Elastic incompressibility
= Elastic incompressibility
{title2=$\det\mathbf A=1$}
Volume preservation by the elastic accommodation in <morphoelasticity>. If $\mathbf F=\mathbf A\mathbf G$, <elastic incompressibility> imposes $\det\mathbf A=1$, and hence $\det\mathbf F=\det\mathbf G$. Total volume can increase through growth while the elastic response remains incompressible. A <hydrostatic pressure> acts as a <Lagrange multiplier> enforcing this constraint in the <Cauchy stress tensor>.