ON THE SYSTEMATICS OF ENERGETIC TERMS IN CONTINUUM MECHANICS, AND A NOTE ON GIBBS (1877)

2008 ◽  
Vol 22 (27) ◽  
pp. 4863-4876 ◽  
Author(s):  
FALK H. KOENEMANN
Keyword(s):  
Energy Conservation ◽  
Stress Tensor ◽  
Elastic Deformation ◽  
Continuum Mechanics ◽  
Conservation Law ◽  
Cauchy Stress ◽  
Cauchy Stress Tensor ◽  
First Law Of Thermodynamics ◽  
Energetic Properties ◽  
Energy Conservation Law

The systematics of energetic terms as they are taught in continuum mechanics deviate seriously from the standard doctrine in physics, resulting in a profound misconception. It is demonstrated that the First Law of Thermodynamics has been routinely reinterpreted in a sense that would make it subordinate to Bernoulli's energy conservation law. Proof is given to the effect that the Cauchy stress tensor does not exist. Furthermore, it is shown that the attempt by Gibbs to find a thermodynamic understanding for elastic deformation does not sufficiently account for all the energetic properties of such a process.

scholarly journals On Fulfillment of Energy Conservation Law in Theory of Elastic Waves V. V. Nevdakh1)

2021 ◽  
Vol 20 (2) ◽  
pp. 161-167
Author(s):  
V. V. Nevdakh
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Energy Conservation ◽  
Elastic Wave ◽  
Total Energy ◽  
Elastic Deformation ◽  
Sound Wave ◽  
Elastic Waves ◽  
Conservation Law ◽  
Energy Conservation Law

In accordance with the energy conservation law, the total energy of a closed physical system must remain constant at any moment of time. The energy of a traveling elastic wave consists of the kinetic energy in the oscillating particles of the medium and the potential energy of  its elastic deformation. In the existing theory of elastic waves, it is believed that the kinetic and potential energy densities of a traveling wave without losses  are the same at any moment of time and vary according to the same law. Accordingly, the total energy density of such wave is different at various moment of time, and only its time-averaged value remains constant. Thus, in the existing theory of elastic waves, the energy conservation law is not fulfilled. The purpose of this work is to give a physically correct description of these waves. A new description of a sound wave in an ideal gas has been proposed and it is based on the use of a wave equation system for perturbing the oscillation velocity of gas particles, which determines their kinetic energy, and for elastic deformation, which determines their potential energy. It has been shown that harmonic solutions describing the oscillations of the gas particles velocity perturbation and their elastic deformation, which are phase shifted by p/2, are considered as physically correct solutions of such equations system for a traveling sound wave. It has been found that the positions of the kinetic and potential energy maxima in the elastic wave, described by such solutions, alternate in space every quarter of the wavelength. It has been established that every quarter of a period in a wave without losses, the kinetic energy is completely converted to potential and vice versa, while at each spatial point of the wave its total energy density is the same at any time, which is consistent with the energy conservation law. The energy flux density of such traveling elastic wave is described by the expression for the Umov vector. It has been concluded that such traveling sound wave without losses  in an ideal gas can be considered as a harmonic oscillator.

scholarly journals Verification of Continuum Mechanics Predictions with Experimental Mechanics

Materials ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 77
Author(s):  
Cesar A. Sciammarella ◽  
Luciano Lamberti ◽  
Federico M. Sciammarella
Keyword(s):  
Stress Tensor ◽  
Continuum Mechanics ◽  
Strain Tensor ◽  
Scalar Fields ◽  
Identification Problem ◽  
Theoretical Concept ◽  
Cauchy Stress ◽  
Cauchy Stress Tensor ◽  
Mathematical Functions ◽  
Eulerian Derivative

The general goal of the study is to connect theoretical predictions of continuum mechanics with actual experimental observations that support these predictions. The representative volume element (RVE) bridges the theoretical concept of continuum with the actual discontinuous structure of matter. This paper presents an experimental verification of the RVE concept. Foundations of continuum kinematics as well as mathematical functions relating displacement vectorial fields to the recording of these fields by a light sensor in the form of gray-level scalar fields are reviewed. The Eulerian derivative field tensors are related to the deformation of the continuum: the Euler–Almansi tensor is extracted, and its properties are discussed. The compatibility between the Euler–Almansi tensor and the Cauchy stress tensor is analyzed. In order to verify the concept of the RVE, a multiscale analysis of an Al–SiC composite material is carried out. Furthermore, it is proven that the Euler–Almansi strain tensor and the Cauchy stress tensor are conjugate in the Hill–Mandel sense by solving an identification problem of the constitutive model of urethane rubber.

Reduced energy conservation law for magnetized plasma

1994 ◽  
Vol 50 (3) ◽  
pp. 293-297 ◽  
Author(s):  
Petro P Sosenko ◽  
Viktor K Decyk
Keyword(s):  
Energy Conservation ◽  
Conservation Law ◽  
Magnetized Plasma ◽  
Energy Conservation Law

A New Highway Safety Model Based on Cellular Automata

2014 ◽  
Vol 989-994 ◽  
pp. 2340-2343
Author(s):  
Li Xing Li
Keyword(s):  
Cellular Automata ◽  
Energy Conservation ◽  
Traffic Safety ◽  
Conservation Law ◽  
Highway Safety ◽  
Traffic Density ◽  
New Model ◽  
The Road ◽  
The Right ◽  
Energy Conservation Law

With the growth of the total mileage of highway. There is great importance in studying highway safety. At the present time, there are little research on traffic safety with the consideration of the Keep-Right-Except-To-Pass Rule, which requires drivers to drive in the right-most lane unless they are passing another vehicle. Based on Cellular Automata, this paper constructs a new model of highway safety with the consideration of the particular Rule. To evaluate the safety of the road, the model proposes a new index based on energy conservation law. After the simulation, the result shows the best traffic density to balance the safety and traffic flux is 20.1133veh/km.

scholarly journals Local energy conservation law for a spatially-discretized Hamiltonian Vlasov-Maxwell system

2017 ◽  
Vol 24 (6) ◽  
pp. 062112 ◽  
Author(s):  
Jianyuan Xiao ◽  
Hong Qin ◽  
Jian Liu ◽  
Ruili Zhang
Keyword(s):  
Energy Conservation ◽  
Conservation Law ◽  
Local Energy ◽  
Maxwell System ◽  
Energy Conservation Law
Sign in / Sign up

Export Citation Format

Share Document