## Are the principal stresses the eigenvalues?

For the stress (strain) tensor, the eigenvalues represent principal stresses (strains), and eigenvectors represent principal axes (i.e., faces with zero shear stress (strain)).

**What is surface traction?**

The external surface forces tangent to the surface are called surface tractions; the force in the other direction is called the normal force or normal traction. The boundary forces are most easily modeled using the stresses, simply because stress is force per area.

**How many stress invariants are there?**

Therefore, the variables of an isotropic yield function can be either the three independent principal invariants of the stress tensor I1, I2, and I3 or the three principal stresses.

### What is the Mori-Tanaka (Mt) method?

The Mori–Tanaka (MT) method ( Benveniste, 1987; Qu and Cherkaoui, 2006; Mori and Tanaka, 1973) is an effective field theory based on Eshelby’s elasticity method for inhomogeneity in an infinite medium. The MT method calculates the average internal stress in the matrix of a material containing inclusions with transformation of the strain.

**What is the Mori-Tanaka Method for elastic moduli?**

The micromechanics-based Mori–Tanaka method ( Mori & Tanaka, 1973) was used to predict the effective elastic moduli C of composite with randomly distributed straight fibers. The orientation distribution of the fibers in a composite is characterized by a probability density function (PDF) p ( α, β) given by:

**What are the constitutive equations of the Mori–Tanaka model?**

In the Mori–Tanaka model, the constitutive equations of a fiber reinforced composite is expressed in terms of the average strain and stress by (82)〈σ〉 = C〈ϵ〉. The effective average elastic moduli C is given by ( Benveniste, 1987)

#### What is the difference between the Mori-Tanaka and interpolative formulations?

The Mori-Tanaka and inversed Mori-Tanaka formulations give the upper and lower bounds of the composite stiffness for low and high volume fractions. The balanced formulation is the interpolative formulation, which can be written as