Viscoplasticity using peridynamics.

*(English)*Zbl 1183.74035Summary: Peridynamics is a continuum reformulation of the standard theory of solid mechanics. Unlike the partial differential equations of the standard theory, the basic equations of peridynamics are applicable even when cracks and other singularities appear in the deformation field. The assumptions in the original peridynamic theory resulted in severe restrictions on the types of material response that could be modeled, including a limitation on the Poisson ratio. Recent theoretical developments have shown promise for overcoming these limitations, but have not previously incorporated rate dependence and have not been demonstrated in realistic applications. In this paper, a new method for implementing a rate-dependent plastic material within a peridynamic numerical model is proposed and demonstrated. The resulting material model implementation is fitted to rate-dependent test data on 6061-T6 aluminum alloy. It is shown that with this material model, the peridynamic method accurately reproduces the experimental results for Taylor impact tests over a wide range of impact velocities. The resulting model retains the advantages of the peridynamic formulation regarding discontinuities while allowing greater generality in material response than was previously possible.

##### MSC:

74C10 | Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) |

74S05 | Finite element methods applied to problems in solid mechanics |

##### Keywords:

peridynamics; peridynamic states; plasticity; non-local theory; integral equations; continuum mechanics; Taylor impact
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\textit{J. T. Foster} et al., Int. J. Numer. Methods Eng. 81, No. 10, 1242--1258 (2010; Zbl 1183.74035)

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##### References:

[1] | Silling, Reformulation of elasticity theory for discontinuities and long-range forces, Journal of the Mechanics and Physics of Solids 48 (1) pp 175– (2000) · Zbl 0970.74030 |

[2] | Silling, Computational Fluid and Solid Mechanics pp 641– (2003) |

[3] | Silling, Deformation of a peridynamic bar, Journal of Elasticity 73 (1) pp 173– (2003) · Zbl 1061.74031 |

[4] | Silling, Peridynamic states and constitutive modeling, Journal of Elasticity 88 pp 151– (2007) · Zbl 1120.74003 |

[5] | Silling, Convergence of peridynamics to classical elasticity theory, Journal of Elasticity 93 pp 13– (2008) · Zbl 1159.74316 |

[6] | Silling, A meshfree method based on the peridynamic model of solid mechanics, Computers and Structures 83 (17-18) pp 1526– (2005) |

[7] | Warren, A non-ordinary state-based peridynamic method to model solid material deformation and fracture, International Journal of Solids and Structures 46 (5) pp 1186– (2009) · Zbl 1236.74012 |

[8] | Monaghan J. An introduction to SPH. Particle Methods in Fluid Dynamics and Plasma Physics, Proceedings from the Workshop held on 13-15 April 1987, Los Almos, U.S.A., 1987; 89. |

[9] | Li, Meshfree and particle methods and their applications, Applied Mechanics Review 55 pp 1– (2002) |

[10] | Gao, Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds, Journal of the Mechanics and Physics of Solids 46 (2) pp 187– (1998) · Zbl 0974.74008 |

[11] | Delaplace, Performance of time-stepping schemes for discrete models in fracture dynamic analysis, International Journal for Numerical Methods in Engineering 65 (9) pp 1527– (2006) · Zbl 1112.74065 |

[12] | Hoover, Smooth Particle Applied Mechanics (2006) · Zbl 1141.76001 · doi:10.1142/6218 |

[13] | Rabczuk, Stable particle methods based on Lagrangian kernels, Computer Methods in Applied Mechanics and Engineering 193 (12-14) pp 1035– (2004) · Zbl 1060.74672 |

[14] | Askari, Peridynamics for multiscale materials modeling, Journal of Physics: Conference Series 125 (2008) |

[15] | Flanagan, An accurate numerical algorithm for stress integration with finite rotations, Computer Methods in Applied Mechanics and Engineering 62 (3) pp 305– (1987) · Zbl 0614.73035 |

[16] | Johnson, A discussion of stress rates in finite deformation problems, International Journal of Solids and Structures 20 (8) pp 725– (1983) |

[17] | Green, A note on invariance under superposed rigid body motions, Journal of Elasticity 9 (1) pp 1– (1977) |

[18] | Hill, The Mathematical Theory of Plasticity (1998) · Zbl 0923.73001 |

[19] | Malvern, Introduction to the Mechanics of a Continuous Medium (1969) · Zbl 0181.53303 |

[20] | Silling SA. Stability and accuracy of differencing schemes for viscoplastic model in wavecodes. SAND Report SAND91-0141, Sandia National Laboratories, 1991. |

[21] | Camacho, Adaptive Lagrangian modelling of ballistic penetration of metallic targets, Computer Methods in Applied Mechanics and Engineering 142 (3-4) pp 269– (1997) · Zbl 0892.73056 |

[22] | Warren, Simulations of the penetration of 6061-T6511 aluminum targets by spherical-nosed VAR 4340 steel projectiles, International Journal of Solids and Structures 37 (32) pp 4419– (2000) · Zbl 0954.74547 |

[23] | Song, Proceedings of the JSME/ASME International Conference on Materials and Processing (2002) |

[24] | Anderson, AIP Conference Proceedings 845 (2006) |

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