PSI - Issue 13

Zhengkun Liu et al. / Procedia Structural Integrity 13 (2018) 781–786

786

6 Z. Liu et al. / Structural Integrity Procedia 00 (2018) 000–000 Next, the influence of the fracture toughness G c on results in terms of force-displacement curve is evaluated in Fig. 4. The plotted results show that the increasing the value of G c can improve the load bearing capacity as well as the maximal peak force. Lastly, the influence of the mobility factor M on the force-displacement behavior is shown in Fig. 5. It can be observed that, when M is chosen large enough, the force-displacement curves converge.

4. Conclusion

In this work, we introduced the finite viscoelastic material behavior and the phase-field model for the brittle fracture at large deformations. Next, the proposed phase-field model for brittle fracture was verified by using a numerical benchmark test. Here, the parameter studies for the proposed phase-field model have been done and the results have been analyzed. The results showed that the maximal peak force and the load bearing capacity in viscoelastic solids can be changed by the di ff erent loading speed. Moreover, the damage and failure analysis of viscoelastic materials using phase-field method should be compared with experimental results in the future.

Acknowledgements

This work was supported by the program of the Federal State of Saxony-Anhalt, Germany. This support is gratefully acknowledged.

References

Amor, H., Marigo, J-J., Maurini, C., 2009. Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments. Journal of the Mechanics and Physics of Solids, 1209–1229. Ambati, M., Gerasimov, T., De Lorenzis, L., 2014. A review on phase-field models of brittle fracture and a new fast hybrid formulation. Computa tional Mechanics, 383–405. Ambati, M., Gerasimov, T., De Lorenzis, L., 2015. Phase-field modeling of ductile fracture. Computational Mechanics, 1017–1040. Ambati, M., Kruse, R., De Lorenzis, L., 2016. A phase-field model for ductile fracture at finite strains and its experimental verification. Computa tional Mechanics, 149-167. Alessi, R., Ambati, M., Gerasimov, T., Vidoli, S., De Lorenzis, L., 2018. Comparison of Phase-Field Models of Fracture Coupled with Plasticity. Advances in Computational Plasticity, 1–21. Borden, MJ., Hughes, TJR., Landis, CM., Anvari, A., Lee, IJ., 2016. A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality e ff ects. Computer Methods in Applied Mechanics and Engineering, 130–166. Heister, T., Wheeler, MF., Wick, T., 2015. A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propa gation using a phase-field approach. Computer Methods in Applied Mechanics and Engineering, 466–495. Miehe, C., Hofacker, M., Welschinger, F., 2010. A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering, 2765–2778. Miehe, C., Sch¨ anzel, LM., Ulmer, H., 2015. Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids. Computer Methods in Applied Mechanics and Engineering, 449–485. Miehe, C., Hofacker, M., Sch¨ anzel, LM., Aldakheel, F., 2015. Phase field modeling of fracture in multi-physics problems. Part II. Coupled brittle to-ductile failure criteria and crack propagation in thermo-elastic-plastic solids. Computer Methods in Applied Mechanics and Engineering, 486–522. Miehe, C., Aldakheel, F., Raina, A., 2016. Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity damage theory. International Journal of Plasticity, 1–32. Reinoso, J., Paggi, M., Linder, C., 2017. Phase field modeling of brittle fracture for enhanced assumed strain shells at large deformations: formu lation and finite element implementation. Computational Mechanics, 981–1001. Taylor, R. L., Govindjee, S., 2017. FEAP - finite element analysis program. Wick, T., 2017. An Error-Oriented Newton / Inexact Augmented Lagrangian Approach for Fully Monolithic Phase-Field Fracture Propagation. SIAM Journal on Scientific Computing, 589–617. Wick, T., 2017. Modified Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation. Computer Methods in Applied Mechanics and Engineering, 577–611. Zienkiewicz, O.C., Taylor, R.L., Fox, D., 2014. The Finite Element Method for Solid and Structural Mechanic (7th Edition), Butterworth Heinemann, Oxford, UK.