Engineering Transactions, 39, 2, pp. 241-253, 1991

### On Irreducible Number of Invariants and Generators in the Constitutive Relationships

S. Jemioło
Warsaw University of Technology, Warszawa
Poland

M. Kwieciński
Warsaw University of Technology, Warszawa
Poland

The Pipkin-Rivlin method for determining the generators of a polynomial representation of a symmetric isotropic second-order tensor-valued function is modified. Generators of an anisotropic and orthotropic symmetric second-order tensor-valued function are thus shown as dependent on a finite number of symmetric second-order tensors. The obtained results coincide with those arrived at by Boehler. Next, irreducible invariants of anisotropic scalar functions, depending on a single symmetric second-order tensor a.re found. Types of anisotropy are considered in which the material symmetry group is described by means of vectors and symmetric second-order tensors. The anisotropic scalar functions derived can be used to construct the constitutive equations for nonlinear elasticity of Green's material as well as potentials and yield conditions in plasticity. As an example, the equations are derived for a material reinforced with two orthogonal families of bars.

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