Topic
Laplace–Carson transform
About: Laplace–Carson transform is a research topic. Over the lifetime, 12 publications have been published within this topic receiving 120 citations.
Papers
TL;DR: In this paper, the authors developed and tested numerical algorithms to invert LCT which are encountered in the context of homogenization of linear viscoelastic materials, as well as the stress concentration and strain localization tensors, are considered.
Abstract: Homogenization of linear viscoelastic materials is possible using the viscoelastic correspondence principle (VCP) and homogenization solutions obtained for linear elastic materials. The VCP involves a Laplace–Carson Transform (LCT) of the material phases constitutive theories and in most cases, the time domain solution must be obtained through numerical inversion of the LCT. The objective of this paper is to develop and test numerical algorithms to invert LCT which are encountered in the context of homogenization of linear viscoelastic materials. The homogenized properties, as well as the stress concentration and strain localization tensors, are considered. The algorithms suggested have the following two key features: (1) an acceptance criterion which allows to reject solutions of unacceptable accuracy and (2) some algorithms lead to solutions for the homogenized properties where the thermodynamics restrictions imposed on linear viscoelastic materials are encountered. These two features are an improvement over the previous algorithms. The algorithms are tested on many examples and the accuracy of the inversion is excellent in most cases.
80 citations
TL;DR: In this paper, the effective linear non-ageing viscoelastic properties of porous media based on a micromechanical approach is modeled as a mixture of a visco-elastic matrix and pore inclusions.
24 citations
TL;DR: In this article, the Fourier series analysis is used to find analytical solutions for the effective rheological viscoelastic properties of 2D periodic structures, which are derived first in the Laplace-Carson space for different inclusion shapes (rectangle or ellipse) and arrangements.
Abstract: This paper presents analytical solutions for the effective rheological viscoelastic properties of 2D periodic structures. The solutions, based on Fourier series analysis, are derived first in the Laplace-Carson (LC) space for different inclusion shapes (rectangle or ellipse) and arrangements. The effective results are obtained in the form of rational functions of the LC transform variable. Two inversion methods are used to find the relaxation behavior. The first one is based on the exact inverse of the LC transform while the second approximates the overall behavior by using a Standard Linear Solid model, which yields very simple analytical formulas for the coefficients entering the constitutive equations. Results of the two methods are compared in the case of an application to real materials.
18 citations
TL;DR: In this article, a method of nonlinear optimization based on the Laplace-Carson transform to determine the parameters of a model of the mechanical behavior of viscous materials is presented.
Abstract: A method of nonlinear optimization based on the Laplace–Carson transform to determine the parameters of a model of the mechanical behavior of viscous materials is presented. The introduction of time-dependent functional relationships between stresses and strains leads to an analysis of the Volterra integral equation of the second kind. In practice, this equation is successfully used in modeling a wide class of structural materials. One of optimum kernels of the operator in the governing equation for describing the deformation of materials with “memory” is the Rabotnov fractional-exponential function. The search for the optimum values of model parameters is reduced to the problem of minimization of a functional. The results of analytic modeling are compared with experimental data obtained in the creep and quasi-static loading of polymer composites containing various carbon modifications in the form of nanotubes. The essential distinctions in the behavior of the nanocomposites are compared. These distinctions are found to correlate with the results of structural investigations by the atomic-force microscopy, scanning electron microscopy, and micro- and nanoindentation.
7 citations
TL;DR: In this paper, the Laplace-Carson integral transform method and numerical inversion of the solutions are used to establish the relationship between hereditary kernels that define the scalar properties of isotropic linear viscoelastic materials in combined stress state.
Abstract: The Laplace–Carson integral transform method and numerical inversion of the solutions are used to establish the relationship between hereditary kernels that define the scalar properties of isotropic linear viscoelastic materials in combined stress state. The hereditary creep kernel characterizing the behavior of the viscoelastic Poisson’s ratio with time is identified. The calculation of shear creep strains and transverse creep under uniaxial loading with allowance for the time-dependent Poisson’s ratio are experimentally validated.
7 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2018 | 1 |
| 2017 | 2 |
| 2016 | 2 |
| 2015 | 1 |
| 2013 | 2 |