The notion of Inertial Balanced Viscosity (IBV) solution to rate-independent evolutionary processes is introduced. Such solutions are characterized by an energy balance where a suitable, rate-dependent, dissipation cost is optimized at jump times. The cost is reminiscent of the limit effect of small inertial terms. Therefore, this notion proves to be a suitable one to describe the asymptotic behavior of evolutions of mechanical systems with rate-independent dissipation in the limit of vanishing inertia and viscosity. It is indeed proved, in finite dimension, that these evolutions converge to IBV solutions. If the viscosity operator is neglected, or has a nontrivial kernel, the weaker notion of Inertial Virtual Viscosity (IVV) solutions is introduced, and the analogous convergence result holds. Again in a finite-dimensional context, it is also shown that IBV and IVV solutions can be obtained via a natural extension of the Minimizing Movements algorithm, where the limit effect of inertial terms is taken into account.
Approximation of balanced viscosity solutions of a rate-independent damage model by combining alternate minimization with a local minimization algorithm
Balanced quasistatic evolutions of critical points in metric spaces
CIT School, Technical University of Munich（慕尼黑工业大学 CIT 学院）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；Munich Data Science Institute (MDSI), Technical University of Munich（慕尼黑工业大学慕尼黑数据科学研究所）
