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Anisotropic Elasticity Matrix

The anisotropic elasticity matrix is a matrix of strain and stress. There are compliance matrix [S] and stiffness matrix [D].

The compliance matrix [S] is also called the flexibility matrix. The stiffness matrix [D] is also called the stress-strain matrix.

Strain and stress are explained in detail at Strain Type and Stress Type respectively.

• The direction of the anisotropic material is set on the Direction tab of the body attribute.

 

The stress and the strain in the compliance matrix [S] are as follows.

 

The stress and the strain in the stiffness matrix [D] are as follows.

 

The stiffness matrix [D] is the reciprocal of the compliance matrix [D].

Since the stiffness matrix [D] and the compliance matrix [S] are symmetric matrix, sij = sji and Dij=Dji (1<= i <=6, 1<= j <=6). You only need to enter the lower half of the matrix in the dialog box.

 

Now we take a look at the elasticity matrix for orthotropic elastic materials.

The compliance matrix is expressed as below with Young's modulus, Poisson's ratio, shear modulus.

 

	Young's modulus in the 3 orthogonal axes direction
	Poisson's ratio
	Shear modulus at face 1-2, face 2-3, and face 1-3

 

 

As the matrix is symmetric, the following equations hold.

 

 

Below is a compliance matrix [s] of the isotropic material

where E is Young's modulus and v is Poisson’s ratio.