On the Smallest Number of Functions Representing Isotropic Functions of Scalars, Vectors and Tensors

Summary In this article, we prove that for isotropic functions depend on $P$ vectors, $N$ symmetric tensors and $M$ non-symmetric (a) the minimal number of irreducible invariants a scalar-valued function is $3P+9M+6N-3,$ (b) vectors vector-valued $3$ (c) tensor-valued at most $9$. The numbers given in (a), are, general, much lower than obtained literature. This significant reduction has potential to substantially reduce modelling complexity.