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Mesh sensitivity in dynamic analyses

Dear all,

I am testing suitability of Drucker-Prager criterion to model concrete under high strain rates (it is well established in literature). In my model (VUMAT in Abaqus/Explicit) I am using linear softening model but I struggle with mesh sensitivity. As soon as material reaches softening the governing equation becomes elliptic and hence propagating wave is trapped inside an element thus mesh sensitivity is encounter. Literature suggests that in order to cope with that higher time derivatives of displacement (either with respect to time or space) should be included in governing equation. In my constitutive equation I am also using Dynamic Intensification Factor (DIF) which increases strength of concrete and is dependent on strain rate (so this is my higher derivative of displacement) but still my results are mesh-biased. Is there any simple way to deal with that without introducing visco-elasticity or gradient-based plasticity? How would you normally cope with mesh sensitivity using standard models in Abaqus?

PS. I attach my constitutive relation.

Regards,

Aleksander

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