Self-consistent estimates for the viscoelastic creep compliances of composite materials

1978 ◽  
Vol 359 (1697) ◽  
pp. 251-273 ◽  
Keyword(s):  
Composite Materials ◽  
Numerical Solutions ◽  
The Self ◽  
Inclusion Problem ◽  
Inclusion Problems ◽  
Viscoelastic Creep ◽  
Self Consistent ◽  
Title Problem ◽  
Consistent Method ◽  
Selection Of

In this paper the viscoelastic creep compliances of various composites are estimated by the self-consistent method. The phases may be arbitrarily anisotropic and in any concentrations but we demand that one of the phases be a matrix and the remaining phases consist of ellipsoidal inclusions. The theory is succinctly formulated with the help of Stieltjes convolutions. In order to solve the title problem, we first solve the misfitting viscoelastic inclusion problem. Numerical solutions are given for a selection of inclusion problems and for two common composite materials, namely an isotropic dispersion of spheres, and a uni-directional fibre reinforced material.

scholarly journals Numerical Boundary Conditions for Solar Magnetic Hydrodynamic Flows Using the Method of Characteristics

1996 ◽  
Vol 154 ◽  
pp. 149-153
Author(s):  
S. T. Wu ◽  
A. H. Wang ◽  
W. P. Guo
Keyword(s):  
Boundary Conditions ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
The Self ◽  
Time Dependent ◽  
Solar Plasma ◽  
The Method Of Characteristics ◽  
Mhd Simulations ◽  
Self Consistent ◽  
Dynamic Structures

AbstractWe discuss the self-consistent time-dependent numerical boundary conditions on the basis of theory of characteristics for magnetohydrodynamics (MHD) simulations of solar plasma flows. The importance of using self-consistent boundary conditions is demonstrated by using an example of modeling coronal dynamic structures. This example demonstrates that the self-consistent boundary conditions assure the correctness of the numerical solutions. Otherwise, erroneous numerical solutions will appear.

Algebraic Multigrid Preconditioning for Finite Element Solution of Inhomogeneous Elastic Inclusion Problems in Articular Cartilage

2011 ◽  
Vol 3 (6) ◽  
pp. 729-744
Author(s):  
Zhengzheng Hu ◽  
Mansoor A Haider
Keyword(s):  
Finite Element ◽  
Articular Cartilage ◽  
Analytical Solution ◽  
Conjugate Gradient ◽  
Numerical Solutions ◽  
Elastic Inclusion ◽  
Algebraic Multigrid ◽  
Inclusion Problem ◽  
Inclusion Problems ◽  
Cpu Time

AbstractIn studying biomechanical deformation in articular cartilage, the presence of cells (chondrocytes) necessitates the consideration of inhomogeneous elasticity problems in which cells are idealized as soft inclusions within a stiff extracellular matrix. An analytical solution of a soft inclusion problem is derived and used to evaluate iterative numerical solutions of the associated linear algebraic system based on discretization via the finite element method, and use of an iterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG). Accuracy and efficiency of the AMG-PCG algorithm is compared to two other conjugate gradient algorithms with diagonal preconditioning (DS-PCG) or a modified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution. While all three algorithms are shown to be accurate, the AMG-PCG algorithm is demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased. In contrast to the other two algorithms, the AMG-PCG algorithm also exhibits little sensitivity of CPU time and number of iterations to variations in material properties that are known to significantly affect model variables. Results demonstrate the benefits of algebraic multigrid preconditioners for the iterative solution of assembled linear systems based on finite element modeling of soft elastic inclusion problems and may be particularly advantageous for large scale problems with many nodal unknowns.

scholarly journals Sinc-Self-consistent method to solve a class of nonlinear eigenvalue differential equation

2021 ◽  
Author(s):  
Seyed Mohammad Ali Aleomraninejad ◽  
Mehdi Solaimani
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Subsequent Development ◽  
The Self ◽  
Infinite Domain ◽  
Numerical Examples ◽  
Smallest Eigenvalue ◽  
Sinc Methods ◽  
Self Consistent ◽  
Consistent Method

In this paper, we combine the sinc and self-consistent methods to solve a class of non-linear eigenvalue differential equations. Some properties of the self-consistent and sinc methods required for our subsequent development are given and employed. Numerical examples are included to demonstrate the validity and applicability of the introduced technique and a comparison is made with the existing results. The method is easy to implement and yields accurate results. We show that the sinc-self-consistent method can solve the equations on an infinite domain and produces the smallest eigenvalue with the most accuracy

Analysis of Mixed Mode Cracks in Two-Dimensional Magnetoelectroelastic Media

2006 ◽  
Vol 324-325 ◽  
pp. 403-406 ◽  
Author(s):  
Han Wang ◽  
Xian Hui Ke ◽  
Ming Hao Zhao
Keyword(s):  
Strain Energy Density ◽  
Mixed Mode ◽  
Strain Energy ◽  
The Self ◽  
Two Dimensional ◽  
Elliptical Cavity ◽  
Self Consistent ◽  
The Matrix ◽  
Consistent Method ◽  
Magnetoelectroelastic Medium

Based on the analytical solution for an elliptical cavity and the self-consistent method, the exact solutions for a crack in a two-dimensional magnetoelectroelastic medium is derived. The strain energy density factors are calculated for mixed mode cracks in a composite made of BaTiO3 as the inclusion and CoFe2O4 as the matrix.

Sign in / Sign up

Export Citation Format

Share Document