On a thermodynamic theory of rods with two temperature fields

Nonlinear dynamics of uniformly loaded Elastica: Experimental and numerical evidence of motion around curled stable equilibrium configurations

“…We are sure of the greater efficiency of Hencky‐type models also when more complicated systems are considered (see []). Therefore we are confident that codes similar to the simple ones which were used in the present paper can be developed, and will be extremely useful, also in the dynamics study of i) Timoshenko beams, ii) lattice systems including many beam structural elements both in the case of 1D systems, in small or large deformations regimes, or in the case 2D and 3D structures, iii) more complex micro‐structures which arise in the theory of metamaterials (see []). We believe that the alternative approach, based on the formulation of continuous models and on their subsequent discretization although is substantially equivalent, may present some difficulties, when the discretization process of the continuous model is obtained without taking into account the physical nature of the modeled mechanical systems.…”

Deformation of an elastic magnetizable square rod due to a uniform electric current inside the rod and an external transverse magnetic field

“…Once the boundary values of the functions A h , A c h , A à r , A *c r  à T have been obtained, one can find all of the physical quantities related to the magnetic potential. The numerical method is next applied to the four functions F, F c , C, and C c (equations (58), (59), (61) and (62)), the two boundary conditions (equations (41), (42)) and the seven boundary conditions (equations (49), (50), (51), (52), (53), (54) and (55)). The resulting system of linear algebraic equations is…”

A multiphysics and multiscale approach for modeling microcracked thermo-elastic materials

“…It is worth mentioning that a theory of thermodynamics of elastic bodies with microstructure whose microelements possess microtemperatures is discussed in [33], where the Clausius-Duhem inequality is modified in order to include microtemperatures, and the first-order moment of the energy equations are added to the usual balance laws of a continuum with microstructure. Moreover, microtemperatures have been considered in [85,84], where were treated as known functions of the temperature and temperature gradients, and no balance equations were given for their determination; an application of a two-temperatures model to rod theory has been proposed in [1]. A study of heat conduction in materials with inner structure has been presented in [81,82,34,36].…”

“…(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article. )1 When a standard (Fourier-like) thermo-elastic theory is considered, the heat equation is:…”