Short-time regularity for dynamic evolution problems in perfect plasticity

ABSTRACT

In this paper, we study the regularity properties of solutions of dynamic evolution problems in perfect plasticity. We prove that for any space dimension and for any closed convex set of constraints containing zero as an interior point, the solutions are regular in space during a short time interval if the data are smooth and compactly supported. The result is based on the hyperbolic structure of the model, namely the finite speed propagation property.

Keywords:

• Elasto-plasticity
• regularity
• finite speed propagation
• comparison principle

2010 Mathematics Subject Classifications:

• 74C05
• 35B65
• 26A45
• 35B51

Acknowledgements

The author wishes to express his thanks to Jean-François Babadjian for many stimulating conversations.

Disclosure statement

No potential conflict of interest was reported by the author(s).