We extend the peridynamic model to inherit irreversible damage. The governing equation is both nonlocal in time and in space and yields an abstract differential equation of Volterra type. We present conditions under which unique global solutions exist.
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Emmrich, E., Lehoucq, R.B., Puhst, D.: Peridynamics: a nonlocal continuum theory. In: Griebel, M., Schweitzer, M.A. (eds.) Meshfree Methods for Partial Differential Equations VI. Lect. N. Comput. Sci. Eng., vol. 89. Springer, Berlin (2013)
Emmrich, E., Puhst, D.: Well-posedness of the peridynamic model with Lipschitz continuous pairwise force function. Commun. Math. Sci. 11, 1039–1049 (2013)
Emmrich, E., Puhst, D.: Measure-valued and weak solutions to the nonlinear peridynamic model in nonlocal elastodynamics. Nonlinearity 28, 285–307 (2015)
Gajewski, H., Gröger, K., Zacharias, K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag, Berlin (1974)
Lipton, R.: Cohesive dynamics and fracture. arXiv:1411.4609v4 (2014)
Silling, S.A.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48, 175–209 (2000)
The authors would like to thank Robert Lipton for all the valuable discussions.
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Emmrich, E., Puhst, D. A Short Note on Modeling Damage in Peridynamics. J Elast 123, 245–252 (2016). https://doi.org/10.1007/s10659-015-9550-5
- Nonlocal continuum mechanics
- Nonlinear models
Mathematics Subject Classification (2010)