Abstract
We give results for the approximation of a laminate with varying volume fractions for multi-well energy minimization problems modeling martensitic crystals that can undergo either an orthorhombic to monoclinic or a cubic to tetragonal transformation. We construct energy minimizing sequences of deformations which satisfy the corresponding boundary condition, and we establish a series of error bounds in terms of the elastic energy for the approximation of the limiting macroscopic deformation and the simply laminated microstructure. Finally, we give results for the corresponding finite element approximation of the laminate with varying volume fractions.
Original language | English (US) |
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Pages (from-to) | 67-87 |
Number of pages | 21 |
Journal | Mathematical Modelling and Numerical Analysis |
Volume | 33 |
Issue number | 1 |
DOIs | |
State | Published - 1999 |
Keywords
- Error estimate
- Finite element
- Martensitic transformation
- Simple laminate
- Volume fraction
- Young measure