Name
Abstract | ||
|---|---|---|
This paper addresses the numerical approximation of microstructures in crystalline phase transitions without surface energy. It is shown that branching of different variants near interfaces of twinned martensite and austenite phases leads to reduced energies in finite element approximations. Such behavior of minimizing deformations is understood for an extended model that involves surface energies. Moreover, the closely related question of the role of different growth conditions of the employed bulk energy is discussed. By explicit construction of discrete deformations in lowest order finite element spaces we prove upper bounds for the energy and thereby clarify the question of the dependence of the convergence rate upon growth conditions and lamination orders. For first order laminates the estimates are optimal. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1007/s00211-003-0483-8 | Numerische Mathematik |
Keywords | Field | DocType |
lamination order,finite element method,nonlinear elasticity,bulk energy,multiscale resolution,growth condition,microstructure,different variant,finite element approximation,different growth condition,lowest order,reduced energy,finite element space,crystalline microstructure,multi-well problem,multiscale analysis,surface energy,non-convex minimization,convergence rate,upper bound,first order,phase transition,microstructures,finite element | Phase transition,Upper and lower bounds,Mathematical analysis,Calculus of variations,Finite element method,Rate of convergence,Numerical analysis,Surface energy,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
96 | 4 | 0029-599X |
Citations | PageRank | References |
2 | 0.67 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sören Bartels | 1 | 355 | 56.90 |
| Andreas Prohl | 2 | 302 | 67.29 |