On uniform fields in heterogeneous media

1990 ◽  
Vol 431 (1881) ◽  
pp. 89-110 ◽  
Keyword(s):  
Heterogeneous Media ◽  
Transversely Isotropic ◽  
Stress And Strain ◽  
Influence Functions ◽  
Uniform Field ◽  
Fibrous Media ◽  
Two Phase ◽  
Strain Fields ◽  
Transverse Geometry ◽  
Concentration Factors

Uniform elastic strain fields are found in two-phase fibrous media of arbitrary transverse geometry, and in two-phase media of any phase geometry. In initially stress-free fibrous solids, a single uniform field can be created by certain proportionally changing tractions derived from a uniform overall stress. In the presence of phase eigenstrains, many overall stress states can be superimposed to create uniform strain fields in fibrous media. The existence of such fields is exploited to establish a number of exact results for two-phase fibre systems. These include universal connections between phase and overall moduli, and between components of phase stress and strain fields; expressions for new transformation influence functions and concentration factors in terms of their mechanical counterparts; and also expressions for the overall stresses and strains caused by phase eigenstrains. Examples are presented for macroscopically monoclinic fibrous composites with transversely isotropic phases. In two-phase media of arbitrary phase geometry there is only a single uniform stress and strain field for each non-vanishing eigenstrain state. The existence of this field is utilized in derivation of exact connections between transformation and mechanical influence functions and concentration factors.

On transformation strains and uniform fields in multiphase elastic media

1992 ◽  
Vol 437 (1900) ◽  
pp. 291-310 ◽  
Keyword(s):  
Concentration Factor ◽  
Elastic Stiffness ◽  
Local Fields ◽  
Influence Functions ◽  
Elastic Solids ◽  
Two Phase ◽  
General Properties ◽  
Multiphase Systems ◽  
Concentration Factors ◽  
Mechanical Influence

The effect of local eigenstrain and eigenstress fields, or transformation fields, on the local strains and stresses is explored in multiphase elastic solids of arbitrary geometry and material symmetry. The residual local fields caused by such transformation fields are sought in terms of certain transformation influence functions and transformation concentration factor tensors. General properties of these functions and concentration factors, and their relation to the analogous mechanical influence functions and concentration factors, are established, in part, with the help of uniform strain fields in multiphase media. Specific estimates of the transformation concentration factor tensors are evaluated by the self-consistent and Mori-Tanaka methods. It is found here that although the two methods use different constraint tensors in solutions of the respective dilute problems, their estimates of the mechanical, thermal, and transformation concentration factor tensors, and of the overall stiffness of multiphase media have a similar structure. Proofs that guarantee that these methods comply with the general properties of the transformation influence functions, and provide diagonally symmetric estimates of the overall elastic stiffness, are given for two-phase and multiphase systems consisting of, or reinforced by, inclusions of similar shape and alignment. One of the possible applications of the results, in analysis of overall instantaneous properties and local fields in inelastic composite materials, is described in the following paper.

Thermal Expansion of Three-Phase Composite Materials

1989 ◽  
Vol 56 (2) ◽  
pp. 418-422 ◽  
Author(s):  
George J. Dvorak ◽  
Tungyang Chen
Keyword(s):  
Thermal Expansion ◽  
Heterogeneous Media ◽  
Transversely Isotropic ◽  
Local Fields ◽  
Stress Fields ◽  
Cylindrical Shape ◽  
Thermal Expansion Coefficients ◽  
Decomposition Procedure ◽  
Transverse Geometry ◽  
Expansion Coefficients

Exact expressions are found for overall thermal expansion coefficients of a composite medium consisting of three perfectly-bonded transversely isotropic phases of cylindrical shape and arbitrary transverse geometry. The results show that macroscopic thermal expansion coefficients depend only on the thermoelastic constants and volume fractions of the phases, and on the overall compliance. The derivation is based on a decomposition procedure which indicates that spatially uniform elastic strain fields can be created in certain heterogeneous media by superposition of uniform phase thermal strains with local strains caused by piecewise uniform stress fields, which are in equilibrium with prescribed surface tractions. The procedure also allows evaluation of thermal stress fields in the aggregate in terms of known local fields caused by axisymmetric overall stresses. Finally, averages of local fields are found with the help of known mechanical stress and strain concentration factors.

