The asymptotic stability of solutions of the Mindlin-type microstructure model for solids is analyzed in the paper. It is shown that short waves are asymptotically stable even in the case of a weakly non-convex free energy dependence on microdeformation.
The Mindlin-type microstructure model cannot describe properly short wave propagation in laminates. A modified Mindlin-type microstructure model with weakly non-convex free energy resolves this discrepancy. It is shown that the improved model with weakly non-convex free energy is asymptotically stable for short waves.
Computational Materials Science
Scholarly Commons Citation
Berezovski, M., & Berezovski, A. (2012). On the Stability of a Microstructure Model. Computational Materials Science, 52(1). https://doi.org/10.1016/j.commatsci.2011.01.027
Mechanics of Materials Commons, Numerical Analysis and Computation Commons, Partial Differential Equations Commons
Dr. Mihhail Berezovski was not affiliated with Embry-Riddle Aeronautical University at the time this paper was published.