# Regularized Finite Element Formulations for Shear Band Instabilities in Metals

## Abstract

The dynamic fracture of metals is a fascinating multiphysics-multiscale phenomena that arises in a variety of important applications. The numerical modeling of dynamic fracture requires a high degree of accuracy and robustness and also poses a number of numerical algorithm challenges due to evolving boundary features, multiple time scales/physical processes, and possible changes in the nature of the underlying equations as a simulation progresses. Dynamic fracture is often associated with brittle or ductile fracture depending on material properties, loading rates and specimen geometry. Impact experiments on metals show that at low strain rates, brittle fracture dominates, while at high rates ductile instability (or shear banding) occurs. Shear bands are driven by large plastic deformations and high temperatures, while cracks are driven by tensile loading. These two failure modes occur at distinct spatial and temporal scales. Shearbanding is an important problem from a physics and mathematics point of view with various applications to metals, soils and granular materials and other material types. It has been an active research area, studied by several groups including a few across the DOE labs (e.g. at Sandia Labs and at Los Alamos Labs). The physics of shearbanding and fracture is extremely complicated and involves amore »

- Authors:

- Publication Date:

- Research Org.:
- Haim Waisman/Columbia University

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- Contributing Org.:
- Columbia University

- OSTI Identifier:
- 1483069

- Report Number(s):
- DE-SC0008196

- DOE Contract Number:
- SC0008196

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; shear bands, fracture, plasticity, stability analysis, modeling, preconditioners, solvers, parallel computing, algorithms

### Citation Formats

```
Waisman, Haim.
```*Regularized Finite Element Formulations for Shear Band Instabilities in Metals*. United States: N. p., 2018.
Web. doi:10.2172/1483069.

```
Waisman, Haim.
```*Regularized Finite Element Formulations for Shear Band Instabilities in Metals*. United States. doi:10.2172/1483069.

```
Waisman, Haim. Thu .
"Regularized Finite Element Formulations for Shear Band Instabilities in Metals". United States. doi:10.2172/1483069. https://www.osti.gov/servlets/purl/1483069.
```

```
@article{osti_1483069,
```

title = {Regularized Finite Element Formulations for Shear Band Instabilities in Metals},

author = {Waisman, Haim},

abstractNote = {The dynamic fracture of metals is a fascinating multiphysics-multiscale phenomena that arises in a variety of important applications. The numerical modeling of dynamic fracture requires a high degree of accuracy and robustness and also poses a number of numerical algorithm challenges due to evolving boundary features, multiple time scales/physical processes, and possible changes in the nature of the underlying equations as a simulation progresses. Dynamic fracture is often associated with brittle or ductile fracture depending on material properties, loading rates and specimen geometry. Impact experiments on metals show that at low strain rates, brittle fracture dominates, while at high rates ductile instability (or shear banding) occurs. Shear bands are driven by large plastic deformations and high temperatures, while cracks are driven by tensile loading. These two failure modes occur at distinct spatial and temporal scales. Shearbanding is an important problem from a physics and mathematics point of view with various applications to metals, soils and granular materials and other material types. It has been an active research area, studied by several groups including a few across the DOE labs (e.g. at Sandia Labs and at Los Alamos Labs). The physics of shearbanding and fracture is extremely complicated and involves a coupled, highly nonlinear thermo-mechanical processes with a multi time/length scale nature, which requires high level of continuum mechanics understanding. The numerical methods developed so far are very limited and are simplified to the point that those are not reliable (e.g. sensitive to the mesh density and will not converge with mesh refinement). These issues are far from being understood and have not yet been resolved from a computational standpoint. In my research I have addressed several fundamental issues of dynamic fracture: 1. established the role of heat conduction as a natural regularizing mechanism in shearband problems (i.e. using the correct physics for this problem), 2. developed a unified model to incorporate fracture through a modified phase field formulation, 3. developed stability analysis tools to determine the onset of localization, 4. developed discretization methods and solvers to solve this problem (on parallel computers) that lead to mesh insensitive results and fast convergence. For such difficult problems, the physics and numerics are strongly coupled. To accurately model the physics, one must develop reliable numerics but reliable numerics depends on correct description of the physics. To this end, we have already made significant progress in the field showing that a fully-coupled implicit solution with heat conduction is the key to obtain reliable results for shear bands (see the next sections for more details). This research fits well within the mission of DOE ASCR program on all aspects: from governing equations to discretization to solvers to parallel computers to applications problems. It also relies on the computational tools developed through the SciDAC institutes FASTMath and SDAV, such as PETSc (and SLEPc), ParaView, Trilinos and Masquite.},

doi = {10.2172/1483069},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {11}

}