Riemann invariants-like solutions for a class of rate-type materials

1994 ◽  
Vol 105 (1-4) ◽  
pp. 23-32 ◽  
Author(s):  
D. Fusco ◽  
N. Manganaro
Keyword(s):  
Riemann Invariants ◽  
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

RIEMANN INVARIANTS INTERACTION IN MHD. DOUBLE WAVES

1979 ◽  
Vol 12 (3) ◽  
Author(s):  
Wojciech Zajczkowski
Keyword(s):  
Riemann Invariants

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 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

Calculations for Uniaxial Stress and Strain Cycling in Plasticity

1984 ◽  
Vol 51 (3) ◽  
pp. 487-493 ◽  
Author(s):  
P. M. Naghdi ◽  
D. J. Nikkel
Keyword(s):  
Type Theory ◽  
Uniaxial Stress ◽  
Mean Value ◽  
Stress And Strain ◽  
Material Response ◽  
Tension And Compression ◽  
Stress Cycling ◽  
The Mean ◽  
Rate Type ◽  
Strain Cycling

Within the framework of an existing purely mechanical, rate-type theory of plasticity, detailed calculations are presented for certain types of material response during stress and strain cycling in a uniaxial homogeneous deformation. These features pertain specifically to material response in stress cycling between fixed values of stress in tension and compression (not necessarily equal in magnitude) resulting in ratcheting of strain, and a type of saturation hardening caused by strain cycling between any two fixed values of strain when the mean value of stress (in tension and compression) tends to zero.

scholarly journals NONLINEAR SYSTEMS DESCRIBING PHASE TRANSITION MODELS COMPATIBLE WITH THERMODYNAMICS

1999 ◽  
Vol 09 (07) ◽  
pp. 1015-1037 ◽  
Author(s):  
PIERLUIGI COLLI ◽  
GIORGIO GENTILI ◽  
CLAUDIO GIORGI
Keyword(s):  
Phase Transition ◽  
Absolute Temperature ◽  
Constitutive Law ◽  
Phase Variable ◽  
Evolution System ◽  
Thermodynamic Compatibility ◽  
Uniqueness Of The Solution ◽  
Rigid Heat Conductor ◽  
Transition Models ◽  
Rate Type

This paper is devoted to analyzing solutions of a nonlinear evolution system describing the phase transition in a rigid heat conductor in the presence of phase relaxation. First, in a general framework, a rate type constitutive law for the phase variable is considered and matched with the Helmholtz free energy involving the state of the material. Thermodynamic compatibility of the resulting models is scrutinized. Moreover, a comparison with a different phase change modelling is performed. Under proper assumptions, a nonlinear system in the (absolute) temperature and phase variable is achieved. For it, existence and uniqueness of the solution is proved and positivity of temperature is recovered.

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