Figure 4.

Kinematics of growing surfaces. Material and spatial configurations ${\mathcal{B}}_0$ and ${\mathcal{B}}_t$ with bulk deformation map F shown in green. Material and spatial surfaces ${\mathcal{S}}_0$ and ${\mathcal{S}}_t$ with boundary deformation gradient $\widehat{\mathit{F}}$ and its multiplicative decomposition $\widehat{\mathit{F}}={\widehat{\mathit{F}}}^{\text{e}}\cdot {\widehat{\mathit{F}}}^{\text{g}}$ into an elastic part ${\widehat{\mathit{F}}}^{\text{e}}$ and a growth part ${\widehat{\mathit{F}}}^{\text{g}}$ shown in red.