TY - JOUR
T1 - Towards stochastic continuum thermodynamics
AU - Ostoja-Starzewski, Martin
N1 - Funding Information:
This material is based upon work supported by the National Science Foundation (Grant CMS-9713764), the US Department of Agriculture (Grant 99-35504-8672), and the Canada Research Chairs program.
PY - 2002
Y1 - 2002
N2 - We explore the relation of a line of studies over the last dozen years on mesoscale material response below the Representative Volume Element with the line of studies on mesoscopic continuum physics. The objective is the development of stochastic continuum thermodynamics able to grasp random microstructural features absent in deterministic continuum theories. We first compare two lines of studies - those dealing with the response on a scale smaller than the Representative Volume Element (RVE) vis-à-vis those on mesoscopic continuum physics - and observe the dilemma of choice of the random field approximation. As a common basis for connecting both approaches, we propose a mesoscale Statistical Volume Element (SVE) and consider bounding its response via two admissible loadings. Employing the paradigm of thermal conductivity, we also present the relevant Legendre transformations. The latter are then generalized to the more general situation of fields governed by a quartet of Legendre transformations.
AB - We explore the relation of a line of studies over the last dozen years on mesoscale material response below the Representative Volume Element with the line of studies on mesoscopic continuum physics. The objective is the development of stochastic continuum thermodynamics able to grasp random microstructural features absent in deterministic continuum theories. We first compare two lines of studies - those dealing with the response on a scale smaller than the Representative Volume Element (RVE) vis-à-vis those on mesoscopic continuum physics - and observe the dilemma of choice of the random field approximation. As a common basis for connecting both approaches, we propose a mesoscale Statistical Volume Element (SVE) and consider bounding its response via two admissible loadings. Employing the paradigm of thermal conductivity, we also present the relevant Legendre transformations. The latter are then generalized to the more general situation of fields governed by a quartet of Legendre transformations.
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U2 - 10.1515/JNETDY.2002.020
DO - 10.1515/JNETDY.2002.020
M3 - Article
AN - SCOPUS:0036906468
SN - 0340-0204
VL - 27
SP - 335
EP - 348
JO - Journal of Non-Equilibrium Thermodynamics
JF - Journal of Non-Equilibrium Thermodynamics
IS - 4
ER -