CAREER: Adapting the Fluid Projection Method to Model Elasto-plastic Materials

Harvard University, Cambridge MA

Investigators

Abstract

There are two main ways that materials deform under an applied force. The deformation can be elastic, so that when the force is removed the material recovers its original shape. Alternatively, the deformation can be plastic, whereby the material undergoes irreversible changes that may subsequently lead to breakage. Many materials of technological importance exhibit a combination of these two types of deformation depending on the applied force, and are called elasto-plastic. One example are bulk metallic glasses (BMGs), which are alloys that have an amorphous atomic arrangement in contrast to most metals. BMGs have desirable properties, such as the ability to be processed like plastics, making them attractive candidates for many applications (e.g. next-generation smartphone cases) due to considerable improvements in manufacturing efficiency. However, experimental measurements of BMG breakage properties show wide variations, limiting their usage. To overcome these limitations, it is essential to develop predictive theoretical and computational models of BMG elasto-plasticity. This project is based on a surprising similarity between the equations for elasto-plastic materials and the equations for incompressible fluids. Using this similarity, computational approaches that were originally developed for fluid flow will be translated to elasto-plasticity. These computational methods will be used in collaboration with theorists and experimentalists to study the fracture properties of BMGs. The ultimate aim is to provide a practical engineering tool for predicting when elasto-plastic materials will break, and how to best design structures using them. This work will be undertaken as part of an integrated program of research, teaching, and mentorship, and will involve outreach activities in New England, including a local library lecture series. The projection method of Chorin (1968) is a well-established approach for simulating the incompressible Navier-Stokes equations for fluid flow. This proposal is based on a surprising mathematical correspondence between fluids in the incompressible limit and elasto-plastic solids in the quasi-static limit (when inertia can be neglected). In this proposal, this correspondence is harnessed to translate several modern numerical approaches derived from Chorin's projection method to quasi-static elasto-plasticity, resulting in a practical and powerful set of new simulation tools for a different class of physical problem. Compared to existing techniques, the resultant numerical methods are likely to be especially well-suited to problems involving large plastic deformations. An example type of elasto-plastic material are the bulk metallic glasses (BMGs), which are alloys with many favorable properties such as excellent strength and wear resistance. The numerical methods developed here will be used in a collaboration with theorists and experimentalists to study the fracture toughness properties of BMGs, with the aim of predicting BMG toughness over a wide range of experimental conditions. The PI plans to expand the graduate curriculum in numerical methods to address a pressing need in this area. Open source software will be released as part of this project, and the PI will train students in best practices to make software accessible to a broad audience. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.