Some remarks on the compressed matrix representation of symmetric second-order and fourth-order tensors

摘要

The mathematical description of physical phenomena requires the use of scalars and tensors of various order. Since many of the second-order and fourth-order tensors used in continuum mechanics possess certain symmetries, a compressed vector or matrix representation, respectively, is frequently used in computational applications such as the FEM and BEM. Use of different storage schemes for different tensors lead to an hypothetical nonuniqueness of such matrix representations.