期刊
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
卷 48, 期 12, 页码 2081-2098出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijengsci.2010.04.003
关键词
Thermodynamics; Calculus of variation; Transversality conditions; Eshelby tensors; Noether's theorem; Generalized Gibbs-Duhem condition; Volumetric growth; Diffusion of nutrients
The connections between the notion of Eshelby tensor and the variation of Hamiltonian like action integrals are investigated, in connection with the thermodynamics of continuous open bodies exchanging mass, heat and work with their surrounding. Considering first a homogeneous representative volume element (RVE), it is shown that a possible choice of the Lagrangian density is the material derivative of a suitable thermodynamic potential. The Euler equations of the so built action integral are the state laws written in rate form. As the consequence of the optimality conditions of the resulting Jacobi action, the vanishing of the surface contribution resulting from the general variation of this Hamiltonian action leads to the well-known Gibbs-Duhem condition. A general three-field variational principle describing the equilibrium of heterogeneous systems is next written, based on the zero potential, the stationarity of which delivers a balance law for a generalized Eshelby tensor in a thermodynamic context. Adopting the rate of the grand potential as the lagrangian density, a generalized Gibbs-Duhem condition is obtained as the transversality condition of the thermodynamic action integral, considering a solid body with a movable boundary. The stationnarity condition of the surface part of the thermodynamic action traduces a relationship between the virtual work of the field variables and the virtual work of the material forces at the moving boundary. This framework is applied to the volumetric growth of spherical tissue elements due to the diffusion of nutrients, whereby a growth model relating the growth velocity gradient to a growth like Eshelby stress built from the grand potential is set up. (C) 2010 Elsevier Ltd. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据