Skip to main content

A Short Note on Modeling Damage in Peridynamics


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.

This is a preview of subscription content, access via your institution.

Fig. 1


  1. 1.

    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)

    Chapter  Google Scholar 

  2. 2.

    Emmrich, E., Puhst, D.: Well-posedness of the peridynamic model with Lipschitz continuous pairwise force function. Commun. Math. Sci. 11, 1039–1049 (2013)

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    Emmrich, E., Puhst, D.: Measure-valued and weak solutions to the nonlinear peridynamic model in nonlocal elastodynamics. Nonlinearity 28, 285–307 (2015)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Gajewski, H., Gröger, K., Zacharias, K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag, Berlin (1974)

    MATH  Google Scholar 

  5. 5.

    Lipton, R.: Cohesive dynamics and fracture. arXiv:1411.4609v4 (2014)

  6. 6.

    Silling, S.A.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48, 175–209 (2000)

    ADS  MathSciNet  Article  MATH  Google Scholar 

Download references


The authors would like to thank Robert Lipton for all the valuable discussions.

Author information



Corresponding author

Correspondence to Etienne Emmrich.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Emmrich, E., Puhst, D. A Short Note on Modeling Damage in Peridynamics. J Elast 123, 245–252 (2016).

Download citation


  • Nonlocal continuum mechanics
  • Nonlinear models
  • Peridynamics
  • Damage
  • Existence

Mathematics Subject Classification (2010)

  • 35Q74
  • 74B20
  • 74H20