A variational multiscale method for inelasticity: application to superelasticity in shape memory alloys. (English) Zbl 1123.74046
Summary: This paper presents a variational multiscale method for developing stabilized finite element formulations for small-strain inelasticity. The multiscale method arises from a decomposition of displacement field into coarse (resolved) and fine (unresolved) scales. The resulting finite element formulation allows arbitrary combinations of interpolation functions for displacement and pressure fields, and thus yields a family of stable and convergent elements. Specifically, equal-order interpolations that are easy to implement but violate the celebrated Babuska-Brezzi condition, become stable and convergent. An important feature of the present method is that it does not lock in the incompressible limit. A nonlinear constitutive model for superelastic behavior of shape memory alloys is integrated in the multiscale formulation. Numerical tests of the performance of elements are presented, and representative simulations of superelastic behavior of shape memory alloys are shown.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74M05 | Control, switches and devices (“smart materials”) in solid mechanics |
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