= Solution
In the <current configuration>, <balance of linear momentum> is the <Cauchy momentum equation>
$$
\boxed{\operatorname{div}_x\tau+\rho b=\rho\left(\partial_t v+(v\cdot\nabla_x)v\right).}
$$
Here $\tau$ is the <Cauchy stress tensor>, $\rho$ is current <mass density>, $b$ is <body force> per unit <mass>, and $v(x,t)$ is the <velocity> of the material particle currently at $x$. The expression in parentheses is the <material acceleration>. The <divergence> is taken in current spatial coordinates, with $(\operatorname{div}\tau)_i=\partial_j\tau_{ij}$.
Equivalently the right side is $\rho\partial_t^2x(X,t)$ evaluated at the particle, because this is the same <material acceleration> in <Lagrangian coordinates>. For the subsequent static inflation with negligible <body force>, the equation reduces to $\operatorname{div}\tau=0$.
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