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I joined for my PhD in mechanical engineering in a Canadian university almost 3 years back. I had completed the necessary coursework and preliminary exam last July. My advisor had approved my research proposal to develop a numerical procedure to predict the damage behavior of composities during a complex loading condition. It is a really challenging topic and I wanted to give my best in solving the problem. My committee members were also satisfied with my research proposal and projected timelines.

Howevever, till now, I have not been able to get any substantial progress on the research topic. I am facing a lot of theoretical issues and my research topic is very loosely related to the expertise of my advisor. As a result his technical suggestions are not quite relevant and helpful. There's no one in the department who can help me in this regard.

Last week, my advisor suggested to change my research topic to a different one within the realm of the grants objectives. The modified researh area won't require the development any numerical procedure. Instead I will be using a commercial software with inbuilt procedures to get the results. I won't be able to publish in a reputed numerical or theoretical journals and will have to settle for decent application oriented journals. I don't want my PhD to just be one where I pressed some buttons to get the answer. I wanted it to be rigorous.

I am not sure what would be the implications if I accept to my advisors suggestion. On one hand the modified direction would guarantee atleast 3 decent publications. On the other hand, I don't know if I will be able to solve the theoretical problem soon enough to generate results. But if solved, will lead to a theoretically intensive paper and a lot of learning opportunity as a researcher.

What should I do? I will be funded for 5 years. And I would like to stay in academia in the future.

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Go with the advisor's suggestion. Based on your current progress, they are in a good position to make an informed decision about the feasibility of completion of your degree within the limited timeframe. Once you are in a good position to write your thesis, you can work on the difficult theoretical problem. You will have a better understanding of the theoretical problem 1-1.5 years from now. Probably you might even solve it. Right now, do as your advisor tells you.

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But if solved, will lead to a theoretically intensive paper and a lot of learning opportunity as a researcher.

The issue here is whether you have done a lot of learning and developed your opportunity as much as you can. If you have hit a the wall from the theoretical point of view then you will likely be wasting your time and have an unsatisfying thesis without any firm conclusions. Unfortunately there is no way to know this definitely from your standpoint.

One way is to expand and develop new collaborations so you can develop your theoretical understanding further. Does your institution allow for collaboration and supervision with another institution? Are there experts that can help you and would be interested in developing this theoretical issue further? Are there networks or groups that you can post and get feedback on specific aspects of your issue (without you having to disclose your whole problem and risking plagiarism)? Maths SE, engineering SE, Facebook groups etc.

Personally, your theoretical problem sounds better suited to a post doc rather than a PhD. It is too high risk and not linked to grant opportunities and practical application right away. Managing and engaging with a grant projects is an important aspect of academia. Applying for further grants and being involved is an important skill in itself. If you are keen for academia, you would need to appreciate how important this skill is. Consistency and regular and high volume publication seems to be more appreciated and valued than solving one big problem resulting in just one important paper. Even after solving the theoretical problem, you would be publishing what you call boring application papers afterwards.

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I'd suggest, pretty strongly, that you go with your advisor's guidance and turn the original project into a longer term goal. Your research career needn't end with the doctorate and it would be good to finish with some work done on a difficult future project.

But the short term goal should be to get out the door with good letters of recommendation and enough of a push to get you into academia. What you can do after that is up to you and the possibilities you can bring to bear on your research.

For what it's worth. I have a friend who is a reputed computer scientist. Top education, works in top level industrial gigs. But he also writes poetry. In fact, for more than ten years he has written a poem every day, without fail. The deadline for the poem is strict. But he described his methodology to me as something like, starting out with high standards and expectations for the day and continually lowering them until he has something acceptable. He gets the job done, and saves the rest for another day.

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