scholarly journals On nonlinear thermo-electro-elasticity

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160170 ◽  
Author(s):  
Markus Mehnert ◽  
Mokarram Hossain ◽  
Paul Steinmann
Keyword(s):  
Boundary Value Problem ◽  
Total Energy ◽  
Constitutive Equations ◽  
Cylindrical Tube ◽  
Polymeric Materials ◽  
Temperature History ◽  
Internal Temperature ◽  
Laws Of Thermodynamics ◽  
Electric Loads ◽  
Coupled Loads

Electro-active polymers (EAPs) for large actuations are nowadays well-known and promising candidates for producing sensors, actuators and generators. In general, polymeric materials are sensitive to differential temperature histories. During experimental characterizations of EAPs under electro-mechanically coupled loads, it is difficult to maintain constant temperature not only because of an external differential temperature history but also because of the changes in internal temperature caused by the application of high electric loads. In this contribution, a thermo-electro-mechanically coupled constitutive framework is proposed based on the total energy approach. Departing from relevant laws of thermodynamics, thermodynamically consistent constitutive equations are formulated. To demonstrate the performance of the proposed thermo-electro-mechanically coupled framework, a frequently used non-homogeneous boundary-value problem, i.e. the extension and inflation of a cylindrical tube, is solved analytically. The results illustrate the influence of various thermo-electro-mechanical couplings.

Computational Rheology with Integral Constitutive Equations

1999 ◽  
Vol 9 (5) ◽  
pp. 198-203 ◽  
Author(s):  
Evan Mitsoulis
Keyword(s):  
Constitutive Equations ◽  
Relaxation Times ◽  
Cylindrical Tube ◽  
Polymeric Materials ◽  
Elastic Behaviour ◽  
Benchmark Problems ◽  
Test Cases ◽  
Viscoelastic Materials ◽  
Extrudate Swell ◽  
Capillary Rheometry

AbstractComputational rheology deals with the formulation and solution of constitutive equations for non-Newtonian materials. From these the emphasis is put on polymeric materials, which exhibit both viscous and elastic behaviour in flow and deformation. These materials are often called viscoelastic materials. Polymer solutions and melts (e.g. commercial plastics and rubber) are good examples of viscoelastic materials. Their processing under continuous (e.g. extrusion) or batch (e.g. injection molding) operations is the main occupation of the plastics and rubber industries, but the corresponding modelling and numerical simulation is a difficult task and a relatively recent undertaking.The present work reviews modelling aspects of viscoelasticity and shows how the complex rheology of these materials is best captured through integral constitutive equations with a spectrum of relaxation times. Using such constitutive equations and the Finite Element Method (FEM), the solution of some benchmark problems of rheology becomes feasible. Examples will be shown from the flow of polymer melts and solutions in a 4:1 axisymmetric contraction encountered in standard capillary rheometry, as well as the flow around a sphere falling in a cylindrical tube. The emphasis will be on demonstrating the flow patterns via streamlines and predicting such viscoelastic phenomena as vortex growth, extrudate swell, and reduction of the drag coefficient, which are of particular interest to the rheological community as test cases of computational results.

Constitutive Equations for the Thermomechanical Response of Rene´ 80: Part 2—Effects of Temperature History

1993 ◽  
Vol 115 (4) ◽  
pp. 358-364 ◽  
Author(s):  
V. S. Bhattachar ◽  
D. C. Stouffer
Keyword(s):  
Constitutive Equations ◽  
Temperature History ◽  
Nickel Base Superalloy ◽  
State Variable ◽  
History Effects ◽  
Variable Approach ◽  
Effects Of Temperature ◽  
Nickel Base ◽  
Nonisothermal Conditions ◽  
Base Superalloy

The unified constitutive equations for Rene´ 80 developed by Bhattachar and Stouffer (1992) are used to predict the thermomechanical fatigue (TMF) response of a Nickel base superalloy Rene´ 80 between 649°C and 1093°C. Predictions using these equations suggest that temperature history effects are significant during TMF, and that the TMF response of Rene´ 80 cannot be predicted completely using only isothermal parameters. It is postulated without metallurgical observations that the two deformation mechanisms in Rene´ 80, planar slip at low temperatures and dislocation climb at high temperatures, produce characteristic microstructures which interact under nonisothermal conditions to produce extra hardening that is not present during isothermal deformation. A state variable approach has been used to model this interaction. The nonisothermal model with temperature history effects could successfully predict the initial and saturated TMF response, and block isothermal response of Rene´ 80 from several tests between 649°C and 1093°C.

scholarly journals Characterization of Air-Based Photovoltaic Thermal Panels with Bifacial Solar Cells

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
P. Ooshaksaraei ◽  
K. Sopian ◽  
R. Zulkifli ◽  
Saleem H. Zaidi
Keyword(s):  
Power Generation ◽  
Total Energy ◽  
Electrical Power ◽  
Exergy Efficiency ◽  
Solar Panels ◽  
First Law Of Thermodynamics ◽  
Laws Of Thermodynamics ◽  
The Cost ◽  
Single Path

