Representative

volume element with random fibers, plaster matrix and a centered nanofiller layer.

Now we describe the finite

volume element discretization of the optimal control problem (6).

Meijer, "Prediction of the large-strain mechanical response of heterogeneous polymer systems: local and global deformation behaviour of a representative

volume element of voided polycarbonate," Journal of the Mechanics and Physics of Solids, vol.

The positional coordinates of the

volume elements after a rotation by angle [gamma] around the z-axis are

Jeulin, "Determination of the size of the representative

volume element for random composites: statistical and numerical approach," International Journal of Solids and Structures, vol.

Y., and Pan, J., "Mechanical behavior of representative

volume elements of lithium-ion battery modules under various loading conditions." Journal of Power Sources 248:789-808, 2014, doi:10.1016/j.jpowsour.2013.09.128.

In order to configure the graphical block diagram for

volume elements, one has to be aware, that the temperatures of the inlet and outlet mass flows are determined by the flow direction depending on the pressure gradient [p.sub.2]/[p.sub.1] (cp.

Let the nonconforming finite

volume element bilinear form [a.sub.h]: [V.sub.h] x [V.sup.*.sub.h] [right arrow] R be defined as:

Since the constitutive relation of the matrix and aggregates in (11) is linear, it is decomposed into two basic problems, one is that the representative

volume element of concrete is subjected by [E.sup.(1)] = 0 and [H.sup.eq(1)] = [H.sup.eq], respectively, the other is that the representative

volume element of concrete is subjected by [E.sup.(2)] = E and [H.sup.eq(2)] = 0, respectively

In order to investigate the flexural and combined loading response of a representative

volume element of the porous titanium implant for all the different combinations of porosity and pore diameters, twenty rectangular parallelepiped finite element models, with pore diameters as listed in Table 1, are modeled.

Vxi = volume of the i'th

volume element ([increment of x]1 x [increment of x]2 x [increment of x]3 x ...

Further, to preserve the conservative characteristics of the interface model (1), [10] developed an immersed finite

volume element (IFVE) method by combining the finite

volume element method [11-16] and the immersed finite element method.