Models and Phenomena in Fracture Mechanics

Abstract

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Shocks versus kinks in a discrete model of displacive phase transitions

“…Assuming V > 0, we obtain that V g ≷ V whenever r ∂g α ∂r (r, V ) ≷ 0. This condition follows from the causality principle [20] and can also be obtained in the limit of zero viscosity [31]. The notation r ± i0 will be used to reflect the effect of the radiation condition on the real roots.…”

“…On the macroscopic level, these waves are invisible, and the energy radiation is perceived as dissipation. This radiative damping phenomenon is commonly observed when a defect (whether it is a dislocation, a crack or a phase boundary) propagates through a lattice, e.g., [2,4,[9][10][11]13,20].…”

Dynamics of a Fault Steadily Propagating within a Structural Interface

“…The numerical computations in Figure 5 suggest that small values of s/c correspond to a wider interval of the values of V describing a stable propagation of the fault. Finally, following a complex motivation provided by Slepyan (2002), we note that the quantity shown in Figure 5 can also have a link to the dissipation energy carried by the waves initiated by the propagating fault. Figure 5 emphasizes the differences between the continuous and discrete models of fault propagation.…”

“…Now, following Slepyan (2002), the discrete problem equations (2) are transformed into a problem depending with continuity on the variable…”

“…Modeling of fracture in an infinite lattice has been initiated by Slepyan (2002Slepyan ( , 2005 and extended in different directions by Movchan and Slepyan (2007) and Slepyan (2008, 2009). Lattice Green's functions have been analyzed by Martinsson and Rodin (2002) and Martin (2006) and applications to subcritical crack growth given by Zhao, Makarov, and Rodin (2011).…”