%0 Journal Article
%T A Lagrangian¨CHamiltonian unified formalism for a class of dissipative systems
%A Hamid Said
%J Mathematics and Mechanics of Solids
%@ 1741-3028
%D 2019
%R 10.1177/1081286518778892
%X Entropy production in classical thermomechanical systems is the result of three sources: transfer of heat; dissipative stresses, such as viscosity; and internal variables. In this paper, a variational treatment for dissipative systems due to internal variables is presented. Specifically, in the context of the theory of internal variables, a novel dissipative Lagrangian¨CHamiltonian formalism is developed. Two fundamental thermodynamic functions (the free energy and the entropy production rate) form the basis of this formalism. The Hamiltonian formulation reveals a new structure on the phase space, and is applied to prove large-time solutions for the semilinear problem. Finally, the formalism is applied to the problem of dynamic brittle fracture
%K Dissipative systems
%K internal variables
%K dissipation function
%K Lagrangian¨CHamiltonian formalism
%K failure waves
%U https://journals.sagepub.com/doi/full/10.1177/1081286518778892