An elastic tensor is a mathematical representation of the relationship between stress and strain in a material. It is a fourth-rank tensor that describes the material's stiffness and how it deforms under applied forces.
Rotating an elastic tensor is often necessary to understand the material's properties in different orientations. This is particularly important in anisotropic materials, where properties vary with direction. Rotation allows one to predict how the material will behave under loads applied in different directions.
The 100 and 711 axes refer to specific crystallographic directions in a material. The 100 axis is a standard direction in cubic crystals, representing one of the primary axes. The 711 axis is a more complex direction, and rotating the tensor to this axis helps in understanding material behavior in non-standard orientations.
Mathematically, rotating an elastic tensor involves using a rotation matrix that aligns the original coordinate system with the new one. The rotated tensor is obtained by applying the rotation matrix to the original tensor using tensor transformation rules. This process involves matrix multiplication and can be complex, requiring careful application of tensor algebra.
Several tools and software can assist in rotating an elastic tensor, including MATLAB, Mathematica, and specialized crystallographic software like VESTA or MTEX. These tools provide functions and algorithms specifically designed to handle tensor operations and crystallographic transformations.