Should one stick to their expertise/experience area post PhD? I am currently writing my Mechanical engineering PhD thesis. My research was based on modeling a 3D printing process. The work was interesting but I feel that there's not much rigoresness in the modeling aspect of the work. I tried to think differently from existing published works by other researchers, but still the inherent problems with the actual process makes it hard to develop an accurate model using current theories and modeling techniques.

Thus, I want to explore different topics post PhD. However, on discussing my future career with her, she advised that I should stick with my area of expertise/experience and should also pursue similar endeavours during post doctoral research. According to her, that would make you stand out as an expert in the modeling aspect of the field.

I don't know what should I do? Should I deviate from the PhD research area post graduation or should I listen to my advisor and stick to my 'less rigorous' area of expertise? I would eventually like to stay in academia.
One of the advantages of academia is that, in general, you get to follow your nose into whatever research corner you want to explore. You can change incrementally over time or you can make big jumps. Of course, you probably want to stay employed, so it is requires a bit of finesse and maybe negotiation. 

But the big lesson is that your early work doesn't constrain your mind from think other thoughts and your past doesn't constrain your future if you are willing to work for it. But the same thing is true for people outside academia where such change is possible, though possibly harder. Resource constraint, for example. 

Do what you love if you are able. 

That, actually, is what keeps a lot of people (most?) in academia even though the pay may be less than what they could earn elsewhere.