The mechanical behaviours of materials are in general stochastic in one way or another, due, by and large, to the spatial or temporal fluctuations in their microstructure. The stochasticity is more severe when the fluctuations take place over a length scale which is not small compared to the size of the material, or a time scale which is comparable to the time over which the material behaviour is monitored. A few examples will be described in this talk, and modelling efforts will also be introduced. The first case concerns low-density materials with porous or network microstructures, which are commonly used as shock-absorbing materials. When externally or internally stressed, a non-uniform strain energy distribution will be developed inside such a material due to its random microstructure, and this causes stochasticity in the mechanical behaviour. The formation of dislocation patterns in deformed crystalline materials is another example with microstructural fluctuations. Both situations are interesting analogues to thermal systems at equilibrium—the structural irregularities qualify for a description by a Shannon-like entropy, and there is also the usual (strain) energy. When an entropy is related to energy, an effective temperature θ which measures the relative importance of entropy versus energy exists, but this is not the Kelvin temperature T because the entropy here is athermal. A constant-(N, V, T, θ) canonical ensemble is proposed in which the compatibility between the thermal and athermal components of the system can be understood more clearly. As in traditional statistical mechanics, such an ensemble can be used as a general approach to calculate the properties of an athermal system.
Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2
- Pub Date:
- September 2009
- Fluctuation phenomena random processes noise and Brownian motion;