Is there a way to redeem your career? Of course there is, but it depends on what you really want out of your career.
The most important questions to answer are, "What do I enjoy doing?" and "What am I good at". You seem to have questions about that latter (at least relative to other PhD candidates in the same field), but it is not clear to most responders here that your feelings are completely based in reality. Many people are unsure of themselves. It can be a very good thing if humility and a rational comprehension of your weaknesses drives you to learn more and work harder. It can be very harmful to your success if a lack of confidence keeps you from attempting hard or unsure things.
What do faculty at research universities actually do? Teach, guide students at various levels, write proposals, creatively think of problems to solve and how to solve them, exercise technical expertise, write and publish papers, travel and speak, serve on department committees, self-promote, and compete against one another. How many of those things do you enjoy doing, or are you good at, or preferably, both? If "not many" is the answer, then whether you are better than 99.9999% or just 99.9% of people in the world at Applied Mechanics is irrelevant: find something else to do. You are smart and quantitative and can compete quite effectively in many many valued roles in society.
What elements of your own work or work you've seen around you actually excite you; do you find inherently interesting just because of who you are and what they are? Find a career that overlaps as much as possible and then pick a post-doc or industrial job or peace corps stint or MBA or whatever that gets you closer to doing those things.
It is actually not all that rare for a smart person to go quite far in their education before they found out that they are not all that interested in their field (or in an academic approach to it). Starting out, the challenges of just going through the process can be interesting enough and obscure an underlying apathy.
If, after reflection, you really do want an academic career in a particlar field, then do whatever honorable things it takes to succeed there. If you are not all that happy with your thesis, then work hard to get a post-doc with the most famous person you can in an area most of interest to you. Who will help you get several really sexy publications?
If you really don't want an academic career, get out asap (after getting the degree...) Write code, design or build machines, solve problems, teach at a different level. Get an industrial job that both overlaps with your applied mechanics background and will expose you as much as possible to other roles in R&D, product development, business, management,and human society in general.
"Do what you love" beats "Follow down the path I'm on because I'll feel like a failure if I don't" by a thousand miles.