Abstract
A model for dynamic damage propagation is developed using nonlocal potentials. The model is posed using a state-based peridynamic formulation. The resulting evolution is seen to be well posed. At each instant of the evolution, we identify a damage set. On this set, the local strain has exceeded critical values either for tensile or hydrostatic strain, and damage has occurred. The damage set is nondecreasing with time and is associated with damage state variables defined at each point in the body. We show that a rate form of energy balance holds at each time during the evolution. Away from the damage set, we show that the nonlocal model converges to the linear elastic model in the limit of vanishing nonlocal interaction.
This is a preview of subscription content, log in via an institution to check access.
References
A. Agwai, I. Guven, E. Madenci, Predicting crack propagation with peridynamics: a comparative study. Int. J. Fract. 171, 65–78 (2011)
F. Bobaru, W. Hu, The meaning, selection, and use of the peridynamic horizon and its relation to crack branching in brittle materials. Int. J. Fract. 176, 215–222 (2012)
F. Bobaru, J.T. Foster, P.H. Geubelle, S.A. Silling, Handbook of Peridynamic Modeling (CRC Press, BOCA Ratone, 2016)
K. Dayal, K. Bhattacharya, Kinetics of phase transformations in the peridynamic formulation of continuum mechanics. J. Mech. Phys. Solids 54, 1811–1842 (2006)
Q. Du, Y. Tao, X. Tian, A peridynamic model of fracture mechanics with bond-breaking. J Elast. (2017). https://doi.org/10.1007/s10659-017-9661-2
E. Emmrich, D. Phust, A short note on modeling damage in peridynamics. J. Elast. 123, 245–252 (2016)
E. Emmrich, O. Weckner, On the well-posedness of the linear peridynamic model and its convergencee towards the Navier equation of linear elasticity. Commun. Math. Sci. 5, 851–864 (2007)
J.T. Foster, S.A. Silling, W. Chen, An energy based failure criterion for use with peridynamic states. Int. J. Multiscale Comput. Eng. 9, 675–688 (2011)
W. Gerstle, N. Sau, S. Silling, Peridynamic modeling of concrete structures. Nuclear Eng. Des. 237, 1250–1258 (2007)
Y.D. Ha, F. Bobaru, Studies of dynamic crack propagation and crack branching with peridynamics. Int. J. Fract. 162, 229–244 (2010)
P. K. Jha, R. Lipton, Numerical analysis of peridynamic models in Hölder space, arXiv preprint arXiv:1701.02818 (2017)
R. Lipton, Dynamic brittle fracture as a small horizon limit of peridynamics. J. Elast. 117, 21–50 (2014)
R. Lipton, Cohesive dynamics and brittle fracture. J. Elast. 124(2), 143–191 (2016)
R. Lipton, S. Silling, R. Lehoucq, Complex fracture nucleation and evolution with nonlocal elastodynamics. arXiv preprint arXiv:1602.00247 (2016)
R. Lipton, E. Said, P.K. Jha, Free damage propagation with memory. J. Elast. To appear in J. Elasticity (2018)
T. Mengesha, Q. Du, Nonlocal constrained value problems for a linear peridynamic Navier equation. J. Elast. 116, 27–51 (2014)
E. Oterkus, I. Guven, E. Madenci, Fatigue failure model with peridynamic theory,in IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), Las Vegas, June 2010, pp. 1–6
K. Pham, J.J. Marigo, From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models. Contin. Mech. Thermodyn. 25, 147–171 (2013)
S.A. Silling, Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48, 175–209 (2000)
S.A. Silling, E. Askari, A meshfree method based on the peridynamic model of solid mechanics. Comput. Struct. 83, 1526–1535 (2005)
S.A. Silling, E. Askari, Peridynamic model for fatigue cracking. Sandia Report, SAND2014-18590, 2014
S.A. Silling, F. Bobaru, Peridynamic modeling of membranes and fibers. Int. J. Nonlinear Mech. 40, 395–409 (2005)
S.A. Silling, M. Epton, O. Weckner, J. Xu, E. Askari, Peridynamic states and constitutive modeling. J. Elast. 88, 151–184 (2007)
S.A. Silling, R.B. Lehoucq, Convergence of peridynamics to classical elasticity theory. J. Elast. 93, 13–37 (2008)
S. Silling, O. Weckner, E. Askari, F. Bobaru, Crack nucleation in a peridynamic solid. Int. J. Fract. 162, 219–227 (2010)
O. Weckner, R. Abeyaratne, The effect of long-range forces on the dynamics of a bar. J. Mech. Phys. Solids 53, 705–728 (2005)
O. Weckner, E. Emmrich, Numerical simulation of the dynamics of a nonlocal, inhomogeneous, infinite bar. J. Comput. Appl. Mech, 6, 311–319 (2005)
Acknowledgements
This material is based upon the work supported by the U S Army Research Laboratory and the U S Army Research Office under contract/grant number W911NF1610456.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this entry
Cite this entry
Lipton, R., Said, E., Jha, P.K. (2018). Dynamic Damage Propagation with Memory: A State-Based Model. In: Voyiadjis, G. (eds) Handbook of Nonlocal Continuum Mechanics for Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-22977-5_45-1
Download citation
DOI: https://doi.org/10.1007/978-3-319-22977-5_45-1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22977-5
Online ISBN: 978-3-319-22977-5
eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering