# An Invariant-Preserving ALE Method for Solids under Extreme Conditions

## Abstract

We are proposing a fundamentally new approach to ALE methods for solids undergoing large deformation due to extreme loading conditions. Our approach is based on a physically-motivated and mathematically rigorous construction of the underlying Lagrangian method, vector/tensor reconstruction, remapping, and interface reconstruction. It is transformational because it deviates dramatically from traditionally accepted ALE methods and provides the following set of unique attributes: (1) a three-dimensional, finite volume, cell-centered ALE framework with advanced hypo-/hyper-elasto-plastic constitutive theories for solids; (2) a new physically and mathematically consistent reconstruction method for vector/tensor fields; (3) advanced invariant-preserving remapping algorithm for vector/tensor quantities; (4) moment-of-fluid (MoF) interface reconstruction technique for multi-material problems with solids undergoing large deformations. This work brings together many new concepts, that in combination with emergent cell-centered Lagrangian hydrodynamics methods will produce a cutting-edge ALE capability and define a new state-of-the-art. Many ideas in this work are new, completely unexplored, and hence high risk. The proposed research and the resulting algorithms will be of immediate use in Eulerian, Lagrangian and ALE codes under the ASC program at the lab. In addition, the research on invariant preserving reconstruction/remap of tensor quantities is of direct interest to ongoing CASL and climate modeling efforts at LANL.more »

- Authors:

- Los Alamos National Laboratory

- Publication Date:

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

- Sponsoring Org.:
- DOE/LANL

- OSTI Identifier:
- 1046528

- Report Number(s):
- LA-UR-12-23069

TRN: US1203821

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 42 ENGINEERING; ALGORITHMS; CHEMICAL EXPLOSIVES; CLIMATES; CONSTRUCTION; DEFORMATION; HYDRODYNAMICS; INERTIAL CONFINEMENT; LAGRANGIAN FUNCTION; LANL; PROCESSING; SIMULATION

### Citation Formats

```
Sambasivan, Shiv Kumar, and Christon, Mark A.
```*An Invariant-Preserving ALE Method for Solids under Extreme Conditions*. United States: N. p., 2012.
Web. doi:10.2172/1046528.

```
Sambasivan, Shiv Kumar, & Christon, Mark A.
```*An Invariant-Preserving ALE Method for Solids under Extreme Conditions*. United States. doi:10.2172/1046528.

```
Sambasivan, Shiv Kumar, and Christon, Mark A. Tue .
"An Invariant-Preserving ALE Method for Solids under Extreme Conditions". United States. doi:10.2172/1046528. https://www.osti.gov/servlets/purl/1046528.
```

```
@article{osti_1046528,
```

title = {An Invariant-Preserving ALE Method for Solids under Extreme Conditions},

author = {Sambasivan, Shiv Kumar and Christon, Mark A},

abstractNote = {We are proposing a fundamentally new approach to ALE methods for solids undergoing large deformation due to extreme loading conditions. Our approach is based on a physically-motivated and mathematically rigorous construction of the underlying Lagrangian method, vector/tensor reconstruction, remapping, and interface reconstruction. It is transformational because it deviates dramatically from traditionally accepted ALE methods and provides the following set of unique attributes: (1) a three-dimensional, finite volume, cell-centered ALE framework with advanced hypo-/hyper-elasto-plastic constitutive theories for solids; (2) a new physically and mathematically consistent reconstruction method for vector/tensor fields; (3) advanced invariant-preserving remapping algorithm for vector/tensor quantities; (4) moment-of-fluid (MoF) interface reconstruction technique for multi-material problems with solids undergoing large deformations. This work brings together many new concepts, that in combination with emergent cell-centered Lagrangian hydrodynamics methods will produce a cutting-edge ALE capability and define a new state-of-the-art. Many ideas in this work are new, completely unexplored, and hence high risk. The proposed research and the resulting algorithms will be of immediate use in Eulerian, Lagrangian and ALE codes under the ASC program at the lab. In addition, the research on invariant preserving reconstruction/remap of tensor quantities is of direct interest to ongoing CASL and climate modeling efforts at LANL. The application space impacted by this work includes Inertial Confinement Fusion (ICF), Z-pinch, munition-target interactions, geological impact dynamics, shock processing of powders and shaped charges. The ALE framework will also provide a suitable test-bed for rapid development and assessment of hypo-/hyper-elasto-plastic constitutive theories. Today, there are no invariant-preserving ALE algorithms for treating solids with large deformations. Therefore, this is a high-impact effort that will significantly advance the state of ALE methods and position LANL as world leaders in advanced ALE methods.},

doi = {10.2172/1046528},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {7}

}