| Abstract Scope |
Higher order gradients and stochasticity effects have already been incorporated in modeling pattern formation and size effects in manmade and naturemade materials. A review of such earlier developments on material mechanics modeling is given first. Then some new elements from fractional/fractal calculus and Tsallis non-extensive entropy statistical thermodynamics are introduced to deal with issues that is not possible to address with combined gradient-stochastic models and conventional Boltzmann-Gibbs statistical thermodynamics. Preliminary results on shear bands, stress-strain serrations, pattern formation and the strength-ductility competition are provided. Certain model analogies between living and nonliving systems are pointed out. Finally, the role of the aforementioned generalizations on extending classical interatomic/intermolecular potentials used in multiscale modeling, is discussed.
Acknowledgements
The lecture was delivered upon invitation of ECA on behalf of all participants I. Tsagrakis/I. Konstantopoulos/A. Sidiropoulos and A.C. Tsolakis/G. Petsos/O. Kapetanou/I.N. Nikolaidis in the HFRI projects MIS 5005134 and MIS 5045454 respectively. Useful discussions with K. Parisis and K.E. Aifantis are acknowledged.
References
E.C. Aifantis, A Concise Review of Gradient Models in Mechanics and Physics, Front. Phys. 7:239, 1 – 8 (2020); E.C. Aifantis, Internal length gradient (ILG) material mechanics across scales & disciplines, Adv. Appl. Mech. 49, 1-110 (2016); I. Tsagrakis, I. Konstantopoulos, A. Sidiropoulos and E.C. Aifantis, On certain applications of gradient nanochemomechanics: deformation and fracture of LIB and SGS, J. Mech. Behav. Mat. 28, 74–80 (2019); A.C. Tsolakis, G. Petsos, O. Kapetanou, I.N. Nikolaidis and E.C. Aifantis, Model analogies between pattern formation in deforming engineering materials & morphogenesis in ageing human brains, J. Mech. Behav. Mat. 28, 95–106 (2019). |