The doctor of philosophy degree in engineering mechanics is offered within a graduate program covering contemporary areas in both theoretical and applied mechanics. With the guidance of a major professor, a program can be designed to meet an individual student's needs and interests.
This program is broadly structured into several main areas of instruction and research interests in fluid and solid mechanics: continuum mechanics, computational mechanics, dynamics and vibration, nanomechanics, and biomechanics. Related fields include civil and environmental engineering, chemical and biological engineering, electrical and computer engineering, materials science, mechanical engineering, nuclear engineering and engineering physics, physics, geological engineering and geology, mathematics, statistics, and computer science.
Current faculty research interests include contact mechanics, elastic instabilities, micromechanics, wave propagation, adhesion and friction, multi-scale and high-performance computational modeling, multi-physics mechanics and transport, biophysics, nanotechnology and nanomaterials, mechanics of soft materials, bio-inspired materials, polymer thin-films, renewable energy, and acoustic/elastic metamaterials.
Laboratories are well equipped for experimental testing and research; these include, atomic force microscopy, vibration testing, and other optical methods for experimental mechanics research. The department has access to collegewide facilities. The Wisconsin Laboratory for Structures and Materials Testing has facilities for testing large structures, fatigue and vibration labs, and complements the department's laboratories. The Nanoscale Imaging and Analysis Center provides state-of-the-art instrumentation, support facilities, and expert technical assistance for research and education in materials. Its facilities include scanning and transmission electron microscopes, image processing and analysis systems, surface and thin film characterization facilities, and x-ray diffraction facilities.
Admissions
Please consult the table below for key information about this degree program’s admissions requirements. The program may have more detailed admissions requirements, which can be found below the table or on the program’s website.
Graduate admissions is a two-step process between academic programs and the Graduate School. Applicants must meet the minimum requirements of the Graduate School as well as the program(s). Once you have researched the graduate program(s) you are interested in, apply online.
| Fall Deadline | December 15 |
| Spring Deadline | September 1 |
| Summer Deadline | December 15 |
| GRE (Graduate Record Examinations) | Not required.* |
| English Proficiency Test | Refer to the Graduate School: Minimum Requirements for Admission policy: https://policy.wisc.edu/library/UW-1241. |
| Other Test(s) (e.g., GMAT, MCAT) | n/a |
| Letters of Recommendation Required | 3 |
- *
Submitted scores will not be used in admission decisions.
Applicant Considerations
Applicants to our program should have the following:
- Degree
- Bachelor of Science in engineering, mathematics, or physical science and an undergraduate record that indicates an ability to successfully pursue graduate study.
- International applicants must have a degree comparable to a regionally accredited US bachelor's degree. Review the Graduate School webpage to learn more about comparable degrees by country.
- GPA
- The minimum required GPA is 3.0/4.0 on the equivalent of the last 60 semester hours from the most recent bachelor's degree or a completed master's degree with a minimum of 3.0/4.0.
- Faculty Advisor
- Applicants must seek out and secure their own faculty advisor as part of the application process. This may be done prior to, during, and/or after submission of the online application.
- To seek out a faculty advisor, review the department Research and People websites. Assistant Professors, Associate Professors, and Professors are eligible to be graduate advisors. Please do not contact Emeritus faculty, lecturers, Research Scientists, or Faculty Associates.
- You are encouraged to inquire about possible funding opportunities. (See Funding tab in the right-side column on this page for funding information.)
- Recommended Preparatory Courses
- It is highly recommended applicants take courses that cover the same material as these UW-Madison courses before entering the program.
- Applicants may be admitted without having taken these courses, however, in such cases the applicant must inform their faculty advisor who will then help them select the correct courses to include the required background for the program.
| Code | Title | Credits |
|---|---|---|
| Advanced Mathematics | 3 | |
| Techniques in Ordinary Differential Equations | ||
or MATH 320 | Linear Algebra and Differential Equations | |
or MATH 321 | Applied Mathematical Analysis 1: Vector and Complex Calculus | |
| Linear Algebra and Matrices | 3 | |
| Linear Algebra and Differential Equations | ||
or MATH 340 | Elementary Matrix and Linear Algebra | |
| Mechanics of Materials | 3 | |
| Mechanics of Materials | ||
| Dynamics | 3 | |
| Dynamics | ||
or PHYSICS 311 | Mechanics | |
Application Materials
In addition to the items listed in the table above, a complete application includes the following uploaded to the online application. The submitted application and all application items are due by the deadline above.
- Unofficial Transcripts (PDF)
- Most up-to-date unofficial transcript(s) from all previous higher education institutions, regardless of whether a degree was earned. Official transcripts are only requested of recommended applicants.
- International academic records must be in the original language accompanied by an official English translation. Review the minimum requirements link above to learn more.
