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Original Articles

The peridynamic equation and its spatial discretisation

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Pages 17-27 | Received 01 Nov 2006, Published online: 14 Oct 2010

References

  • Bažant , Z.P and &Jir;aacute;sek , M. 2002 . Nonlocal integral formulations of plasticity and damage: survey and progress . J. Eng. Mech. , 128 (11) : 1119 – 1149 .
  • Chen , Y. , Le , J. D. and Eskandarian , A. 2002 . Dynamic meshless method applied to nonlocal crack problems . Theor. Appl. Fract. Mech. , 38 : 293 – 300 .
  • Dayal , K. and Bhattacharya , K. 2006 . Kinetics of phase transformations in the peri‐dynamic formulation of continuum mechanics . J. Mech. Phys. Solids , 54 (9) : 1811 – 1842 .
  • Emmrich , E. and Weckner , O. 2005 . Analysis and numerical approximation of an integro‐differential equation modelling non‐local effects in linear elasticity . Math. Mech. Solids ,
  • Eringen , A. C. 1992 . Vistas of nonlocal continuum physics . Int. J. Eng Sci. , 30 (10) : 1551 – 1565 .
  • Kunin , I. A. 1982/83 . Elastic Media with Micro structure , Berlin : Springer .
  • Pisano , A. A. and Puschi , P. 2003 . Closed form solution for a nonlocal elastic bar in tension . Int. J. Solids Structures , 40 (1) : 13 – 23 .
  • Polizzotto , C. 2001 . Nonlocal elasticity and related variational principles . Int. J. Solids Structures , 38 : 42 – 43 . 7359 – 7380 .
  • Rogula , D. 1982 . Nonlocal Theory of Material Media , Berlin : Springer .
  • S. A. Silling About Emu http://www.sandia.gov/emu/emu.htm.
  • Silling , S. A. 2000 . Reformulation of elastic theory for discontinuities and long‐range forces . J. Mech. Phys. Solids , 48 (1) : 175 – 209 .
  • Silling , S. A. and Askari , E. 2005 . A meshfree method based on the peridynamic model of solid mechanics . Computers & Structures , 83 : 1526 – 1535 .
  • Silling , S. A. and Bobaru , F. 2005 . Peridynamic modeling of membranes and fibers . Int. J. Non‐linear Mech. , 40 : 395 – 409 .
  • Silling , S. A. , Zimmermann , M. and Abeyaratne , R. 2003 . Deformation of a peridynamic bar . J. Elasticity , 73 : 173 – 190 .
  • Weckner , O. and Abeyaratne , R. 2005 . The effect of long‐range forces on the dynamics of a bar . J. Mech. Phys. Solids , 53 (3) : 705 – 728 .
  • Weckner , O. and Emmrich , E. 2005 . Numerical simulation of the dynamics of a nonlocal, inhomogeneous, infinite bar . JCAM , 6 (2) : 311 – 319 .

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