Matrix deformation

A simple springs-in-series model represents the representative volume element loaded in the 2-direction as in Figure 3-11. There, the matrix is the soft link in the chain of stiffnesses. Thus, the spring stiffness for the matrix is quite low. We would expect, on this basis, that the matrix deformation dominates the deformation of the composite material. 

On a microscopic scale, the deformations are shown in Figure 3-15. Note that the matrix deforms more than the fiber in shear because the matrix has a lower shear modulus. The total shearing deformation is... 

The fibers continue to deform elastically, but the matrix deforms plastically... 

Dispersive forces due to the tortuous path of the fluid, matrix deformation, and diffusion are neglected. Taking the same steps as for the continuity equation, we get... 

Bradley W.L. and Cohen R.N. (1987). Matrix deformation and fracture in graphite-reinforced epoxies. In Toughened Composites, ASTM STP 937 (N.J. Johnston ed.), ASTM, Philadelphia, PA, pp. 389-410. 

Considering that the concentration of the reinforcement phase is small (0.8 vol% at the maximum) and that the NWs are randomly dispersed through the matrix one would expect the E values of the composites to be closer to the lower bound, as the matrix deformation dominates the overall response of the composite. In contrast, a near doubling of E with only 0.8% loading of SiC NWs is observed. There can be several possible reasons for this large increase as detailed below. 

The exact laws, based on continuum analysis of the fibers and the matrix, would be very complicated. The analysis would involve equilibrium of stresses around, and in, the fibers and compatibility of matrix deformation with the fiber strains. Furthermore, end and edge effects near the free surfaces of the composite material would introduce complications. However, a simplified model can be developed for the interior of the composite material based on the notion that the fibers and the matrix interact only by having to experience the same longitudinal strain. Otherwise, the phases behave as two uniaxially stressed materials. McLean5 introduced such a model for materials with elastic fibers and he notes that McDanels et al.6 developed the model for the case where both the fibrous phase and the matrix phase are creeping. In both cases, the longitudinal parameters are the same, namely... 

Compared with BD13, at low strain of 0.2, the matrix appearance is similar, but less particles are debonded from the matrix. At 0.4 true strain, the matrix deformation and microvoids formation are less important than BD13 as well. Large matrix deformation and large quantity of microvoids appear when the tme strain reaches 0.6. The microfilaments across the interface can still be seen for some small size particles. Even though the microvoid formation and growth are developed greatly, the horizontal... 

When the blends are subjected to tensile testing, a certain fraction of the overall strain is accommodated by conservative deformation of the material. In the PP matrix, deformation results from the combination of amorphous phase hyperelasticity and crystal plasticity, as discussed earlier (50). The PA6 phase is also capable of deforming plastically, but its flow stress in the plastic stage is much higher than that of PP. Consequently, in the PP/PA6 blends the isolated PA6 particles exhibit less... 

Supposing that the solid matrix has an elasto-plastic behavior, the theory of plasticity can then be used to describe the matrix deformation in oil reservoir. Equations of the solid deformation include the following three groups equilibrium equations, geometry equations and constitutive equations. 

The numerical solution method for the above fluid-solid coupling model is an iterative computation process. To reduce the computational complexity, the solid deformation and fluid flow are regarded as two coupled equation systems, solved by FEM. The equilibrium in solid matrix is solved using Eq.(6) with an added coupling item apS j and the pore pressure is treated as an equivalent initial stress term. The flow equation (5) is solved with an added term of volume strain, reflecting the effect of solid deformation on fluid flow. It can be treated as a source or converge. In each iterative loop, the solid matrix deformation is solved firstly. The stress and strain results are then taken as inputs for the flow calculation with modified hydraulic parameters. After flow model is solved, the pore pressure values are transferred into solid matrix deformation model and begins next iterative loop. In this way, the flow and deformation of oil reservoir can be simulated. 

Step 2 cracks form in the transverse yams and in the interply matrix (deformations between 0.12% and 0.2%). 

Li and Chou [73,74] have reported a multiscale modeling of the compressive behavior of CNT/polymer composites. The nanotube is modeled at the atomistic scale, and the matrix deformation is analyzed by the continuum FEM. The nanotube arrd polymer matrix are assttmed to be bonded by vdW interactions at the interface. The stress distributiorrs at the nanotube/polymer interface under isostrain and isostress loading conditiorrs have been examined. They have used beam elements for SWCNT using molectrlar structural mechanics, truss rod for vdW links and cubic elements for matrix. The rule of mixtrrre was used as for comparision 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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