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Dynamic Fragmentation of Geological Materials

Continuum Damage Mechanics (CDM) is a way to understand material damage from a continuum level. Borrowing ideas from plasticity, CDM quantifies damage in a material by introducing a fictitious 'undamaged' configuration mapped by a damage deformation tensor. Based on the type of damage under consideration, an evolution law for the damage tensor can be prescribed. There are different variants of CDM that deal with this fictitious configuration in different ways. The theoretical framework including thermodynamical constraints and consistency with conventional mechanics is an important issue.

CDM can be used to understand dynamic fragmentation of brittle materials. One of the prominent models for dynamic fragmentation was introduced by Grady and Kipp in 1980s. Grady-Kipp model is based on a single variable theory, which introduces D (the volume fraction of microcracks in the material) as the damage variable. Our work focuses on using CDM to understand dynamic fragmentation of geological materials such as rocks, basalt, ice, etc. The applications include micro-meteorite impact on satellites, fragmentation of rocky or icy surface of planetary entities upon high velocity impact and fragmentation response of armor upon ballistic impact.

Our current numerical framework implements damage modeling in a very general way by using deformation tensors. We are conducting fragmentation simulations through high velocity impact using a Grady-Kipp model. One of the primary objectives is to go beyond the Grady-Kipp model and introduce a thermodynamically consistent model that accounts for the anisotropic effects. Further, a direct relation between crack phenomenon and the anisotropic CDM model needs to be established.

Ferroic and Multiferroic Materials

Due to the nonlinear nature, materials like ferroelectrics and ferromagnets have found a lot of applications in the real world. It is important to understand how these materials behave under different loading conditions. One of the widely accepted ways to understand the continuum nature of such materials is to analyze the domain wall motions. In a ferroelectric material, the internal energy is a function of various parameters including spontaneous polarization, polarization gradient, deformation gradient and entropy. The spontaneous polarization behavior is thus coupled with mechanical distortion. Application of external electrical and mechanical loading can drive domain walls inside the material.  This makes the dynamic study of such materials even more important. 

Ferromagnetic materials offer a rich spectrum of physics due to the complex underlying dynamics of electron spins. Recently, ferromagnets have found plenty of applications due to their properties like large magnetostriction, magnetoelasticity and shape memory effects. These range from bio-medical stent implants to flux magnetic generators and even to space applications. Hence, it is important to develop physics based models that can capture the behavior of these materials effectively. While significant efforts have been put in towards understanding the underlying physics, a lot of questions still remain. Unlike ferroelectricity, the magneto-mechanical coupling appears indirectly in the material. I am interested in developing physics based models that describe the behavior of ferromagnetic materials taking into account the mechanical coupling like shape memory effects, magnetoelasticity and zero hysteresis materials.

It has been experimentally observed that under high strain rate deformation conditions (like plate impact), a ferroelectric material loses its polarization. The sudden depolarization causes a large electric discharge and generates huge electric fields. Impact induced shock wave propagates through the ferroelectric material causing phase transformation. At low impact speeds, the pressures are not high enough to cause complete depolarization while at very high speeds dielectric breakdown can happen. In case of a ferroelectric ceramic, one can also observe compaction. I am interested in understanding this large deformation dynamic behavior of such materials. The theoretical framework for ferroelectrics can be implemented to ferromagnets with some modifications.

Mechanics of Heterogeneous Materials

Every material is heterogeneous at some length scale - from point defects in crystals to different components in composites. While numerous studies have been conducted to understand heterogeneous materials at different length scales, plenty more still remains to be understood. It has been known for a while that the response of heterogeneous materials under dynamic load differs significantly from the static response. One such loading regime is high pressure, high strain rate conditions. Typically these conditions are achieved during high velocity impacts. Characterizing materials under this regime gives valuable information of material strength, plastic response, energy dissipation and phase transitions.

Upon high velocity impact, shock waves travel through the heterogeneous medium. Due to the heterogeneous nature of the material, shock undergoes reflections and scattering as it travels through the medium leading to even more complex interactions. While this goes on in the macro-scale, many complex processes happen at the micro and meso scales. Plate impact experimental studies have shown that a structured steady shock develops as it propagates through the medium. I am interested in developing an overarching theoretical framework that takes into account the processes like scattering, viscoplasticity, fracture, and dissipation and explains the observed trends. This requires understanding the material behavior under these conditions at different length scales - dislocation motion and void growth in the micro-scale; grain boundary motions, cracking and growth of grains in the meso scale; and finally interfacial interactions and overall yielding in the macro-scale.