A unified procedure for construction of theories of deformable media. I. Classical continuum physics

1995 ◽  
Vol 448 (1934) ◽  
pp. 335-356 ◽  
Keyword(s):  
Energy Balance ◽  
Companion Paper ◽  
Balance Laws ◽  
Kinematic Variable ◽  
Material Behaviour ◽  
Classical Formulation ◽  
Deformable Media ◽  
Basic Equations ◽  
Basic Features ◽  
Continuum Theories

A new unified procedure for constructing continuum theories of deformable media is presented and used in this and a companion paper. The procedure starts with a balance of energy and derives from it all the relevant balance laws that may also include those that are associated with thermal, electrical and magnetic effects; the basic energetic ingredients that are included in the balance of energy depend, of course, on the nature of the particular theory of material behaviour desired. The advantage of the new procedure becomes especially apparent when one considers formulation of a new theory of material behaviour for which additional balance laws (involving new kinetic quantities) are required to accompany any additional basic kinematic and thermal variables additional to those in the classical formulation. Indeed, in the formulation of such new theories, usually little or no previous information is available concerning properties of the new kinetic quantities in the additional balance laws; and, in this connection, the unified procedure of this paper provides a simple attractive setting for deriving the basic equations that are automatically consistent with the energy balance. In this paper, first the basic features of the new procedure are illustrated in the context of classical thermomechanics. Generalizations of this thermomechanical theory are then discussed in two cases: (1) in the presence of an additional kinematic variable and (2) in the presence of full electromagnetic effects. Both of these generalizations bring out some interesting novel features when new theories are being constructed.

A unified procedure for construction of theories of deformable media. III. Mixtures of interacting continua

1995 ◽  
Vol 448 (1934) ◽  
pp. 379-388 ◽  
Keyword(s):  
Single Phase ◽  
Balance Laws ◽  
First Law Of Thermodynamics ◽  
Thermomechanical Theory ◽  
Form Invariance ◽  
Deformable Media ◽  
Basic Equations

This paper is a continuation of parts I and II under the same title (Green & Naghdi 1995 a , b , Proc . R . Soc . Lond . A 448, 335, 357). In contrast to the earlier two papers which dealt with single phase continua, this paper is concerned with a new thermomechanical theory of multiphase interacting continua. We use the same unified procedure as in part I but now the various energies that enter the balance of energy must be modified to accommodate energetic contributions arising from N interacting finite constituents. Again, our derivation of the various basic balance laws is effected by an appeal to the form invariance of the balance of energy and leads to a system of basic equations of mixtures which are automatically consistent with the balance of energy or the first law of thermodynamics for mixtures of N constituents.

scholarly journals The mass and energy balance of ice within the Eisriesenwelt cave, Austria

2011 ◽  
Vol 5 (1) ◽  
pp. 245-257 ◽  
Author(s):  
F. Obleitner ◽  
C. Spötl
Keyword(s):  
Energy Balance ◽  
Balance Model ◽  
Wave Radiation ◽  
Rock Surface ◽  
Seepage Water ◽  
Cave System ◽  
Calculated Energy ◽  
Sensitivity Studies ◽  
Major Loss ◽  
Basic Features

Abstract. Meteorological measurements were performed in a prominent ice cave (Eisriesenwelt, Austria) during a full annual cycle. The data show the basic features of a dynamically ventilated cave system with a well distinguished winter and summer regime. The calculated energy balance of the cave ice is largely determined by the input of long-wave radiation originating at the host rock surface. On average the turbulent fluxes withdraw energy from the surface. This is more pronounced during winter due to enhanced circulation and lower humidity. During summer the driving gradients reverse sign and the associated fluxes provide energy for melt. About 4 cm of ice were lost at the measurement site during a reference year. This was due to some sublimation during winter, while the major loss resulted from melt during summer. Small amounts of accumulation occurred during spring due to refreezing of seepage water. These results are largely based on employing a numerical mass and energy balance model. Sensitivity studies prove reliability of the calculated energy balance regarding diverse measurement uncertainties and show that the annual mass balance of the ice strongly depends on cave air temperature during summer and the availability of seepage water in spring.

