TY - JOUR

T1 - Efficient integration of evolution equations for a fiber-like Maxwell body

AU - Shutov, A. V.

AU - Tagiltsev, I. I.

PY - 2019/7/16

Y1 - 2019/7/16

N2 - Fiber-like Maxwell body is frequently used to model the mechanical behaviour of advanced composite materials, which appear in engineering and bio-mechanical applications. Here we consider a material model of the fiber-like Maxwell body based on the Sidoroff decomposition of the deformation gradient. In our case this decomposition yields a multiplicative split of the fiber stretch into inelastic and elastic parts. One of the advantages of the model is that various hyperelastic potentials can be employed for a greater accuracy. Three different potentials are analyzed in this paper: the classical Holzapfel potential and its modifications. The first modification accounts for a fiber slackness and the second one is intended for applications with a local fiber buckling. In terms of these three potentials, we analyze the performance of a universal iteration-free time-stepping scheme. Robustness and accuracy of this algorithm are tested. The iteration-free method is shown to compare favourably to the classical Euler-backward which includes the Newton iteration process.

AB - Fiber-like Maxwell body is frequently used to model the mechanical behaviour of advanced composite materials, which appear in engineering and bio-mechanical applications. Here we consider a material model of the fiber-like Maxwell body based on the Sidoroff decomposition of the deformation gradient. In our case this decomposition yields a multiplicative split of the fiber stretch into inelastic and elastic parts. One of the advantages of the model is that various hyperelastic potentials can be employed for a greater accuracy. Three different potentials are analyzed in this paper: the classical Holzapfel potential and its modifications. The first modification accounts for a fiber slackness and the second one is intended for applications with a local fiber buckling. In terms of these three potentials, we analyze the performance of a universal iteration-free time-stepping scheme. Robustness and accuracy of this algorithm are tested. The iteration-free method is shown to compare favourably to the classical Euler-backward which includes the Newton iteration process.

KW - FINITE STRAINS

UR - http://www.scopus.com/inward/record.url?scp=85073914742&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1268/1/012078

DO - 10.1088/1742-6596/1268/1/012078

M3 - Conference article

AN - SCOPUS:85073914742

VL - 1268

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012078

T2 - All-Russian Conference and School for Young Scientists, devoted to 100th Anniversary of Academician L.V. Ovsiannikov on Mathematical Problems of Continuum Mechanics, MPCM 2019

Y2 - 13 May 2019 through 17 May 2019

ER -