scholarly journals Multipoint Approximation of Statistical Descriptors of Local Strain and Stress Fields in Heterogeneous Media Using Integral Equation Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Mikhail Tashkinov
Keyword(s):  
Correlation Functions ◽  
Heterogeneous Media ◽  
Boundary Value ◽  
Local Strain ◽  
Statistical Characteristics ◽  
Stress And Strain ◽  
Strain Fields ◽  
Representative Volume ◽  
Multipoint Approximation ◽  
Analytical Expressions

This paper is devoted to derivation of analytic expressions for statistical descriptors of stress and strain fields in heterogeneous media. Multipoint approximations of solutions of stochastic elastic boundary value problems for representative volume elements are investigated. The stress and strain fields are represented in the form of random coordinate functions, for which analytical expressions for the first- and second-order statistical central moments are obtained. Such moments characterize distribution of fields under prescribed loading of a representative volume element and depend on the geometry features and location of components within a volume. The information of the internal geometrical structure is taken into account by means of multipoint correlation functions. Within the framework of the second approximation of the boundary value problem, the correlation functions up to the fifth order are required to calculate the statistical characteristics. Using the method of Green’s functions, analytical expressions for the moments in distinct phases of the microstructure are obtained explicitly in a form of integral equations. Their analysis and comparison with previously obtained results are performed.

The Stress and Strain Concentrations in Curved Beams of Finite Thickness with End Moments

2010 ◽  
Vol 163-167 ◽  
pp. 2953-2963
Author(s):  
Ling Ling Zhang ◽  
Zheng Yang ◽  
Jian Hou ◽  
Zhi Qian Wang
Keyword(s):  
Finite Thickness ◽  
Radius Of Curvature ◽  
Stress And Strain ◽  
Curved Beams ◽  
Element Analysis ◽  
Strain Fields ◽  
Strain Concentration ◽  
Maximum Value ◽  
Concentration Factors ◽  
Different Thickness

In this paper, the elastic stress and strain fields in curved beams of finite thickness with end moments are systematically investigated using 3D finite element analysis. For a curved beam of finite thickness, the through-thickness distributions of the stress and strain concentration factors are not uniform and their distributions are different. The radius of curvature and the thickness of the beam have significant effect on the stress and stain concentrations. The relations of the maximum value and the value at the corner root of surface of the stress and strain concentration factors with different thickness for various radius of curvature are respectively obtained.

Mathematical Model of the Effective Properties of a Fiber Reinforced Composite with a Linearly Graded Transition Zone

2010 ◽  
Vol 38 (4) ◽  
pp. 286-307
Author(s):  
Carey F. Childers
Keyword(s):  
Mathematical Model ◽  
Transition Zone ◽  
Effective Properties ◽  
Local Stress ◽  
Stress And Strain ◽  
Fiber Reinforced ◽  
Strain Fields ◽  
Shear Moduli ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite

Abstract Tires are fabricated using single ply fiber reinforced composite materials, which consist of a set of aligned stiff fibers of steel material embedded in a softer matrix of rubber material. The main goal is to develop a mathematical model to determine the local stress and strain fields for this isotropic fiber and matrix separated by a linearly graded transition zone. This model will then yield expressions for the internal stress and strain fields surrounding a single fiber. The fields will be obtained when radial, axial, and shear loads are applied. The composite is then homogenized to determine its effective mechanical properties—elastic moduli, Poisson ratios, and shear moduli. The model allows for analysis of how composites interact in order to design composites which gain full advantage of their properties.

The stress and strain fields in the neighbourhood of a notch in polyethylene

Polymer ◽  
1989 ◽  
Vol 30 (8) ◽  
pp. 1456-1461 ◽  
Author(s):  
Xue-qin Wang ◽  
Norman Brown
Keyword(s):  
Stress And Strain ◽  
Strain Fields
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