A Self-Consistent Analysis of the Stiffening Effect of Rigid Inclusions on a Power-Law Material

1984 ◽  
Vol 106 (4) ◽  
pp. 317-321 ◽  
Author(s):  
J. M. Duva
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Constitutive Relation ◽  
Power Law ◽  
Nonlinear Boundary ◽  
Viscous Material ◽  
Spherical Inclusions ◽  
Self Consistent ◽  
Infinite Power ◽  
Stiffening Effect

An approximate constitutive relation is derived for a power-law viscous material stiffened by rigid spherical inclusions using a differential self-consistent analysis. This approach consists of two parts: the formulation of a self-consistent differential equation, and the solution of an associated kernel problem, a nonlinear boundary value problem for an isolated inclusion in an infinite power-law viscous matrix.

The Stiffening Effect of Rigid Elliptical Inclusions on a Power-Law Material

1989 ◽  
Vol 111 (4) ◽  
pp. 368-371 ◽  
Author(s):  
J. M. Duva ◽  
Dirck Storm
Keyword(s):  
Plane Strain ◽  
Constitutive Relation ◽  
Power Law ◽  
Cross Sections ◽  
Particle Shape ◽  
Elliptical Cross ◽  
Plane Strain Deformation ◽  
Self Consistent ◽  
Single Inclusion ◽  
Stiffening Effect

An approximate constitutive relation is derived for plane strain deformation in a power-law viscous matrix reinforced with long rigid inclusions with elliptical cross sections. The analysis is based on the differential self-consistent scheme and numerical calculations estimating the influence of a single inclusion on the material surrounding it. In particular, the effects of particle shape and material nonlinearity are reported.

scholarly journals On a nonlinear boundary value problem involving a small parameter

1962 ◽  
Vol 2 (4) ◽  
pp. 425-439 ◽  
Author(s):  
A. Erdéyi
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Small Parameter ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Ordinary Differential Equation ◽  
Nonlinear Boundary Value Problem ◽  
Image Position

In this paper we shall discuss the boundary value problem consisting of the nonlinear ordinary differential equation of the second order, and the boundary conditions.

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