$\newcommand{\Dev}{\operatorname{Dev}}$ $\newcommand{\dev}{\operatorname{dev}}$ $\newcommand{\grad}{\operatorname{grad}}$ $\newcommand{\Grad}{\operatorname{Grad}}$ $\newcommand{\divg}{\operatorname{div}}$ $\newcommand{\Ei}{\operatorname{Ei}}$ $\newcommand{\tr}{\operatorname{tr}}$ $\newcommand{\Divg}{\operatorname{Div}}$ $\newcommand{\cay}{\operatorname{cay}}$ $\newcommand{\rot}{\operatorname{rot}}$

The virtual work integral $\delta W_{\text{int}}$ in (3.3-5) may be linearized term by term along increments in $\Delta\mathbf{u}$ , $\Delta\tilde{p}$ and $\Delta\tilde{c}$ using the general form $$\begin{equation} D\left(\int_{B}F\,dV\right)\left[\Delta q\right]=\int_{B}DF\left[\Delta q\right]\,dV=\int_{b}f\,dv\,.\label{eq232} \end{equation}$$ For notational simplicity, the integral sign is omitted and the linearization of each term is presented in the form $DF\left[\Delta q\right]\,dV=f\,dv$ .