- Statement of Purpose
- In this document, applicants should explain why they want to pursue further education in Engineering Mechanics, specifically this program, research interests, and which UW faculty they are interested in working with.
- The program does not have a required font, word limit, etc. However, we do recommend (not require) a maximum of 2 pages.
- See the Graduate School for more advice on how to structure a personal statement.
- Resume
- Three Letters of Recommendation
- These letters are required from people who can accurately reflect on the applicant's academics and/or work performance. It is highly recommended these letters be from faculty familiar with the applicant.
- Letters of recommendation are submitted electronically through the online application.
- See the Graduate School FAQs regarding letters of recommendation.
- Application Fee
- Application submission must be accompanied by the application fee. See the Graduate School FAQs regarding fees.
- Fee grants are available through the conditions outlined here by the Graduate School.
Reentry Admissions
Review the Graduate School requirements for previously enrolled students. Contact the Department of Mechanical Engineering Graduate Student Services (see Contact Box for link) with questions.
Currently Enrolled Graduate Student Admissions
Students currently enrolled as graduate students at UW-Madison wishing to apply to this degree programs should contact the Department of Mechanical Engineering Graduate Student Services (see Contact Box for link) to inquire about the process and deadlines.
Questions
Contact the Department of Mechanical Engineering Graduate Student Services (see Contact Box for link).
Funding
Graduate School Resources
The Bursar’s Office provides information about tuition and fees associated with being a graduate student. Resources to help you afford graduate study might include assistantships, fellowships, traineeships, and financial aid. Further funding information is available from the Graduate School. Be sure to check with your program for individual policies and restrictions related to funding.
Program Resources
There are three mechanisms for Graduate Student funding through the university for Engineering Mechanics PhD students:
- Fellowships
- Graduate assistantships: project assistantships, teaching assistantships, and research assistantships
- Traineeships
Funding is awarded based on the qualifications of the student, the number of applicants, the amount of available funding, the number of continuing students receiving support, and the degree program a student is enrolled in. You can apply for funding for research assistantships by contacting individual faculty members directly. Review our website to look for faculty (only those listed with titles of assistant professor, associate professor, or professor can serve as graduate student advisors). Search for faculty who have research interests that align closely with your own by viewing faculty directory entries, visiting the faculty’s website (linked from the directory page), and reviewing publications by the faculty member. After you have identified faculty with interests close to your own, you are encouraged to contact them by email to inquire regarding available research assistant positions. The admissions office does not know if a particular professor has research assistant positions available.
Students who apply to the PhD program will be automatically considered for fellowship opportunities within the department. Admitted students will be eligible to apply for Teaching Assistantship positions. More information, including the application, will be available to students after admission is complete.
More information on graduate student funding is available from the UW-Madison Graduate School.
Additional Resources
Office of Student Financial Aid
For information regarding student financial aid, scholarships, and more, visit the Office of Student Financial Aid website.
International Student Services Funding and Scholarships
For information regarding international student funding and scholarships, visit the International Student Services website.
Minimum Graduate School Requirements
Review the Graduate School minimum degree requirements and policies, in addition to the program requirements listed below.
Major Requirements
Mode of Instruction
| Face to Face | Evening/Weekend | Online | Hybrid | Accelerated |
|---|---|---|---|---|
| Yes | No | No | No | No |
Mode of Instruction Definitions
Accelerated: Accelerated programs are offered at a fast pace that condenses the time to completion. Students typically take enough credits aimed at completing the program in a year or two.
Evening/Weekend: Courses meet on the UW–Madison campus only in evenings and/or on weekends to accommodate typical business schedules. Students have the advantages of face-to-face courses with the flexibility to keep work and other life commitments.
Face-to-Face: Courses typically meet during weekdays on the UW-Madison Campus.
Hybrid: These programs combine face-to-face and online learning formats. Contact the program for more specific information.
Online: These programs are offered 100% online. Some programs may require an on-campus orientation or residency experience, but the courses will be facilitated in an online format.
