For the quarter domain of an RVE in Figure 3.23, a uniform transverse normal stress \(\bar{\sigma}_{x}\) is applied on the plane \(x=D / 2\). Set up the equations describing the boundary conditions and the constraints on geometrically compatible displacements for a finite element micromechanics analysis of this model.

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Matrix Coating (interphase) Transverse loading FIGURE 3.23 Fiber ANAA Xx D/2 D/2 (D/2) D/2