Nonsmooth and Nonconvex Mechanics
The field of nonsmooth and nonconvex
mechanics is a newly developed multi-interdisciplinary research area, which
involves a powerful combination of theoretical analysis in mathematical modelling
of natural systems, finite deformation theory, modern physics, material science,
nonlinear partial differential equations, global
optimization, variational methods, dynamical systems, global optimization,
numerical algorithms and scientific computations. This field has undergone
very considerable development in a remarkably short time.
Nonsmooth mechanics is a research topic that integrates fundamental
work in nonsmooth analysis, nonlinear partial differential equations, finite
deformation theory, high pressure/high rate response, damage and failure
mechanics, and computational mathematics. 
Nonconvex phenomena arise from large deformation mechanics, chaotic
dynamical systems, buckling analysis and phase transitions, where the total
potential energies are usually nonconvex.
Nonconvex mechanics cover many research fields of applications, such as:
New book on Nonsmooth and
Nonconvex Mechanics:
Nonconvex/Nonsmooth
Mechanics: Modeling, Analysis and Numerical Methods
By
David Y. Gao, Ray W. Ogden and G.E. Stavroulakis
Kluwer Academic Publishers, Dordrecht/Boston
Hardbound, ISBN 0-7923-6786-3
February 2001, 516 pp.
EUR 145.00 / USD 157.00 / GBP
99.00
The First International Symposium on
Nonsmooth/Nonconvex Mechanics was held at Virginia
Tech, June 27-30, 1999. The second one will be held in Greece, 2002, Click here for details
Chaotic
Systems
Reason for chaos: Nonconvexity
(multi-potential wells).
Examples:
New phenomena in chaotic
systems
1. Meta-chaos:
Fig
1. Fig. 2 (Chaos vase)
2. Trio-bifurcantion and trio-chaos:
Life of a nonlinear beam vibration
Some movies about
finite element simulations for dynamically post-buckling analysis of a rubber
diaphragm created by my Ph.D. student Axinte Ionita:
