Fig. 2

Configurations in updated Lagrangian method. Initial, latest known and unknown configurations of the solid domain, \(\Omega ^s_0\), \(\Omega ^s_n\) and \(\Omega ^s_{n+1}\); maps \(\varvec{\varphi }_a^b\) between configurations \(\Omega _a^s\) and \(\Omega ^s_b\) and the corresponding deformation gradients \(\varvec{F}_a^b\)