Isostrain condition composites

Stress Shielding. Beyond the traditional biocompatibility issues, hard tissue biomaterials must also be designed to minimize a phenomenon known as stress shielding. Due to the response of bone remodeling to the loading environment, as described by Wolffs law, it is important to maintain the stress levels in bone as close to the preimplant state as possible. When an implant is in parallel with bone, such as in a bone plate or a hip stem, the engineered material takes a portion of the load— which then reduces the load, and as a result, the stress, in the remaining bone. When the implant and bone are sufficiently well bonded, it can be assumed that the materials deform to the same extent and therefore experience the same strain. In this isostrain condition, the stress in one of the components of a two-phase composite can be calculated from the equation ... 

Prediction of the modulus of a short-fiber composite needs to take into account end effects since isostrain conditions are not satisfied at the fiber ends. Stress builds up along each fiber from zero at its end to a maximum at its center. As shown in Figure 1.4, at the interface, the matrix is severely sheared at the fiber... 

The mechanical properties (modulus, tensile strength and strain at break) as well as the electrical conductivity of the various monofilaments are shown in Figure V.1. The data clearly indicate that the tenacity and modulus systematically increase with increasing PPTA content. In fact, a simple, nearly linear, relation was observed between the mechanical properties and the fiber composition. This behavior is in accord with that generally found for composites loaded under isostrain conditions [71]. The enhancement of the mechanical properties with increased PPTA (not unexpectedly) came at the expense of the electrical conductivity of the polyblend fibers. 

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 maximum stiffness is obtained when a uniaxial stress is applied parallel with the layers, as indicated in Figure 8.1. ft is assumed that the strain is the same in all the composite layers, a form of loading known as the isostrain (or homogeneous strain) condition. 

Let us now consider the elastic behavior of a continuous and oriented fibrous composite that is loaded in the direction of fiber ahgnment. First, it is assumed that the fiber-matrix interfacial bond is very good, such that deformation of both matrix and fibers is the same (an isostrain situation). Under these conditions, the total load sustained by the composite is equal to the sum of the loads carried by the matrix phase and the fiber phase Ff, or... 

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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