Unified Constitutive Modelling of Nonlinear Time-Dependent Materials

1989 ◽  
Vol 42 (11S) ◽  
pp. S78-S82
Author(s):  
P. G. Glockner ◽  
W. Szyszkowski
Keyword(s):  
Strain Softening ◽  
Strain Tensor ◽  
Damage Function ◽  
Constitutive Modelling ◽  
Constitutive Law ◽  
Time Dependent ◽  
Type Integral ◽  
Characteristic Features ◽  
Stress Dependent ◽  
Semi Empirical

A semi-empirical engineering constitutive law modelling in a unified and continuous manner the main characteristic features of time-dependent materials, including creep, strain softening, relaxation and recovery and tensile brittleness, is briefly reviewed. The model, which contains 13 parameters, is a hereditary single Volterra-type integral representation of material response with stress/strain nonlinearity assumed in the form of a power law, the strain tensor dependent on the entire stress history and the stress-anisotropy/brittleness feature handled by means of a tensile-stress dependent damage function. The capability/versatility of the model is illustrated by examples for several materials.

scholarly journals Modelling of Flexible Adhesives in Simple Mechanical States with the Use of the Darijani–Naghdabadi Strain Tensors and Kirchhoff–de Saint-Venant Elastic Potential

Polymers ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1639
Author(s):  
Paweł Szeptyński ◽  
Matija Gams ◽  
Arkadiusz Kwiecień
Keyword(s):  
Simple Shear ◽  
Strain Tensor ◽  
Limited Range ◽  
Constitutive Modelling ◽  
Elastic Potential ◽  
Experimental Results ◽  
Constitutive Law ◽  
Stress And Strain ◽  
Simple Tension ◽  
Non Linear

Practical aspects of modelling of flexible adhesives with the energy conjugate measures of stress and strain of the Darijani–Naghdabadi (D-N) family are discussed. A possibility of description of materials exhibiting non-linear physical characteristics with the use of non-linear geometric relationships and linear elastic constitutive law is considered. Nominal stress vs. stretch relations are specified in cases of simple tension and simple shear with the use of the Kirchhoff–de Saint-Venant elastic potential and D-N energy conjugate stress and strain measures. Obtained theoretical estimates were compared with experimental results of simple tension and simple shear tests performed on Sika PM polyurethane (Cracow, Sika Poland). The deformation rate was fixed in order to minimize the influence of viscosity. Values of parameters in the definition of the D-N strain tensor were optimized in order to provide good agreement between model predictions and experimental results. Observed discrepancies indicate that the proposed approach is not appropriate for constitutive modelling of the PM polymer. The presented approach is proposed to be used as a simple design model providing practical formulas describing the behavior of materials of non-linear characteristics in chosen mechanical states. Admissible values of exponents are discussed regarding its bijectivity in a limited range of variation of principal stretches.

The solution of an infinite set of differential-difference equations occurring in polymerization and queueing problems

1963 ◽  
Vol 59 (1) ◽  
pp. 117-124 ◽  
Author(s):  
A. Wragg
Keyword(s):  
Difference Equations ◽  
Queueing Theory ◽  
Bessel Functions ◽  
Formal Solution ◽  
Monomer Concentration ◽  
Arrival Rate ◽  
Time Dependent ◽  
Type Integral ◽  
Dependent Parameter ◽  
Infinite Set

AbstractThe time-dependent solutions of an infinite set of differential-difference equations arising from queueing theory and models of ‘living’ polymer are expressed in terms of modified Bessel functions. Explicit solutions are available for constant values of a parameter describing the arrival rate or monomer concentration; for time-dependent parameter a formal solution is obtained in terms of a function which satisfies a Volterra type integral equation of the second kind. These results are used as the basis of a numerical method of solving the infinite set of differential equations when the time-dependent parameter itself satisfies a differential equation.

Semi-Empirical Fitting of Partial Pair Correlation Functions of Amorphous Alloys

1995 ◽  
Vol 50 (12) ◽  
pp. 1205-1218
Author(s):  
E. Sváb ◽  
F. Hajdu ◽  
Gy. Mészáros
Keyword(s):  
Amorphous Alloys ◽  
Structural Parameters ◽  
Pair Correlation ◽  
Analytical Formula ◽  
Partial Structure ◽  
Fitting Procedure ◽  
Atomic Pair ◽  
Structure Factors ◽  
Characteristic Features ◽  
Semi Empirical

Abstract A semi-empirical fitting procedure has been developed and used in analysing the characteristic features of the partial structure factors of binary amorphous alloys. An analytical formula is given to fit the experimental atomic pair correlation function as a sum of Gaussians. The inverse Fourier transform of the fitted terms reproduces all features of the experimental structure function. In addition to the structural parameters, the modelling gives a quantitative explanation for the complex origin of characteristic features in the diffraction pattern such as pre-peak, pre-minimum, and split peaks in the partial structure factor.

scholarly journals A complete analytical solution of the Fokker–Planck and balance equations for nucleation and growth of crystals

2018 ◽  
Vol 376 (2113) ◽  
pp. 20170327 ◽  
Author(s):  
Eugenya V. Makoveeva ◽  
Dmitri V. Alexandrov
Keyword(s):  
Distribution Function ◽  
Analytical Description ◽  
Supercooled Liquid ◽  
Intermediate Stage ◽  
Nucleation And Growth ◽  
Time Dependent ◽  
Supersaturated Solution ◽  
Nucleation Kinetics ◽  
Type Integral ◽  
Laplace Type

This article is concerned with a new analytical description of nucleation and growth of crystals in a metastable mushy layer (supercooled liquid or supersaturated solution) at the intermediate stage of phase transition. The model under consideration consisting of the non-stationary integro-differential system of governing equations for the distribution function and metastability level is analytically solved by means of the saddle-point technique for the Laplace-type integral in the case of arbitrary nucleation kinetics and time-dependent heat or mass sources in the balance equation. We demonstrate that the time-dependent distribution function approaches the stationary profile in course of time. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

Models for the Directional Distribution of the Diffuse Sky Radiance

1990 ◽  
Vol 112 (2) ◽  
pp. 102-109 ◽  
Author(s):  
F. M. F. Siala ◽  
M. A. Rosen ◽  
F. C. Hooper
Keyword(s):  
Angular Distribution ◽  
Stochastic Models ◽  
Continuous Distribution ◽  
Time Dependent ◽  
Distribution Models ◽  
Directional Distribution ◽  
Sky Radiance ◽  
Semi Empirical ◽  
Sky Type

Both traditional and recently proposed models for the angular distribution of diffuse sky radiance are reviewed and compared. The models considered include basic models, sky-type-specific models, empirical and semi-empirical continuous distribution models, models which account for time-dependent cloud effects and stochastic models.

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