Section 6: Material modelling in solid mechanics - GAMM 2012

34 Section 6: Material modelling in solid mechanics
incorporated since the boundary value problem of the non-convex energy function is ill posed [2].
Dealing with multiple energy wells is numerically very challenging. The solution is not deterministic
as any twin configuration can be activated from the parent configuration, which is unknown
initially. Therefore, to have a complete energy landscape in hand at the beginning is impossible.
The material response is instantaneously calculated depending on which twin configuration is
activated. However, the minimum strain energy approach faces its limitation because of elastic
strain energy invariance, which occurs due to the crystallographic equivalence of possible twin
configurations. Having identified the preferred twin configuration, the secondary and, hence, the
multiple twinning are modeled.
[1] Christian J. W., Mahajan S., Deformation Twinning, Prog Mat Sci, 39, 1-157 (1995)
[2] Carstensen C., Ten Remarks on Non-convex Minimization for Phase Transition Simulations,
Comp Meth App Mech Eng, 194, 169-193 (2005)