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The Third International Conference on Computational Modeling of Fracture and Failure of Materials and Structures
Numerical Simulation of Fracture in Viscoelastic Materials Based on Material Forces
K. Özenç∗ , M. Kaliske
Institute for Structural Analysis, Technische Universität Dresden, Germany,
[email protected]
The crack growth mechanism of elastomers is of
great importance and interest in engineering applications, however, the correlation between numerical and theorical studies is not well established due
to the complexity of the problem. The contribution
presents an r-adaptive crack propagation scheme for
the description of the viscoelastic fracture response
of rubber-like materials at large strains. A similar
algorithm is proposed by Miehe et al. [1]. The approach is extended for a generalized finite inelastic
continuum by Kaliske et al. [2]. Key feature of this
procedure is restructuring the overall system by duplication of crack front degrees of freedom based
on minimization of the overall energy via the Griffith criterion. Use of the presented framework enables to study fracture behaviour of elastomers at
different deformation rates. The experimental evidence from previous studies favors that the fracture toughness of non-strain-crystallising elastomers
shows strong rate-dependency and the energy release
rate versus the rate of tearing or crack propagation
relation appears to be a fundamental material property [3]. Therefore, in this contribution, a dynamic
fracture criterion, which is a function of the rate of
crack growth, is shown to be more adequate in numerical simulations.
In addition, in previous studies, it is shown that
the fracture energy per unit area of crack advancement appears to be the result of two contributions in
terms of the change in elastic energy and in terms of
the viscous dissipation by a configurational change
[4]. In other words, the elastic part is the intrinsic strength of the interface which does not depend
on the crack growth rate, whereas the second part,
which reflects energy dissipated by viscosity, is a
function of the crack growth rate. The separation
of the fracture energy is obtained by the global energy momentum balance. To this end, a consistent
thermodynamic framework for the combined configurational motion in viscoelastic continua at the finite strain regime is discussed. For the sake of simplicity, all results are obtained neglecting thermoCFRAC 2013
mechanical phenomena and inertia effects. In addition, branching instability triggered by a significantly increased deformation speed is investigated.
A crack speed limiter, which is a constant branching
velocity, is used in order to explain the phenomenon
in elastomers.
The Bergstörm-Boyce model is considered to introduce hyperelastic and finite viscoelastic behaviour
of rubber-like bulk material. The crack driving force
and the crack direction are predicted by the material
force approach. The predictive capability of the proposed method is demonstrated by representative numerical examples. In conclusion, experimental and
numerical results are discussed in order to clarify the
relation between the tearing phenomenon and material force approach in viscoelastic materials.
References
[1] C. Miehe, E. Gürses, Robust Algorithm for
Configurational-Force-Driven Brittle Crack
Propagation with R-Adaptive Mesh Alignment,
Int J Numer Meth Eng 72 (2007) 127–155.
[2] M. Kaliske, K. Ozenc, H. Dal, Aspects of crack
propagation in small and finite strain continua,
in: Constitutive models for rubber VII : proceedings of the 7th European Conference on Constitutive Models for Rubber, Dublin, 137–142,
2011.
[3] G. J. Lake, C. C. Lawrence, A. G. Thomas,
High-Speed Fracture of Elastomers: Part I, Rubber Chem Technol 73 (2000) 801–817.
[4] B. Näser, M. Kaliske, H. Dal, C. Netzker, Fracture mechanical behaviour of visco-elastic materials: Application to the so-called dwell-effect, Z
Angew Math Mech 89 (2009) 677–686.
Prague, Czech Republic, 5–7 June 2013