In the present work, a modified model of heat conduction including higher order of time derivative is derived by extending Green and Naghdi theory without energy dissipation. We introduce two phase lag times to include the thermal displacement gradient and the heat flux in the heat conduction and depict microscopic responses more precisely. The constructed model is applied to s...

The three-phase-lag model and Green–Naghdi theory without energy dissipation are employed to study the deformation of a two-temperature fiber-reinforced medium with an internal heat source that is moving with a constant speed under a hydrostatic initial stress and the gravity field.  The modulus of the elasticity is given as a linear function of the reference temperature. The exact expressions ...

The objective of this paper is to propose a hyperbolic relaxation technique for the dispersive Serre-Green-Naghdi equations (also known as fully non-linear Boussinesq equations) with full topography effects introduced in Green, A.E. and Naghdi, P.M. (J. Fluid Mech., 78, 237-246, 1976) Seabra-Santos el al Mec.h, 176, 117-134, 1997). This done by revisiting similar Guermond Comput. Phys., 399, 10...

The main aim of the paper is to study impact delay times in a poro-elastic medium using finite element approach and three-phase lag thermo-elastic theory. governing equations were obtained for model with six times. Consideration was given one-dimensional application half-space. Because complex form basic equations, used solve this problem. Asymmetric symmetric tensors represent all physical qua...

The present paper is aimed at studying the effect of gravity on the general model of the equations of the generalized thermomicrostretch for a homogeneous isotropic elastic half-space solid whose surface is subjected to a Mode-I crack problem. The problem is in the context of the Green and Naghdi theory (GN). The normal mode analysis is used to obtain the exact expressions for the displacement ...

The hydroelastic response of mat-type Very Large Floating Structures (VLFSs) to severe sea conditions, such as tsunamis and hurricanes, must be assessed for safety and survivability. An efficient and robust nonlinear hydroelastic model is required to predict accurately the motion of and the dynamic loads on a VLFS due to such large waves. We develop a nonlinear theory to predict the hydroelasti...

The objective stress rates used in most commercial finite element programs are the Jaumann rate of Kirchhoff stress, Jaumann rates of Cauchy stress, or Green–Naghdi rate. The last two were long ago shown not to be associated by work with any finite strain tensor, and the first has often been combined with tangential moduli not associated by work. The error in energy conservation was thought to ...