On the Symmetry and Stability of Thermoelastic Solids

1978 ◽  
Vol 45 (4) ◽  
pp. 740-744 ◽  
Author(s):  
J. L. Ericksen
Keyword(s):  
Phase Transitions ◽  
Continuum Theory ◽  
Nonlinear Continuum Theory ◽  
Nonlinear Continuum ◽  
Local Nature

For the most part, nonlinear continuum theory has been based on the premise that the symmetry of a material never really changes. To analyze common phase transitions, we need to revise such theory of symmetry, but this is easier said than done. What seems to be needed is a theory of symmetry which is, in some sense, more local. Classical linear theories have a local nature, dealing only with the neighborhood of some state, so it seems worthwhile to rethink what is involved in symmetry considerations for them. Here, and not only here, symmetry is strongly linked to stability. Our purpose is to elaborate these matters.

Static and Dynamic Analysis of Carbon Nanotube-Based Switches

2004 ◽  
Vol 126 (3) ◽  
pp. 230-237 ◽  
Author(s):  
Marc Dequesnes ◽  
Zhi Tang ◽  
N. R. Aluru
Keyword(s):  
Molecular Dynamics ◽  
Carbon Nanotube ◽  
Ground Plane ◽  
Continuum Theory ◽  
Continuum Approach ◽  
Nonlinear Beam ◽  
Static And Dynamic Analysis ◽  
Nonlinear Continuum Theory ◽  
Nonlinear Continuum ◽  
Beam Theories

In this paper, we report on molecular dynamics (MD), continuum (based on linear and nonlinear beam theories) and combined molecular dynamics/continuum simulation of carbon nanotube based nanoelectromechanical switches. As a prototype device, we study the pull-in voltage characteristics of a nanoelectromechanical switch made of a suspended single wall nanotube over a ground plane. The various simulations (MD, continuum and combined MD/continuum) have been performed accounting for the electrostatic and van der Waals forces between the nanotube and the ground plane. The results from the nonlinear continuum theory compared well with the results from MD, except, for cases, where nanotube buckling was observed. When buckling occurs, the electromechanical behavior of the switch is simulated by employing a combined MD/continuum approach. The combined MD/continuum approach is computationally more efficient compared to the MD simulation of the entire device. Static and dynamic pull-in, pull-in time and fundamental frequency analysis is presented for fixed-fixed and cantilever carbon nanotube switches.

scholarly journals An Alternative Material Model Using a Generalized J2 Finite-Strain Flow Plasticity Theory with Isotropic Hardening

2018 ◽  
Vol 23 (2) ◽  
pp. 339-353 ◽  
Author(s):  
L. Écsi ◽  
P. Élesztős
Keyword(s):  
Finite Strain ◽  
Biaxial Tension ◽  
Time Derivative ◽  
Continuum Theory ◽  
Material Model ◽  
Plasticity Theory ◽  
Isotropic Hardening ◽  
Return Mapping ◽  
Alternative Material ◽  
Nonlinear Continuum

Abstract In this paper an alternative material model using a generalized J2 finite-strain flow plasticity theory with isotropic hardening is presented. The model is based on a new nonlinear continuum mechanical theory of finite deformations of elasto-plastic media which allows for the development of objective and thermodynamically consistent material models. As a result, the constitutive equation, the evolution equation and even the ‘normality rule’, characterising the plastic flow in the material during return mapping, can be expressed in various forms, using several instances of the yield surface and corresponding pairs of stress measures and strain rates, respectively, which are conjugate with respect to the internal mechanical power and its arbitrary higher order time derivative. Therefore the results of the material model when used in numerical analyses are not affected by the description and particularities of the material model formulation. Here, we briefly outline the nonlinear continuum theory along with a detailed description of the material model and finally present the model in a numerical example using a cross-shaped specimen in biaxial tension.

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