in terms of existing experimental data. Emphasis is placed on Tsallis q-statistics and the related modification of classical PDFs (e.g. q-Gaussian, q-exponential). Then some example problems from the composites’ literature are discussed.

## Keywords:

Micromaterials;

## References:

E.C. Aifantis, Internal length gradient (ILG) material mechanics across scales &disciplines, Adv. Appl. Mech. 49, 1-110 (2016).

A.A. Konstantinidis, K.E. Aifantis and J.Th.M. De Hosson, Capturing the stochastic mechanical behavior of micro and nanopillars, Mater. Sci. Eng. A 597, 89-94 (2014).

A.A. Konstantindis, X. Zhang and E.C. Aifantis, On the combined gradient-stochastic plasticity model: Application to Mo-micropillar compression, AIP Conf. Proc. 1646, 3-9 (2015).

A.A. Konstantinidis and K.E. Aifantis, Capturing slip band formation in Ni3Al nanocubes during compression, Mater. Sci. Technol. 35, 571-576 (2019).## Cite this article as:

Konstantinidis A and Aifantis E. (2022).
Combined Gradient – Stochastic Models for Composites [K].
In F. Kongoli, E. Aifantis, R. Das, V.Eremeyev, N. Fantuzzi.
(Eds.), *Sustainable Industrial Processing Summit
SIPS2022 Volume 12 Trovalusci Intl. Symp Multiscale & Multiphysics Modelling of Complex Materials*
(pp. 89-90).
Montreal, Canada: FLOGEN Star Outreach