On a variational model for phase transformation in SiO2 glass
The compaction mechanisms of SiO2 glass under pressure include under certain conditions a specific reduction of the elastic moduli and a complex inelastic behavior whose nature is not yet fully understood. In our work we establish a variational framework describing the evolution of SiO2 glass under hydrostatic pressure. Based on a previous work that presents a model for multi-phase transformations in inelastic materials, we assume isothermal conditions during a compaction process and interpret the typical sigmoidal stress response as indicator of a binary phase transformation. During the process, two volume fractions coexist macroscopically and microstructures such as shear bands or disclination pattern develop in between. We restrict our approach to resolve only the volume fractions, not the corresponding microstructures. Nevertheless, the resulting model is shown to match experimental findings very well. Numerical examples successfully illustrate the relationship between the changes in the elastic moduli and the corresponding change in volume with respect to pressure.