Coordinate Systems and Material Orientation
The material orientation is defined in COMSOL Multiphysics by means of a local coordinate system. The local coordinate system is the coordinate system that corresponds to the physical property axes of the material, that is, the orthogonal coordinate system in which the material properties are defined (see section 4.3 of Ref. 2). For materials with orthogonal crystallographic axes, the physical property axes correspond to the crystallographic axes. For other crystals a definition of the orientation of these axes should be provided with the material properties — often the standard described in Ref. 2 is used. In COMSOL Multiphysics, the equations of solid mechanics are usually solved in the local coordinate system, whilst the electric currents equations are solved in the global system. Appropriate coordinate transforms of the relevant physical quantities have been implemented in the Piezoresistivity interfaces.
Reduced subscript matrices and vectors do not obey the usual tensor transformation rules for coordinate transforms. The COMSOL Multiphysics software uses the quadratic transformation laws to transform these quantities between coordinate systems where this is necessary. See Ref. 1 for further details.
The local coordinate system for a material is set within the Linear Elastic Material, Piezoresistive Material, or Conductive Material features (or their equivalents). These features default to using the global system, but alternative systems can be defined by adding one of the coordinate system nodes to the Definitions node level of the Model Builder. Often the Rotated System feature is used to specify the new coordinate system in terms of Euler angles.
Converting from Miller indices and wafer flat orientations to the appropriate Euler angles is not straightforward and a carefully drawn diagram is recommended.
Coordinate Systems in the COMSOL Multiphysics Reference Manual