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Important physical observations in rupture dynamics such as static faultfriction, short-slip, self-healing, and supershear phenomenon in cracks arestudied. A continuum model of rupture dynamics is developed using the fielddislocation mechanics (FDM) theory. The energy density function in our modelencodes accepted and simple physical facts related to rocks and granularmaterials under compression. We work within a 2-dimensional ansatz of FDM wherethe rupture front is allowed to move only in a horizontal fault layersandwiched between elastic blocks. Damage via the degradation of elasticmodulus is allowed to occur only in the fault layer, characterized by theamount of plastic slip. The theory dictates the evolution equation of theplastic shear strain to be a Hamilton-Jacobi (H-J) equation, resulting in therepresentation of a propagating rupture front, which is fully coupled toelastodynamics in the whole domain. Our simulations recover static frictionlaws as emergent features of our model, without putting in by hand any suchdiscontinuous criteria. Estimates of material parameters of cohesion andfriction angle are deduced. Short-slip and slip-weakening (crack-like)behaviors are also reproduced as a function of the degree of damage behind therupture front. The long-time behavior of a moving rupture front is probed, andit is deduced that the equilibrium profiles under no shear stress are nottraveling wave profiles under non-zero shear load. However, it is shown that atraveling wave structure is likely attained in the limit of long times.Finally, a crack-like damage front is driven by an initial impact loading, andit is observed in our simulations that an upper bound to the crack speed is thedilatational wave speed of the material unless the material is put underpre-stressed conditions, in which case supersonic motion can be obtained.

Emergent fault friction and supershear in a continuum model of geophysical rupture