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Abstract

Waves can propagate in a continuum only when the tangent stiffness tensor of the material is positive definite. The wave equation appears to lose its hyperbolicity with the advent of material softening. To overcome this difficulty, a partitioned-modeling approach with the use of local elastodamage models is applied to solving wave problems involving material degradation. A closed-form solution for wave propagation in a damaged bar is derived in this paper, with the use of the similarity method in the partitioned domain. The initial point of the localization is taken as the point at which the type of governing differential equation transforms from a hyperbolic one to an elliptic one due to material damage. The evolution of localization is represented by a moving material surface between the damaged domain and non-damaged domain. The motion of the material surface is of diffusion type, representing macroscopically the progressive percolation of heterogeneous microdamage. Based on the analytical solution, a numerical procedure is then proposed for the partitioned-modeling approach. The fast convergence of the proposed numerical procedure is shown by comparing the numerical solutions with the analytical ones. The numerical procedure is then applied to the simulation of failure wave with the use of a local damage model. It is shown that the evolution of dynamic localization can be simulated without invoking higher order terms if a moving material surface of discontinuity is introduced.

Keywords

elastodamage dynamic failure localization moving surface of discontinuity

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An Analytical and Numerical Study to Simulate the Evolution of Dynamic Failure with Local Elastodamage Models

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