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

TL;DR

This paper develops a geometrically nonlinear simulation method for fiber-reinforced viscoelastic composites using a multiplicative approach, introducing new hyperelastic potentials and efficient algorithms for accurate modeling of local buckling and viscoelastic effects.

Contribution

It introduces a novel multiplicative framework with iteration-free algorithms for simulating viscoelastic fiber-reinforced structures, improving accuracy and computational efficiency.

Findings

Accurate modeling of local fiber buckling and matrix viscosity.

Efficient iteration-free algorithms for viscoelastic simulation.

Validation through pressurized composite pipe example.

Abstract

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 (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.