TY - JOUR

T1 - Simulating cylinder torsion using Hill’s linear isotropic hyperelastic material models

AU - Korobeynikov, S. N.

AU - Larichkin, A. Yu

AU - Rotanova, T. A.

N1 - The support from Russian Federation government (Grant No. P220-14.W03.31.0002) is gratefully acknowledged.

PY - 2023

Y1 - 2023

N2 - Hill’s linear isotropic hyperelastic material models based on the one-parameter (r) Itskov family of strain tensors (including the Hencky, Pelzer, and Mooney strain tensors generating the H, P, and M material models, respectively) were used to obtain exact solutions of the simple torsion problem for circular cross-section rods from the H, P, and M materials. The “exact” solutions available in the literature for the problem of generalized torsion of cylindrical rods with free edges in the axial direction were analyzed. The objectives of the present study are to develop and implement new formulations of these material models in the commercial MSC.Marc nonlinear FE software and to verify these formulations using the above-mentioned exact solutions. Computer simulations of the simple and generalized torsion of cylindrical specimens were carried out using three material models (H, P, and M) and the standard Mooney–Rivlin model. The results of computer simulations of the resultant moment and the resultant axial force (in the problem of simple torsion) or axial elongation (in the problem of generalized torsion) were compared with exact solutions. For the simple torsion problem, the solutions obtained by the two methods are similar, but for the problem of generalized torsion, these solutions are similar only for sufficiently small values of the torsion parameter. We explain the discrepancy for sufficiently large values of the torsion parameter by the fact that the so-called “exact” solutions cease to be exact because of the assumptions made by other authors in obtaining these solutions. We assume that for all values of the torsion parameter, our numerical solutions are close to the true exact solutions. Computer simulations showed that the Pelzer material model is similar in performance to the Mooney–Rivlin model.

AB - Hill’s linear isotropic hyperelastic material models based on the one-parameter (r) Itskov family of strain tensors (including the Hencky, Pelzer, and Mooney strain tensors generating the H, P, and M material models, respectively) were used to obtain exact solutions of the simple torsion problem for circular cross-section rods from the H, P, and M materials. The “exact” solutions available in the literature for the problem of generalized torsion of cylindrical rods with free edges in the axial direction were analyzed. The objectives of the present study are to develop and implement new formulations of these material models in the commercial MSC.Marc nonlinear FE software and to verify these formulations using the above-mentioned exact solutions. Computer simulations of the simple and generalized torsion of cylindrical specimens were carried out using three material models (H, P, and M) and the standard Mooney–Rivlin model. The results of computer simulations of the resultant moment and the resultant axial force (in the problem of simple torsion) or axial elongation (in the problem of generalized torsion) were compared with exact solutions. For the simple torsion problem, the solutions obtained by the two methods are similar, but for the problem of generalized torsion, these solutions are similar only for sufficiently small values of the torsion parameter. We explain the discrepancy for sufficiently large values of the torsion parameter by the fact that the so-called “exact” solutions cease to be exact because of the assumptions made by other authors in obtaining these solutions. We assume that for all values of the torsion parameter, our numerical solutions are close to the true exact solutions. Computer simulations showed that the Pelzer material model is similar in performance to the Mooney–Rivlin model.

KW - Computer simulations

KW - Hyperelastic material models

KW - Torsion of cylindrical rods

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85150158785&origin=inward&txGid=04cf0f4f5583e8f3031cfb04d1fe4bae

UR - https://www.mendeley.com/catalogue/cb279156-bb49-3d49-94c9-e02073593782/

U2 - 10.1007/s11043-023-09592-1

DO - 10.1007/s11043-023-09592-1

M3 - Article

JO - Mechanics of Time-Dependent Materials

JF - Mechanics of Time-Dependent Materials

SN - 1573-2738

ER -