Renewal of basic laws and principles for polar continuum theories (VII) —Incremental rate type

2003 ◽  
Vol 24 (12) ◽  
pp. 1375-1380 ◽  
Author(s):  
Dai Tian-min
Keyword(s):  
Incremental Rate ◽  
Incremental Rate Type ◽  
Continuum Theories ◽  
Rate Type

A new rate-type gradient-dependent viscoplastic approach for stop-and-go strain band propagation. Numercial vs. physical experiments

1998 ◽  
Vol 08 (PR8) ◽  
pp. Pr8-143-Pr8-150 ◽  
Author(s):  
C. Faciu ◽  
A. Molinari ◽  
M. Dablij ◽  
A. Zeghloul
Keyword(s):  
Physical Experiments ◽  
Stop And Go ◽  
Rate Type

scholarly journals A thermodynamic approach to rate-type models in deformable ferroelectrics

2020 ◽  
Author(s):  
Claudio Giorgi ◽  
Angelo Morro
Keyword(s):  
Free Energy ◽  
Electric Field ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Energy Models ◽  
Polarization Electric Field ◽  
Field Plane ◽  
Vector Valued ◽  
Rate Type ◽  
Hysteretic Properties

AbstractThe purpose of the paper is to establish vector-valued rate-type models for the hysteretic properties in deformable ferroelectrics within the framework of continuum thermodynamics. Unlike electroelasticity and piezoelectricity, in ferroelectricity both the polarization and the electric field are simultaneously independent variables so that the constitutive functions depend on both. This viewpoint is naturally related to the fact that an hysteresis loop is a closed curve in the polarization–electric field plane. For the sake of generality, the deformation of the material and the dependence on the temperature are allowed to occur. The constitutive functions are required to be consistent with the principle of objectivity and the second law of thermodynamics. Objectivity implies that the constitutive equations are form invariant within the set of Euclidean frames. Among other results, the second law requires a general property on the relation between the polarization and the electric field via a differential equation. This equation shows a dependence fully characterized by two quantities: the free energy and a function which is related to the dissipative character of the hysteresis. As a consequence, different hysteresis models may have the same free energy. Models compatible with thermodynamics are then determined by appropriate selections of the free energy and of the dissipative part. Correspondingly, major and minor hysteretic loops are plotted.

scholarly journals SHEARING TESTS APPLIED TO PANTOGRAPHIC STRUCTURES

2016 ◽  
Vol 7 ◽  
pp. 1 ◽  
Author(s):  
Gregor Ganzosch ◽  
Francesco Dell’Isola ◽  
Emilio Turco ◽  
Tomasz Lekszycki ◽  
Wolfgang H. Müller
Keyword(s):  
Rapid Manufacturing ◽  
Pantographic Structures ◽  
Deformation Response ◽  
Shear Loads ◽  
Generalized Continuum ◽  
Complete Failure ◽  
Elastic Cylinders ◽  
Inextensible Fibers ◽  
Fabric Materials ◽  
Continuum Theories

With the advancements in 3D printing technology, rapid manufacturing of fabric materials with complex geometries became possible. By exploiting this technique, different materials with different structures have been developed in the recent past with the objective of making generalized continuum theories useful for technological applications. So-called pantographic structures are introduced: Inextensible fibers are printed in two arrays orthogonal to each other in parallel planes. These superimposed planes are inter-connected by elastic cylinders. Five differently-sized samples were subjected to shear-like loading while their deformation response was analyzed. Results show that deformation behavior is strong non-linear for all samples. Furthermore, all samples were capable to resist considerable external shear loads without leading to complete failure of the whole structure. This extraordinary behavior makes these structures attractive to serve as an extremely tough metamaterial.

Continuum theories of optical phonons and polaritons in superlattices: A brief critique

1991 ◽  
Vol 43 (11) ◽  
pp. 9096-9101 ◽  
Author(s):  
B. K. Ridley ◽  
M. Babiker
Keyword(s):  
Optical Phonons ◽  
Continuum Theories

The Atomistic and the Continuum Theories of Crystal Elasticity

1961 ◽  
Vol 463 (3-4) ◽  
pp. 121-136 ◽  
Author(s):  
R. S. Krishnan ◽  
E. S. Rajagopal
Keyword(s):  
Continuum Theories ◽  
The Continuum

scholarly journals Rigid-Plastic Finite Element Method Using Rate-Type Constitutive Equation

1989 ◽  
Vol 32 (1) ◽  
pp. 107-112
Author(s):  
Yoshihiro TOMITA ◽  
Akio SHINDO ◽  
Hirokazu GOTOH ◽  
Man-Seok CHU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Constitutive Equation ◽  
Rigid Plastic ◽  
Rate Type ◽  
Element Method

An instability in some rate-type viscoelastic constitutive equations

1967 ◽  
Vol 22 (8) ◽  
pp. 1079-1082 ◽  
Author(s):  
R.I. Tanner ◽  
J.M. Simmons
Keyword(s):  
Constitutive Equations ◽  
Rate Type
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