Microstructural Randomness Versus Representative Volume Element in Thermomechanics

Author:

Ostoja-Starzewski M.1

Affiliation:

1. Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montre´al, Que´bec H3A 2K6, Canada

Abstract

Continuum thermomechanics hinges on the concept of a representative volume element (RVE), which is well defined in two situations only: (i) unit cell in a periodic microstructure, and (ii) statistically representative volume containing a very large (mathematically infinite) set of microscale elements (e.g., grains). Response of finite domains of material, however, displays statistical scatter and is dependent on the scale and boundary conditions. In order to accomplish stochastic homogenization of material response, scale-dependent hierarchies of bounds are extended to dissipative/irreversible phenomena within the framework of thermomechanics with internal variables. In particular, the free-energy function and the dissipation function become stochastic functionals whose scatter tends to decrease to zero as the material volume is increased. These functionals are linked to their duals via Legendre transforms either in the spaces of ensemble average velocities or ensemble-average dissipative forces. In the limit of infinite volumes (RVE limit (ii) above) all the functionals become deterministic, and classical Legendre transforms of deterministic thermomechanics hold. As an application, stochastic continuum damage mechanics of elastic-brittle solids is developed.

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference45 articles.

1. Maugin, G. A., 1999, The Thermomechanics of Nonlinear Irreversible Behaviors—An Introduction, World Scientific, Singapura.

2. Ziegler, H., 1963, “Some Extremum Principles in Irreversible Thermodynamics With Applications to Continuum Mechanics,” Progress in Solid Mechanics, Vol. 42, North-Holland, Amsterdam, pp. 91–191.

3. Muschik, W., and Fang, J., 1989, “Statistical Foundations of Non-equilibrium Contact Quantities. Bridging Phenomenological and Statistical Non-equilibrium Thermodynamics,” Acta Phys. Hung., 66, pp. 39–57.

4. Lemaitre, J., and Chaboche, J.-L., 1990, Mechanics of Solid Materials, Cambridge University Press, Cambridge, UK.

5. Maugin, G. A., 1992, The Thermomechanics of Plasticity and Fracture, Cambridge University Press, Cambridge, UK.

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