diff options
Diffstat (limited to 'content/know/concept/cauchy-strain-tensor')
| -rw-r--r-- | content/know/concept/cauchy-strain-tensor/index.pdc | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/content/know/concept/cauchy-strain-tensor/index.pdc b/content/know/concept/cauchy-strain-tensor/index.pdc index 2994674..f150723 100644 --- a/content/know/concept/cauchy-strain-tensor/index.pdc +++ b/content/know/concept/cauchy-strain-tensor/index.pdc @@ -54,7 +54,7 @@ $$\begin{aligned} Let us choose two nearby points in the deformed solid, and call them $\va{x}$ and $\va{x} + \va{a}$, where $\va{a}$ is a tiny vector pointing from one to the other. -Before the displacement, these points respectively had these positions, +Before the displacement, those points respectively had these positions, where we define $\va{A}$ as the "old" version of $\va{a}$: $$\begin{aligned} @@ -159,7 +159,7 @@ $$\begin{aligned} = 2 \va{a} \cdot \hat{u} \cdot \va{b} \end{aligned}$$ -The Cauchy strain tensor $\hat{u}$ is a second-order tensor, +The Cauchy strain tensor $\hat{u}$ is a second-rank tensor, and can alternatively be expressed like so: $$\begin{aligned} @@ -320,7 +320,7 @@ we remove it, and isolate the rest for $\delta(\dd{\va{S}})$: $$\begin{aligned} \boxed{ \delta(\dd{\va{S}}) - = \big( (\nabla \cdot \va{u}) \va{1} - \nabla \va{u} \big) \cdot \dd{\va{S}} + = \big( (\nabla \cdot \va{u}) \hat{1} - \nabla \va{u} \big) \cdot \dd{\va{S}} } \end{aligned}$$ |