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Description of the Analytical Solution Algorithm

Six types of deformations are applied to a representative volume, each of which corresponds to its own form of the effective deformation tensor Ee:

1. X-axis stretch/compression

2. Tension/compression along the Y axis

3. Tension/compression along the Z axis

4. Tension/compression along the XY axis

5. Tension/compression along the XZ axis

6. Tension/compression along the YZ axis

For each of the six boundary value problems, an effective deformation tensor was specified Ee - and the effective stress tensor σe is obtained.

The linear dependence of σe on q is presented as:

Since the magnitude of deformations q and the corresponding tensor σe are known - the tensor dependence coefficient aij is calculated according to the formula:

Since effective properties are assessed in the form of a generalized law Guka

taking into account the form of Ee in each problem, formulas for coefficients Cijkl are represented as:

1)

2)

3)

4)

5)

6)

From here the coefficients Cijkl are calculated from the corresponding aij:

1)

2)

3)

4)

5)

6)

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2. Christensen R. Introduction to the mechanics of composites. – M.: “Mir”, 1982. – 334 pp.

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