Dynamic Relaxation and Recovery of Shear Strength in Porous Compaction

Under quasistatic loading, the shear strength of granular materials is pressure dependent due to frictional resistance at contact points, and the strength increases with pressure and with the solid volume fraction until at high pressure, plasticity in the solid phase limits the strength in the material. For an initially porous material that has been compacted to zero porosity, the high-pressure shear strength is often assumed to equal that of the solid phase, in the absence of additional damage or thermal softening. New methods for modeling comminution and compaction for shock-loaded brittle materials were developed to numerically investigate the validity of this assumption. Mesoscale simulations of shock compression of both ductile and brittle powders reveal that the shear stress in a shocked material may be far below the quasistatic strength or the porosity-scaled shear strength of the solid phase – even in the absence of damage or thermal effects.

A dynamic relaxation mechanism is identified that results from heterogenous deformation and locking of misaligned shear stresses, but we show that strength may be recovered under re-shock or sustained shear deformation up until thermal softening dominates the response. These results imply that the apparent strength that should be used when computing hydrostatic pressure from the shock stress in a 1-D Hugoniot experiment may be much lower than the shear strength needed to match the material response in high-shear applications such as wellbore completion, ballistic penetration, or asteroid deflection. Additional relaxation mechanisms may be active for architected materials with long-range order where local buckling can lead to cascading pore collapse and shear banding.

We present mesoscale modeling results and propose a new continuum strength and compaction model forms to describe these relaxation and recovery effects. We also provide numerical simulations of various shock-shear experimental platforms to assess the extent to which the observables in these experiments are sensitive to the relaxed vs. the recovered shear strength and provide a path towards validation of the new strength models.