TY - JOUR

T1 - Simulation of fiber-reinforced viscoelastic structures subjected to finite strains: multiplicative approach

AU - Tagiltsev, I. I.

AU - Laktionov, P. P.

AU - Shutov, A. V.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - The study is devoted to the geometrically nonlinear simulation of fiber-reinforced composite structures. The applicability of the multiplicative approach to the simulation of viscoelastic properties of a composite material is assessed, certain improvements are suggested. For a greater accuracy in applications involving local compressive fiber buckling, a new family of hyperelastic potentials is introduced. This family allows us to account for the variable critical compressive stress, which depends on the fiber-matrix interaction. For the simulation of viscoelasticity, the well-established Sidoroff decomposition of the deformation gradient is implemented. To account for the viscosity of the matrix material, the model of Simo and Miehe (Comput Methods Appl Mech Eng 98:41–104, 1992) is used; highly efficient iteration-free algorithms are implemented. The viscosity of the fiber is likewise described by the multiplicative decomposition of the deformation gradient, leading to a scalar differential equation; an efficient iteration-free algorithm is proposed for the implicit time stepping. The accuracy and convergence of the new iteration-free method is tested and compared to that of the standard scheme implementing the Newton iteration. To demonstrate the applicability of the approach, a pressurized multi-layer composite pipe is modelled; the so-called stretch inversion phenomenon is reproduced and explained. The stress distribution is obtained by a semi-analytical procedure; it may serve as a benchmark for FEM computations. Finally, the issue of the parameter identification is addressed.

AB - The study is devoted to the geometrically nonlinear simulation of fiber-reinforced composite structures. The applicability of the multiplicative approach to the simulation of viscoelastic properties of a composite material is assessed, certain improvements are suggested. For a greater accuracy in applications involving local compressive fiber buckling, a new family of hyperelastic potentials is introduced. This family allows us to account for the variable critical compressive stress, which depends on the fiber-matrix interaction. For the simulation of viscoelasticity, the well-established Sidoroff decomposition of the deformation gradient is implemented. To account for the viscosity of the matrix material, the model of Simo and Miehe (Comput Methods Appl Mech Eng 98:41–104, 1992) is used; highly efficient iteration-free algorithms are implemented. The viscosity of the fiber is likewise described by the multiplicative decomposition of the deformation gradient, leading to a scalar differential equation; an efficient iteration-free algorithm is proposed for the implicit time stepping. The accuracy and convergence of the new iteration-free method is tested and compared to that of the standard scheme implementing the Newton iteration. To demonstrate the applicability of the approach, a pressurized multi-layer composite pipe is modelled; the so-called stretch inversion phenomenon is reproduced and explained. The stress distribution is obtained by a semi-analytical procedure; it may serve as a benchmark for FEM computations. Finally, the issue of the parameter identification is addressed.

KW - Efficient numerics

KW - Fiber-reinforced composite

KW - Hyperelasticity

KW - Large strain

KW - Multiplicative decomposition

KW - Viscoelasticity

KW - BEHAVIOR

KW - FIELD

KW - STATE

KW - COMPOSITES

KW - MODEL

KW - LINEAR VISCOELASTICITY

KW - FORMULATION

KW - MECHANICS

KW - ARTERIES

KW - FREE-ENERGY

UR - http://www.scopus.com/inward/record.url?scp=85055703456&partnerID=8YFLogxK

U2 - 10.1007/s11012-018-0909-0

DO - 10.1007/s11012-018-0909-0

M3 - Article

AN - SCOPUS:85055703456

VL - 53

SP - 3779

EP - 3794

JO - Meccanica

JF - Meccanica

SN - 0025-6455

IS - 15

ER -