Generalization of the ordinary state-based peridynamic model for isotropic linear viscoelasticity
- 304 Downloads
This paper presents a generalization of the original ordinary state-based peridynamic model for isotropic linear viscoelasticity. The viscoelastic material response is represented using the thermodynamically acceptable Prony series approach. It can feature as many Prony terms as required and accounts for viscoelastic spherical and deviatoric components. The model was derived from an equivalence between peridynamic viscoelastic parameters and those appearing in classical continuum mechanics, by equating the free energy densities expressed in both frameworks. The model was simplified to a uni-dimensional expression and implemented to simulate a creep-recovery test. This implementation was finally validated by comparing peridynamic predictions to those predicted from classical continuum mechanics. An exact correspondence between peridynamics and the classical continuum approach was shown when the peridynamic horizon becomes small, meaning peridynamics tends toward classical continuum mechanics. This work provides a clear and direct means to researchers dealing with viscoelastic phenomena to tackle their problem within the peridynamic framework.
KeywordsLinear viscoelasticity Relaxation Creep Peridynamics Classical continuum mechanics Thermodynamics
Fruitful discussions with Marc Alexander Schweitzer, Serge Prud’homme and Patrick Diehl are gratefully acknowledged. The help with the mathematics given by Valentine Roos, Mathieu and Francisque Delorme is also gratefully acknowledged.
- Agwai, A., Guven, I., Madenci, E.: Predicting crack initiation and propagation using XFEM, CZM and peridynamics: a comparative study. In: 2010 Proceedings 60th Electronic Components and Technology Conference, ECTC (2010) Google Scholar
- Dorduncu, M., Barut, A., Madenci, E.: Peridynamic truss element for viscoelastic deformation. In: 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, p. 1721 (2016) Google Scholar
- Du, Q.: Chapter 4 local limits and asymptotically compatible discretizations. In: Handbook of Peridynamic Modeling, pp. 87–108. CRC Press, Boca Raton (2016) Google Scholar
- Irwin, G.R.: Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 24, 361–364 (1957) Google Scholar
- Knauss, W., Ravi-Chandar, K.: Some basic problems in stress wave dominated fracture. In: Dynamic Fracture, pp. 1–17. Springer, Berlin (1985) Google Scholar
- Mitchell, J.A.: A non-local, ordinary-state-based viscoelasticity model for peridynamics. Sandia National Lab., Report 8064, pp. 1–28 (2011) Google Scholar