סמינר מחלקתי Prof. Lucas Máximo Alves
School of Mechanical Engineering Seminar
Monday, March 21, 2016 at 15:00
Wolfson Building of Mechanical Engineering, Room 206
NEWS PERSPECTIVES ON THE PRINCIPLE OF MAXIMUM ENERGY DISSIPATION RATE
from Non-Equilibrium Thermodynamics to Chaos Theory
Prof. Lucas Máximo
Some unstable physical systems that have extreme energy dissipation need a principle able to provide the dynamical equations to describe its evolution as the pattern formation associated to its dissipation. Branching cracks in materials is a good example of such systems. Inspired in the Maximum Dissipation Principle (MDP) of the Plasticity Theory (PT) an in the Maximum Energy Released Rate (MERR) in Fracture Mechanics (FM) Slepyan proposed a MDP to describe a dynamic fracture and explain the unattainability of Rayleigh waves velocity by the cracks. This MDP proposed by Slepyan was modified adding in its mathematical formulation a local rugosity and a time delay between the micro- and macroscopic velocities, now associated to input and output velocities of a dissipative system. This was done to include rugged or branched fractal structures in the dynamical equations obtained from this principle. The inclusion of a time delay, as a hypothesis of an onset instability, present itself promissory to provide a mathematical description of the dissipative systems by means of iterated equations and logistic maps. The results shows a clear framework and a complete non-equilibrium phenomenological sequence, able to explain the instability from the dynamics equations until the growth of the dissipation structure or formation of fractal patterns as a branching cracks for example.