scholarly journals Reconnoitering the effect of shallow groundwater on land surface temperature and surface energy balance using MODIS and SEBS

2012 ◽  
Vol 16 (7) ◽  
pp. 1833-1844 ◽  
Author(s):  
F. Alkhaier ◽  
Z. Su ◽  
G. N. Flerchinger
Keyword(s):  
Energy Balance ◽  
Surface Energy ◽  
Surface Temperature ◽  
Water Table ◽  
Land Surface Temperature ◽  
Land Surface ◽  
Surface Energy Balance ◽  
Shallow Groundwater ◽  
Companion Paper ◽  
Daily Evaporation

Abstract. The possibility of observing shallow groundwater depth and areal extent using satellite measurements can support groundwater models and vast irrigation systems management. Moreover, these measurements can help to include the effect of shallow groundwater on surface energy balance within land surface models and climate studies, which broadens the methods that yield more reliable and informative results. To examine the capacity of MODIS in detecting the effect of shallow groundwater on land surface temperature and the surface energy balance in an area within Al-Balikh River basin in northern Syria, we studied the interrelationship between in-situ measured water table depths and land surface temperatures measured by MODIS. We, also, used the Surface Energy Balance System (SEBS) to calculate surface energy fluxes, evaporative fraction and daily evaporation, and inspected their relationships with water table depths. We found out that the daytime temperature increased while the nighttime temperature decreased when the depth of the water table increased. And, when the water table depth increased, net radiation, latent and ground heat fluxes, evaporative fraction and daily evaporation decreased, while sensible heat flux increased. This concords with the findings of a companion paper (Alkhaier et al., 2012). The observed clear relationships were the result of meeting both conditions that were concluded in the companion paper, i.e. high potential evaporation and big contrast in day-night temperature. Moreover, the prevailing conditions in this study area helped SEBS to yield accurate estimates. Under bare soil conditions and under the prevailing weather conditions, we conclude that MODIS is suitable for detecting the effect of shallow groundwater because it has proper imaging times and adequate sensor accuracy; nevertheless, its coarse spatial resolution is disadvantageous.

scholarly journals Urban Energy Balance Obtained from the Comprehensive Outdoor Scale Model Experiment. Part I: Basic Features of the Surface Energy Balance

2010 ◽  
Vol 49 (7) ◽  
pp. 1341-1359 ◽  
Author(s):  
Toru Kawai ◽  
Manabu Kanda
Keyword(s):  
Energy Balance ◽  
Surface Energy ◽  
Surface Energy Balance ◽  
Heat Storage ◽  
Heat Fluxes ◽  
Eddy Correlation ◽  
Scale Model ◽  
Surface Geometry ◽  
Urban Energy Balance ◽  
Basic Features

Abstract The objective of this study is to examine the basic features of the surface energy balance (SEB) using the data obtained from the Comprehensive Outdoor Scale Model (COSMO). COSMO is an idealized miniature city that has no vegetation, no human activity, and no heterogeneity of the surface geometry. The basic features of the SEB such as energy balance closure, the ensemble mean of the diurnal variation of the energy balance, and the daytime and daily statistics of the energy balance were investigated. The following were the main findings of the study: 1) A surface energy imbalance was observed. The sum of sensible and latent heat fluxes estimated by the eddy correlation method underestimated the available energy by 1% during the daytime and by 44% during the night. 2) Large heat storage in the daytime and small radiative cooling at night sustained positive sensible heat fluxes throughout the night in all seasons and in all sunshine conditions. 3) The daytime ratio of heat storage ΔQS to net radiation Q*, ΔQS/Q*, depended on the friction velocity u* and decreased with increasing u*. 4) The values of ΔQS/Q* tended to be larger in winter than in summer. The annual averaged value of this ratio was approximately 0.6. 5) The large volumetric heat capacity of the surface materials and the resulting large energetic hysteresis produced nonzero total daily values of heat storage. The total daily values of heat storage largely depended on the weather (i.e., sunshine condition and with or without rainfall) and showed positive and negative values on clear-sky days and rainy days, respectively.

