Effective Constitutive Relations Research Articles

A class of one-dimensional stiffness microstructures resulting in identical macroscale response

Multiresolution analysis is used to derive an effective constitutive relation pertaining to a one-dimensional microscale stiffness variation in a thin elastic plate. It is shown that it is possible to synthesize classes of different stiffness microstructures that have the same footprint on the macroscale component of the plate response. An effective, smooth, stiffness heterogeneity associated with the classes is derived.

Application of the homogenization method to a suspension of fibres

The homogenization method is applied to the determination of a continuum model for an assembly of cylindrical parallel fibres suspended in the longitudinal flow of a viscous incompressible fluid. Whatever the solids concentration is, the homogenization gives the variations of the velocity and the pressure at the level of the microstructure and furnishes a rigorous deductive procedure for obtaining the governing equations of the homogenized bulk medium. The effective constitutive relation is that of a Newtonian incompressible anisotropic fluid. The viscosity is expressed by a second order tensor completely determined by the microstructure. Lower bounds of the viscosity coefficients are found when the microstructure exhibits symmetries. Numerical results are obtained for two cases of macroscopic isotropy. They emphasize the good approximation arising from the lower bounds and the importance of the microstructure geometry for nondilute suspensions. As a matter of fact the solids concentration is not able to describe correctly the influence of the microstructure on the bulk behaviour of concentrated suspensions.

Effective constitutive behavior of nonlinear solids containing penny-shaped cracks

This article studies the effective constitutive relations of brittle and ductile solids containing either aligned or randomly oriented penny-shaped cracks. The matrix material considered is linear before yielding and behaves with a pure power-law after yielding. An explicit yield function is obtained for the cracked body under general external loading conditions, and the effective stress potential is given in a simple optimization procedure. The results show that the presence of microcracks inside solids significantly lowers the strength of materials.

Analysis of metal-matrix composite structures—I. Micromechanics constitutive theory

The nonlinear behavior of continuous-fiber-reinforced metal-matrix composite structures is examined using a micromechanical constitutive theory. Effective lamina constitutive relations based on the Aboudi micromechanics theory are presented. The inelastic matrix behavior is modeled by the unified viscoplasticity theory of Bodner and Partom. Debonding between fiber and matrix phases is also considered. In Part II of this paper, the laminate constitutive relations are incorporated into a first-order shear deformation plate theory. The resulting boundary value problem is solved by the finite element method.

Constitutive relations for the thermomechanical behavior of fiber-reinforced inelastic laminates

The thermomechanical behavior of laminated composites in which every lamina is unidirectional fiber-reinforced thermoinelastic material is determined by a micromechanical analysis followed by a macromechanical one. In the micromechanical analysis, effective constitutive relations are derived for unidirectional fibrous materials in which the matrix and fiber phases are thermoelastic in the linear region and thermoinelastic in the nonlinear region. The derivation is based solely on the material properties of fibers and matrix and amount of reinforcement. By a macromechanics analysis the gross behavior of the laminated composite in stretching and bending deformation is determined. Applications are given for the deformation field developed in cooling and reheating of graphite/aluminium laminated plates.

Effective constitutive relations for large repetitive frame-like structures

Effective mechanical properties for large repetitive frame-like structures are derived using straight forward combinations of strength of material orthogonal transformation techniques. Once the actual structure is identified symmetry considerations are used in order to identify its independent property constants. The actual values of these constants are constructed according to a building block format which is carried out in the three consecutive steps: (a)All bask planar lattices are identified(b)effective continuum properties are derived for each of these planar basic grids using matrix structural analysis methods and(c)orthogonal transformations are finally used to determine the contribution of each basic set to the overall effective continuum properties of the structure.