Improved concept of representative directions: cluster approach

The concept of representative directions is a method for constitutive modelling that generalises uniaxial constitutive equations to the general multiaxial case. The simplicity of the concept allows both novice and experienced users to develop advanced material models, covering a wide range of nonlinear phenomena. This paper introduces the cluster approach, a new version of the concept that operates with clusters of fibres. Similar to the original concept, the cluster approach ensures objectivity and inherits the thermodynamic consistency of uniaxial models. The paper details the computational algorithms and presents numerical tests, highlighting the advantages of the new approach. Due to the smearing of fibres in orientation space, the cluster approach efficiently represents initially isotropic material behaviour with fewer clusters, making it computationally more efficient than the classical concept of representative directions. As a demonstration, the paper shows the adequacy of the cluster approach in capturing the actual inelastic behaviour of certain polymers and metals. •A novel extension of a classical robust modelling approach is proposed, enabling the development of advanced material models.•Geometrical and physical nonlinearities are addressed in a straightforward and effective way.•As a key feature, the new approach utilises clusters of distributed fibres to extend uniaxial material laws to multiaxial constitutive relations.•The new approach is advantageous over the classical concept in terms of fexibility and computational costs.•Practical utility is demonstrated through the characterisation of the inelastic behaviour of two real materials.