Linear piezoelectricity

2020 ◽  
pp. 327-354
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Energy Balance ◽  
Energy Transport ◽  
Constitutive Relations ◽  
Electric Displacement ◽  
Balance Laws ◽  
Third Order ◽  
Static Limit ◽  
Electrical Boundary Conditions ◽  
Linear Piezoelectricity ◽  
Electromechanical Energy

This chapter presents the elements of linear piezoelectricity including mechanical and electrostatic balance laws and coupled mechanical electrical constitutive relations. The thermodynamically consistent constitutive relations are determined from a coupled electromechanical energy balance argument and expressions are given alternately considering the electric field and the electric displacement as independent fields. Appropriate electrical boundary conditions are also discussed. The theory is also specialized to poled piezoceramics. A chapter appendix provides a brief discussion of Maxwell’s equations for electromagnetics and energy transport in the quasi-static limit. A second chapter appendix discusses the properties of third order tensors.

scholarly journals Reconnoitering the effect of shallow groundwater on land surface temperature and surface energy balance using MODIS and SEBS

2011 ◽  
Vol 8 (5) ◽  
pp. 8671-8700 ◽  
Author(s):  
F. Alkhaier ◽  
Z. Su ◽  
G. N. Flerchinger
Keyword(s):  
Energy Balance ◽  
Surface Energy ◽  
Surface Temperature ◽  
Water Table ◽  
Land Surface Temperature ◽  
Land Surface ◽  
Surface Energy Balance ◽  
Shallow Groundwater ◽  
Companion Paper ◽  
Daily Evaporation

Abstract. The possibility of observing shallow groundwater depth and areal extent using satellite measurements can support groundwater models and vast irrigation systems management. Besides, these measurements help bringing groundwater effect on surface energy balance within land surface models and climate studies. To inspect the MODIS capacity of detecting shallow groundwater effect on land surface temperature and surface energy balance in an area within Al-Balikh River basin in northern Syria, we investigated the interrelationship between in-situ measured water table depths and land surface temperatures of MODIS. Further, we used the Surface Energy Balance System (SEBS) to calculate surface energy fluxes, evaporative fraction and daily evaporation, and inspected their relationships with water table depths. In agreement with the findings of a companion paper (Alkhaier et al., 2011), we found that daytime temperature increased and nighttime temperature decreased with increasing water table depth. Where water table depth increased, net radiation, latent and ground heat fluxes, evaporative fraction and daily evaporation decreased, while sensible heat flux increased. The clear observed relationships resulted from meeting both conditions concluded in the companion paper, i.e. high potential evaporation and big contrast in air temperature. Moreover, the prevailing conditions in this study area helped SEBS producing accurate estimates. We conclude that MODIS is suitable for shallow groundwater effect detection since it has proper imaging times and appropriate sensor accuracy; nevertheless, its coarse spatial resolution is disadvantageous.

The energy of elastic defects: a distributional approach

1994 ◽  
Vol 445 (1923) ◽  
pp. 23-37 ◽  
Keyword(s):  
Energy Balance ◽  
Surface Energy ◽  
Energy Distribution ◽  
Dislocation Line ◽  
Additional Term ◽  
Balance Laws ◽  
Two Dimensional ◽  
Elastic Materials ◽  
Defect Area ◽  
Defect System

An analysis of moving defects in homogeneous elastic materials is given in this paper. The laws of linear momentum, moment of momentum and energy are obtained in a distributional form. The motion of singularities gives rise to new terms in these balance laws. A quasistatic propagation criterion of energetic nature is used to obtain the balance of energy in the form of a conservation law for the material-defect system. The energy of this system consists of the elastic energy of the material and an additional term called the energy of the defect. It is uniformly distributed on the defect and its density represents, for two-dimensional bodies, the energy required to form a new unit defect area (or length). For cracks the existence of a Griffith-type surface energy distribution is obtained. For notches and cavities we show that an energy distributed over their boundary does not agree with the distributional form of the energy balance, which conduces to an energy distribution on the whole cavity. When the defect is an edge or screw dislocation, an energy distributed on the slip plane is obtained, its density being related to the Peach-Koehler force acting on the dislocation line.

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