Isostress condition

The upper and lower bounds of the elastic moduli of the. composites, E, can be written in terms of a simple rule-of-mixtures given below (derived by imposing iso-strain and isostress conditions, respectively) ... 

The equivalent elastic modulus, Gip, for the mechanically interlocked interphase is calculated by assuming an isostress condition for the interphase, illustrated in Pig. 23.13. In other words, the adhesive and the adherend surface (projections) are subjected to the same level of shear stress, tjp, at the interphase, while the composite interfacial shear strain, yjp, is a volumetric weighted average of the adhesive and adherend strains, that is,... 

Loading perpendicular to fibers. When a load is applied to a composite material perpendicular to the direction of fibers, the load is supported by a series of resistances of the fibers and the matrix. Therefore the stress encountered in the matrix, fibers and the composite are equal. This particular condition is called isostress and is characterized by ... 

It is important to note that isostress and isostrain loading conditions represent theoretical limits for the design of a composite material reinforced by continuous fibers. In practice, most of the time, mechanical performances fall between these limits. On the other hand, in the isostrain loading situation, a lower volume fraction of fibers is required to obtain a similar stiffness of the composite. 

The modulus is, however, much lower in the direction transverse to the layered structure (Figure 8.2). In this case each layer is subjected to the same force, and hence to the same stress, because the area remains constant through the stack. Loading of this form is known as the isostress (or homogeneous stress) condition. 

For the series model Figure 10.66, an isostress strain condition exists. The strains are additive. 

Li and Chou [73, 74] have reported a multiscale modeling of the compressive behavior of carbon nanotube/polymer composites. The nanotube is modeled at the atomistic scale, and the matrix deformation is analyzed by the continuum finite element method. The nanotube and polymer matrix are assumed to be bonded by van der Waals interactions at the interface. The stress distributions at the nanotube/polymer interface under isostrain and isostress loading conditions have been examined. They have used beam elements for SWCNT using molecular structural mechanics, truss rod for vdW links and cubic elements for matrix. The rule of mixture was used as for comparison in this research. The buckling forces of nanotube/ polymer composites for different nanotube lengths and diameters are computed. The results indicate that continuous nanotubes can most effectively enhance the composite buckling resistance. 

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