Curricular Requirements
| Minimum Credit Requirement | 60 credits |
| Minimum Residence Credit Requirement | 32 credits |
| Minimum Graduate Coursework Requirement | 30 credits must be graduate-level coursework. Refer to the Graduate School: Minimum Graduate Coursework (50%) Requirement policy: https://policy.wisc.edu/library/UW-1244. In addition, at least 18 of the non-research credits must be in classes having the graduate-level designation. |
| Overall Graduate GPA Requirement | 3.00 GPA required. Refer to the Graduate School: Grade Point Average (GPA) Requirement policy: https://policy.wisc.edu/library/UW-1203. |
| Other Grade Requirements | Students must earn a C or above in all formal coursework. Students may not have more than two Incompletes on their record at any one time. |
| Assessments and Examinations | PhD qualifying examination is required of all students. After acceptance of the student’s doctoral plan of study, the student must take an oral preliminary examination. Final oral examination is required at the end of the thesis work. |
| Language Requirements | No language requirements. |
| Graduate School Breadth Requirement | All doctoral students are required to complete a doctoral minor or graduate/professional certificate. Refer to the Graduate School: Breadth Requirement in Doctoral Training policy: https://policy.wisc.edu/library/UW-1200. Students should consult with advisor. |
Required Courses
At least 36 of the required 60 credits must be in classes satisfying the following: general requirements, mathematics requirements, breadth requirement, and depth requirement. All courses must be numbered 500 and above, except for the 400-level courses identified in the pre-defined course lists. It is acceptable for students who earned an MS degree in Engineering Mechanics at UW-Madison to use coursework completed while in the MS degree program to meet the requirements below.
| Code | Title | Credits |
|---|---|---|
| Seminar Requirement | ||
| Two terms of M E 903 are required and must be successfully completed. These should be taken in the first two terms of enrollment. | 0 | |
| Graduate Seminar (taken twice) | ||
| General Requirements 1 | ||
| At least 21 credits must be in coursework numbered 600 and above OR from the following list: | 21 | |
| Aerodynamics Laboratory | ||
| Flight Dynamics and Control | ||
| Composite Materials | ||
| Fracture Mechanics | ||
| Experimental Vibration and Dynamic System Analysis | ||
| Heterogeneous and Multiphase Materials | ||
| Engineering Analysis I | ||
| Engineering Analysis II | ||
| Experimental Mechanics | ||
| Mathematics Requirements 1 | ||
| At least 6 credits (2 courses) must be in applied mathematics from the following list: | 6 | |
| Engineering Analysis I | ||
| Engineering Analysis II | ||
| Ordinary Differential Equations | ||
| Analysis I | ||
| Analysis II | ||
| Linear Algebra II | ||
| Analysis of Partial Differential Equations | ||
| Complex Analysis | ||
| Methods of Applied Mathematics 1 | ||
| Methods of Applied Mathematics-2 | ||
| Methods of Computational Mathematics I | ||
| Methods of Computational Mathematics II | ||
| Breadth Requirement 1 | ||
| As part of their MS or PhD, students must complete courses from at least 2 of the 3 areas defined below (Solid Mechanics, Fluid Mechanics, Dynamics). For each of the 2 areas, the student must complete at least 2 courses. | 12 | |
| Solid Mechanics | ||
| Aerospace Structures | ||
| Composite Materials | ||
| Fracture Mechanics | ||
| Heterogeneous and Multiphase Materials | ||
| Experimental Mechanics | ||
| Introduction to Finite Elements | ||
| Advanced Mechanical Testing of Materials | ||
| Micro- and Nanoscale Mechanics | ||
| Viscoelastic Solids | ||
| Theory of Elasticity | ||
| Plasticity Theory and Physics | ||
| Advanced Topics in Finite Elements | ||
| Advanced Composite Materials | ||
| Introduction to Polymer Rheology | ||
| Mechanics of Continua | ||
| Finite Elements for Biological and Other Soft Materials | ||
| Friction, Lubrication and Wear | ||
| Fluid Mechanics | ||
| Aerodynamics | ||
| Flight Dynamics and Control | ||
| Gasdynamics | ||
| Mechanics of Continua | ||
| Intermediate Fluid Dynamics | ||
| Computational Fluid Dynamics | ||
| Combustion Processes | ||
| Advanced Experimental Instrumentation | ||
| Chem Kinetics of Combust Systems | ||
| Turbulent Heat and Momentum Transfer | ||
| Mathematical Fluid Dynamics | ||
| Dynamics | ||
| Mechanical Vibrations | ||
| Advanced Dynamics | ||
| Orbital Mechanics | ||
| Experimental Vibration and Dynamic System Analysis | ||
| Structural Finite Element Model Validation | ||
| Satellite Dynamics | ||
| Advanced Methods in Structural Dynamics | ||
| Nonlinear and Random Mechanical Vibrations | ||
| Automatic Controls Laboratory | ||
| Advanced Vibrations | ||
| Advanced Computer Control of Machines and Processes | ||
| Advanced Computer Control of Machines and Processes | ||
| Optimum Design of Mechanical Elements and Systems | ||
| Depth Requirement 1 | ||
| At least 4 courses (12 credits) must be numbered 700 or above in mechanics, applied mathematics, or computer science. At least 2 of the courses (6 credits) must be from List 1 (below), and the remaining 2 courses (6 credits) may be from List 1 or List 2. | 12 | |
| List 1 | ||
