# Probabilistic Upscaling of Material Failure Using Random Field Models – A Preliminary Investigation

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## Abstract

**:**

## 1. Introduction

## 2. Micro-to-Meso Upscaling

#### 2.1 Micro-cracking in a random field

#### 2.2 Numerical simulation

#### 2.3 Probabilistic characterization of SRVE strength

**Figure 6.**Mixed Weibull-Gaussian statistics for strength of flawed inert silicon nitride (SNW-1000).

## 3. Meso-to-Macro Upscaling

#### 3.1 Mesoscale damage model

#### 3.2 Numerical example

## 4. Conclusion

## Acknowledgements

## References

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**MDPI and ACS Style**

Hu, K.; Xu, X.F.
Probabilistic Upscaling of Material Failure Using Random Field Models – A Preliminary Investigation. *Algorithms* **2009**, *2*, 750-763.
https://doi.org/10.3390/a2020750

**AMA Style**

Hu K, Xu XF.
Probabilistic Upscaling of Material Failure Using Random Field Models – A Preliminary Investigation. *Algorithms*. 2009; 2(2):750-763.
https://doi.org/10.3390/a2020750

**Chicago/Turabian Style**

Hu, Keqiang, and X. Frank Xu.
2009. "Probabilistic Upscaling of Material Failure Using Random Field Models – A Preliminary Investigation" *Algorithms* 2, no. 2: 750-763.
https://doi.org/10.3390/a2020750