The partitioned-modeling and similarity methods are applied in this paper to derive a closed-form solution for localized dynamic failure problems, with a nonlinear local damage model. The initial point of the localization is taken as the point at which the type of governing differential equation transforms from being hyperbolic to elliptic for dynamic case due to material damage. The evolution of localization is represented by a moving material surface of discontinuity between the elliptic domain and hyperbolic domain. A closed-form solution for a static loading case is also given as a complementary note to show evolution of the localized failure. The effects of model parameters on the structural response are investigated, and the evolution of relevant field variables is illustrated to demonstrate the essential feature of the localized failure evolution.

Issue Section:
Technical Papers
Keywords:
differential equations, elliptic equations, hyperbolic equations, stress analysis, elastic deformation
Topics:
Damage, Differential equations, Failure, Stress, Modeling
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