Photovoltaic (PV) panels account for a majority of the cost of photovoltaic thermal (PVT) panels. Bifacial silicon solar panels are attractive for PVT panels because of their potential to enhance electrical power generation from the same silicon wafer compared with conventional monofacial solar panels. This paper examines the performance of air-based bifacial PVT panels with regard to the first and second laws of thermodynamics. Four air-based bifacial PVT panels were designed. The maximum efficiencies of 45% to 63% were observed for the double-path-parallel bifacial PVT panel based on the first law of thermodynamics. Single-path bifacial PVT panel represents the highest exergy efficiency (10%). Double-path-parallel bifacial PVT panel is the second preferred design as it generates up to 20% additional total energy compared with the single-path panel. However, the daily average exergy efficiency of a double-path-parallel panel is 0.35% lower than that of a single-path panel.

Material Behavior Under Thermal Loading

1986 ◽  
Vol 108 (1) ◽  
pp. 113-119 ◽  
Author(s):  
Huseyin Sehitoglu
Keyword(s):  
Mechanical Loading ◽  
Constitutive Equations ◽  
Thermal Loading ◽  
Mechanical Deformation ◽  
Cyclic Stress ◽  
Material Behavior ◽  
Temperature History ◽  
Strain History ◽  
History Effects ◽  
Temperature Strain

Material behavior under thermo-mechanical and isothermal loading cases is studied. The influence of constraint on thermo-mechanical deformation behavior is identified using a two-bar structure. Some of the possible microstructural mechanisms that may be operative under thermo-mechanical loading conditions are discussed. Isothermal tests are reported in the temperature range 20 to 600°C. Additional isothermal tests with step increases and decreases in temperature are performed to study the influence of temperature history on material behavior. During these tests, transient material behavior indicated temperature-strain history effects. Constitutive equations that capture essential features of material behavior under isothermal and thermo-mechanical loading cases are examined. Preliminary predictions of cyclic stress-strain loops are compared to experimental response. Further work is needed to incorporate temperature-strain history effects into constitutive equations.

The edge conditions and field representation theorems in the theory of electromagnetic diffraction

1955 ◽  
Vol 51 (1) ◽  
pp. 149-161 ◽  
Author(s):  
A. E. Heins ◽  
S. Silver
Keyword(s):  
Boundary Value Problem ◽  
Total Energy ◽  
Boundary Value ◽  
Diffraction Theory ◽  
Sharp Edge ◽  
Representation Theorems ◽  
Field Representation ◽  
Simple Operation ◽  
Edge Conditions ◽  
Electromagnetic Diffraction

In 1897 Rayleigh(14) pointed out that it is possible to obtain a family of solutions to certain problems in diffraction theory, notably those involving plane obstacles, by the simple operation of differentiation of some one solution. This, of course, alters the nature of the solution, especially so in the neighbourhood of a sharp edge. For, at an edge the parent solution may be finite and yet its derivative can become infinite. Further, such a differentiated solution may produce an infinite total energy in the neighbourhood of the edge. It is, therefore, natural to ask what conditions are required to make the solutions of these problems physically and mathematically acceptable and thus define the boundary-value problem uniquely.

A variational property of the von Kármán plate problem

2020 ◽  
pp. 108128652095122
Author(s):  
Cesare Davini ◽  
Roberto Paroni
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Saddle Point ◽  
Total Energy ◽  
Energy Functional ◽  
Point Property ◽  
Von Karman ◽  
Complementary Part ◽  
Variational Property ◽  
Von Kármán

The solution of the boundary value problem of anisotropic Föppl–von Kármán plates is shown to be a critical point for a suitable energy functional. Moreover, under the assumption that the minimum of the total energy exists, we prove a saddle-point property and also deduce from it the form of the boundary conditions for plates clamped on part of the boundary and loaded on the complementary part.

Nonlinear Viscoelastic Constitutive Equations for Composites Based on Work Potentials

1994 ◽  
Vol 47 (6S) ◽  
pp. S269-S275 ◽  
Author(s):  
R. A. Schapery
Keyword(s):  
Constitutive Equations ◽  
Viscoelastic Behavior ◽  
Polymeric Materials ◽  
Time Dependent ◽  
Inelastic Behavior ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Effects ◽  
Residual Strains ◽  
Viscoelastic Composites ◽  
Independent Behavior

Constitutive equations for nonlinear viscoelastic composites are discussed. The effects of time-independent inelastic behavior, microcracking and time-dependent residual strains are considered along with the viscoelastic effects that are traditionally associated with the behavior of monolithic and reinforced polymeric materials. Time-independent behavior is discussed first, in which the experimentally observed insensitivity of mechanical work to deformation or load paths is used as the basis for a simplified constitutive model. This representation is then modified to account for time- or rate-effects due to microcrack-like evolution laws. Effects due to broad spectrum nonlinear, viscoelastic behavior of the polymer matrix are reviewed and then used in a generalized constitutive equation with both time-independent and time-dependent effects. Emphasis of this paper is on a thermodynamically-based phenomenological description of deformation response and the use of simplifications based on experimental observations. However, there is a limited discussion of physical mechanisms for nonlinear time-dependent behavior.

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