TY - JOUR

T1 - Extending uniaxial material laws to multiaxial constitutive relations

T2 - H-approach

AU - Shutov, A. V.

AU - Laktionov, P. P.

AU - Nekrasova, Y. S.

PY - 2020/5/1

Y1 - 2020/5/1

N2 - A simple method is presented, allowing us to extend any one-dimensional material model to a general material law suitable for arbitrary multiaxial loading conditions. The resulting system of constitutive equations respects the general principles of constitutive modelling, thus preserving thermodynamic consistency and objectivity. The method is based on a certain modification of the concept of representative directions. Since it operates with logarithmic Hencky strains we call it H-approach. In contrast to the conventional concept of representative directions, which we call now C-approach, the H-approach does not require artificial deviatorization of the stress tensor. Moreover, the H-approach allows one to model initially isotropic materials with a smaller number of representative directions, thus reducing the computational costs. The performance of the H-approach regarding the description of second-order effects under simple shear is tested. The flexibility of the H-approach in describing mechanical response of a real material is also demonstrated. Toward that end, a complex mechanical behaviour of certain electrospun polymer is rendered.

AB - A simple method is presented, allowing us to extend any one-dimensional material model to a general material law suitable for arbitrary multiaxial loading conditions. The resulting system of constitutive equations respects the general principles of constitutive modelling, thus preserving thermodynamic consistency and objectivity. The method is based on a certain modification of the concept of representative directions. Since it operates with logarithmic Hencky strains we call it H-approach. In contrast to the conventional concept of representative directions, which we call now C-approach, the H-approach does not require artificial deviatorization of the stress tensor. Moreover, the H-approach allows one to model initially isotropic materials with a smaller number of representative directions, thus reducing the computational costs. The performance of the H-approach regarding the description of second-order effects under simple shear is tested. The flexibility of the H-approach in describing mechanical response of a real material is also demonstrated. Toward that end, a complex mechanical behaviour of certain electrospun polymer is rendered.

KW - Concept of representative directions

KW - Constitutive modelling

KW - Electrospun polymer

KW - Finite strains

KW - Hencky strain

KW - ELASTICITY

KW - TENSORS

KW - SPHERE MODEL

KW - MICRO-MACRO APPROACH

KW - FIBER DISPERSION

KW - RUBBER-LIKE MATERIALS

UR - http://www.scopus.com/inward/record.url?scp=85077737743&partnerID=8YFLogxK

U2 - 10.1016/j.euromechsol.2019.103937

DO - 10.1016/j.euromechsol.2019.103937

M3 - Article

AN - SCOPUS:85077737743

VL - 81

JO - European Journal of Mechanics, A/Solids

JF - European Journal of Mechanics, A/Solids

SN - 0997-7538

M1 - 103937

ER -