A Displeasing Interest

The Wife reports that the dogs have begun to take an interest in the tomato plants. I bet they're starting to smell like tomatoes. We've also seen the tendrils that will become the base of cucumbers form on that plant, too. How do we keep our beloved but highly destructive and pathologically hungry dogs from eating our vegetables? I thought about netting, but our "aggressive chewer" will work through that pretty quickly -- probably treating the netting like a snack, too. Maybe I have to assemble a wire cage?