Derivation of generalized Gibbs equations with higher-order stresses and its microscopic discussions
Yasui Yoshihiro; Kaneko Akira; Matsuzaki Dai; Takahashi Kunihiro
Abstract:Balance equations for higher-order materials have been widely studied. In this paper, Gibbs equations for higher-order materials are formulated introducing a concept of the equivalence between higher-order stress powers and heat flux. Gibbs equations for higher-order materials and simple materials are expressed with microscopic quantities by use of the microscopic expressions such as stress power, higher-order stress powers and internal energy. The results obtained from the simulation of molecular dynamics can be substituted into the microscopic expressions of Gibbs equations. The values of entropies for higher-order materials and simple materials can be calculated in this procedure. It is shown that the difference in entropies between higher-order materials and simple materials becomes notable in an example of the calculation. Key Words:Solid mechanics, Gibbs equation, Entropy, Higher-order stress, Molecular dynamics, Lattice dynamics, Mesodomain