## This content will become publicly available on May 3, 2020

## Statistically informed upscaling of damage evolution in brittle materials

## Abstract

The presence and growth of micro-cracks degrade the strength of brittle solids, greatly impacting the overall material response. Hence, the evolution of these micro-cracks must be accounted for in models describing the relationship between stress and strain so that accurate predictions of material failure can be made. The evolution of individual cracks and crack networks can be simulated with high-fidelity microscale models utilizing highly resolved meshes that can be computationally expensive to a point in which it limits the simulation scale. Hence, for many engineering applications that require simulations of large components, continuum-scale models, which cannot explicitly resolve individual cracks and thus lose important physical information, are required. In this work, we bridge these two scales by developing and implementing a continuum-scale effective moduli constitutive model that is informed by crack statistics generated from a high-fidelity model resolved using a finite-discrete element method (FDEM) implementation. Using statistical information describing the evolution of crack lengths and orientations, this model can capture the effects of brittle damage evolution without the need to resolve individual cracks. We have successfully captured the stress-strain behavior of the high-fidelity simulations using the statistics-based constitutive model shown through direct comparison of stress-strain curves. The curves match withinmore »

- Authors:

- Univ. of Michigan, Ann Arbor, MI (United States)
- Univ. of Illinois at Urbana-Champaign, Champaign, IL (United States)
- Broadridge Financial Solutions, Edgewood, NY (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1512769

- Report Number(s):
- LA-UR-18-30006

Journal ID: ISSN 0167-8442

- Grant/Contract Number:
- 89233218CNA000001

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Theoretical and Applied Fracture Mechanics

- Additional Journal Information:
- Journal Volume: 102; Journal Issue: C; Journal ID: ISSN 0167-8442

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; Brittle fracture; Finite-discrete element method; Effective elastic moduli; Crack statistics

### Citation Formats

```
Vaughn, Nathanial Joesph, Kononov, Alina, Moore, Bryan Alexander, Rougier, Esteban, Viswanathan, Hari S., and Hunter, Abigail. Statistically informed upscaling of damage evolution in brittle materials. United States: N. p., 2019.
Web. doi:10.1016/j.tafmec.2019.04.012.
```

```
Vaughn, Nathanial Joesph, Kononov, Alina, Moore, Bryan Alexander, Rougier, Esteban, Viswanathan, Hari S., & Hunter, Abigail. Statistically informed upscaling of damage evolution in brittle materials. United States. doi:10.1016/j.tafmec.2019.04.012.
```

```
Vaughn, Nathanial Joesph, Kononov, Alina, Moore, Bryan Alexander, Rougier, Esteban, Viswanathan, Hari S., and Hunter, Abigail. Fri .
"Statistically informed upscaling of damage evolution in brittle materials". United States. doi:10.1016/j.tafmec.2019.04.012.
```

```
@article{osti_1512769,
```

title = {Statistically informed upscaling of damage evolution in brittle materials},

author = {Vaughn, Nathanial Joesph and Kononov, Alina and Moore, Bryan Alexander and Rougier, Esteban and Viswanathan, Hari S. and Hunter, Abigail},

abstractNote = {The presence and growth of micro-cracks degrade the strength of brittle solids, greatly impacting the overall material response. Hence, the evolution of these micro-cracks must be accounted for in models describing the relationship between stress and strain so that accurate predictions of material failure can be made. The evolution of individual cracks and crack networks can be simulated with high-fidelity microscale models utilizing highly resolved meshes that can be computationally expensive to a point in which it limits the simulation scale. Hence, for many engineering applications that require simulations of large components, continuum-scale models, which cannot explicitly resolve individual cracks and thus lose important physical information, are required. In this work, we bridge these two scales by developing and implementing a continuum-scale effective moduli constitutive model that is informed by crack statistics generated from a high-fidelity model resolved using a finite-discrete element method (FDEM) implementation. Using statistical information describing the evolution of crack lengths and orientations, this model can capture the effects of brittle damage evolution without the need to resolve individual cracks. We have successfully captured the stress-strain behavior of the high-fidelity simulations using the statistics-based constitutive model shown through direct comparison of stress-strain curves. The curves match within error bars present in the strain-softening portions of the stress-strain curve of the high-fidelity results due to the statistical variation of the initial pre-existing crack network. In conclusion, the stress-strain curves are also compared to experimental results for similar loading conditions and show good qualitative agreement.},

doi = {10.1016/j.tafmec.2019.04.012},

journal = {Theoretical and Applied Fracture Mechanics},

number = C,

volume = 102,

place = {United States},

year = {2019},

month = {5}

}