TY - JOUR

T1 - Improved concept of representative directions: cluster approach

AU - Shutov, A. V.

AU - Vardosanidze, O. D.

N1 - The study was supported by the State task project FWGG-2021-0012 2.3.1.3.1. (development of visco-elasto-plastic model for the electrospun material) and by the Russian Science Foundation, project 23-19-00514 (cluster approach and the model for the steel alloy).

PY - 2024/9

Y1 - 2024/9

N2 - 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.

AB - 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.

KW - Cluster approach

KW - Concept of representative directions

KW - Constitutive modelling

KW - Finite strain

KW - Visco-elasto-plasticity

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85196645771&origin=inward&txGid=5f1aba3ee43a8c9b84daa7b2a83b2d08

UR - https://www.elibrary.ru/item.asp?id=67932184

UR - https://www.mendeley.com/catalogue/aade50b4-e6a9-391b-acb6-ba563b8577ee/

U2 - 10.1016/j.ijsolstr.2024.112934

DO - 10.1016/j.ijsolstr.2024.112934

M3 - Article

VL - 301

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

M1 - 112934

ER -