### Abstract

The spatial averaging integral and weight function that have so far been employed in the macroscopic nonlocal models for strain-softening damage have been obtained by semi-intuitive arguments and justified by the need to limit damage localization in numerical computations. Some micromechanics arguments have recently also been presented, but microcrack interactions and growth have been neglected. The present conference paper gives a preliminary, abbreviated exposition of a new micromechanics analysis of a system of interacting and growing microcracks. The result is a new form of the spatial integral for nonlocal damage, in which the nonlocal stress field is a solution of a Fredholm integral equation over the neighborhood of a point. While in previous formulations the weight function has been assumed as a scalar, it is now found to be a tensor. Furthermore, the weight function is not axisymmetric (isotropic) but varies with the spherical angles (i.e., is anisotropic) and exhibits sectors of shielding and amplification. For long distances, the weight function decays as r^{-2} in two dimensions and as r^{-3} in three dimensions. Application of the Gauss-Seidel iteration method, which can be conveniently combined with iterations in each loading step of a nonlinear finite element code, simplifies the handling of the nonlocality since the nonlocal inelastic stress increments can be evaluated explicitly using directly the crack influence function. A detailed article is in preparation.

Original language | English (US) |
---|---|

Title of host publication | Macroscopic Behavior of Heterogeneous Materials From the Microstructure |

Publisher | Publ by ASME |

Pages | 153-160 |

Number of pages | 8 |

Volume | 147 |

ISBN (Print) | 0791811018 |

State | Published - Dec 1 1992 |

Event | Winter Annual Meeting of the American Society of Mechanical Engineers - Anaheim, CA, USA Duration: Nov 8 1992 → Nov 13 1992 |

### Other

Other | Winter Annual Meeting of the American Society of Mechanical Engineers |
---|---|

City | Anaheim, CA, USA |

Period | 11/8/92 → 11/13/92 |

### ASJC Scopus subject areas

- Mechanical Engineering

## Fingerprint Dive into the research topics of 'New concept of nonlocal continuum damage: Crack influence function'. Together they form a unique fingerprint.

## Cite this

*Macroscopic Behavior of Heterogeneous Materials From the Microstructure*(Vol. 147, pp. 153-160). Publ by ASME.