Abstract
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.
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