## Abstract

For the design of materials, it is important to faithfully model the physics due to interactions at the microstructural scales [18, 17, 19]. While bruteforce modeling of all the details of the microstructure is too costly, current homogenized continuum models suffer from their inability to sufficiently capture the correct physics - especially where localization and failure are concerned. To overcome this limitation, a multi-scale continuum theory is proposed so that kinematic variables representing the deformation at various scales are incorporated. The method of virtual power is then used to derive a system of coupled governing equations, each equation representing a particular scale and its interactions with the macro-scale. A constitutive relation is then introduced to preserve the underlying physics associated with each scale. The inelastic behavior is represented by multiple yield functions, each representing a particular scale of microstructure, but collectively coupled through the same set of internal variables. The proposed theory is applied to model porous metals and high strength steel. For the high strength steel the microstructure of interest consists of two populations of inclusions at distinct scales, in an alloy matrix.

Original language | English (US) |
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Title of host publication | Computational Plasticity |

Editors | Eugenio Onate, Roger Owen |

Publisher | Springer |

Pages | 1-11 |

Number of pages | 11 |

ISBN (Print) | 9781402065767 |

DOIs | |

State | Published - 2007 |

Externally published | Yes |

Event | 8th International Conference on Computational Plasticity, 2005 - Barcelona, Spain Duration: Sep 5 2005 → Sep 8 2005 |

### Publication series

Name | Computational Methods in Applied Sciences |
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Volume | 7 |

ISSN (Print) | 1871-3033 |

### Other

Other | 8th International Conference on Computational Plasticity, 2005 |
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Country/Territory | Spain |

City | Barcelona |

Period | 09/5/05 → 09/8/05 |

### Bibliographical note

Publisher Copyright:© 2007 Springer. Printed in the Netherlands.

## ASJC Scopus subject areas

- Civil and Structural Engineering
- Modeling and Simulation
- Biomedical Engineering
- Computer Science Applications
- Fluid Flow and Transfer Processes
- Computational Mathematics
- Electrical and Electronic Engineering