On the theory of porous elastic rods

Abstract

a b s t r a c tWe consider the direct approach to the theory of rods, in which the thin body is modelled as a deformable curve with a triad of rigidly rotating orthonormal vectors attached to every material point. In this context, we employ the theory of elastic materials with voids to describe the mechanical behavior of porous rods. First, we derive the dynamical nonlinear field equations of the model. Then, in the framework of linear theory, we prove the uniqueness of the solution to the associated boundary-initial-value problem. We identify the relevant field quantities from the theory of directed curves by comparison with the three-dimensional equations of straight porous rods. Finally, for orthotropic and homogeneous rods, we determine the constitutive coefficients in terms of the three-dimensional elasticity constants by solving several problems in the two different approaches.

On a thermodynamic theory of rods with two temperature fields

“…We mention that the assigned body loads F and L also include the contributions of the loads acting on the lateral boundaries of the three-dimensional rod [40].…”

“…(38)(39)(40)(41) into Eq. (36) we find the explicit form of the constitutive equations for N · P, M · P, η and F. For instance, the constitutive equations for η and F are expressed by…”

“…-porosity effects in the mechanics of rods [40,41], using the theory of thermoelastic materials with voids [42]; -functionally graded materials in the mechanics of rods [43] or -electrical and magnetic fields, phase transitions, diffusion, and other coupled effects known in 3D continuum mechanics or in 2D shell theories.…”

Theory of thin thermoelastic rods made of porous materials

“…. ,K 7 of thin rods are analyzed in [39]. In what follows, we shall extend the analysis concerning the structure of constitutive tensors to the thermoelastic coefficients G 1 , G 2 , and the scalars G 3 , G 4 , and G.…”

“…. , K 7 are given in [39]. Let us turn our attention to rods without natural twisting, i.e., we have σ = 0.…”