E M A 601 Special Topics courses may only be counted as numbered 700 or above if designated as such by the instructor. | ||
| Microhydrodynamics, Brownian Motion, and Complex Fluids | ||
| Engineering Properties of Soils | ||
| Mathematical Fluid Dynamics | ||
| Advanced Vibrations | ||
| Dynamics of Controlled Systems | ||
| Dynamics of Controlled Systems | ||
| Advanced Computer Control of Machines and Processes | ||
| Advanced Computer Control of Machines and Processes | ||
| Optimum Design of Mechanical Elements and Systems | ||
| Advanced Computational Dynamics | ||
| Friction, Lubrication and Wear | ||
| Precision Measurements | ||
| Combustion Processes | ||
| Advanced Experimental Instrumentation | ||
| Chem Kinetics of Combust Systems | ||
| Turbulent Heat and Momentum Transfer | ||
| List 2 | ||
| Methods of Computational Mathematics I | ||
| Methods of Computational Mathematics II | ||
| Machine Learning | ||
| Linear Systems | ||
| Mathematical Foundations of Machine Learning | ||
| Theoretical Foundations of Machine Learning | ||
| Methods of Applied Mathematics 1 | ||
| Methods of Applied Mathematics-2 | ||
| Modeling and Simulation in Polymer Processing | ||
| Solid Modeling | ||
| Topics in Thermodynamics | ||
| Advanced Heat Transfer I-Conduction | ||
| Structural Analysis of Materials | ||
| Imperfections and Mechanical Properties | ||
| Molecular Modeling of Materials | ||
| Theoretical Physics-Dynamics | ||
| Statistical Mechanics | ||
| Theoretical Physics-Electrodynamics | ||
| Quantum Mechanics | ||
| Quantum Mechanics | ||
| Advanced Solid State Physics | ||
| Special Topics in Theoretical Physics (when taught as Nanostructures in Science and Technology) | ||
| Remaining Credits 2 | ||
| Remaining credits to reach minimum degree requirement. Courses must be approved by the student faculty advisor. | 9 | |
| Total Credits | 60 | |
- 1
Requirements may overlap. At least 36 of the required 60 credits must be in classes satisfying the following: general requirements, mathematics requirements, breadth requirement, and depth requirement. The remaining 24 credits may be satisfied by courses approved by the student faculty advisor and may include E M A 890 and E M A 990.
- 2
Up to 24 credits of E M A 890 and E M A 990 may be used to satisfy the minimum degree credit requirement.
Graduate School Policies
The Graduate School’s Academic Policies and Procedures serve as the official document of record for Graduate School academic and administrative policies and procedures and are updated continuously. Note some policies redirect to entries in the official UW-Madison Policy Library. Programs may set more stringent policies than the Graduate School. Policies set by the academic degree program can be found below.
Major-Specific Policies
Prior Coursework
Graduate Credits Earned at Other Institutions
With faculty advisor and Department of Mechanical Engineering Graduate Committee approval, students may transfer up to 15 credits of prior graduate coursework that led to a relevant MS degree. Alternatively, with advisor and the Department of Mechanical Engineering Graduate Committee approval, students may use up to 6 credits of relevant coursework from a prior graduate program. Please review the Graduate Program Handbook (see contact box) for information about use and restrictions to this policy. Coursework earned ten or more years prior to admission is not allowed to satisfy requirements.
Undergraduate Credits Earned at Other Institutions or UW-Madison
With faculty advisor approval, a maximum of 7 credits from a UW-Madison undergraduate degree or an ABET-accredited undergraduate degree (from an other institution) may be applied toward the minimum graduate degree credit requirement. Only coursework that is applicable to the degree curriculum is eligible (based on UW-Madison course/course equivalency number). These credits will not be allowed to count toward the Minimum Graduate Coursework (50%) Requirement unless taken in courses numbered 700 or above (UW-Madison course equivalent). No credits can be counted toward the minimum graduate residence credit requirement. Coursework earned ten or more years prior to admission is not allowed to satisfy requirements.
Credits Earned as a Professional Student at UW-Madison (Law, Medicine, Pharmacy, and Veterinary careers)
Refer to the Graduate School: Transfer Credits for Prior Coursework policy.
Credits Earned as a University Special Student at UW–Madison
With faculty advisor approval, students are allowed to transfer up to 15 credits of coursework taken as a UW–Madison University Special student toward the minimum graduate degree credit requirement. Only coursework that is applicable to the degree curriculum is eligible. UW–Madison coursework taken as a University Special student would not be allowed to count toward the minimum graduate coursework (50%) requirement unless taken in courses numbered 700 or above or are taken to meet the requirements of a capstone certificate and has the “Grad 50%” designation. Coursework earned ten or more years prior to admission is not allowed to satisfy requirements.
Probation
The Department of Mechanical Engineering graduate programs satisfactory academic progress policy may be reviewed in the Graduate Handbook (see Contact box for link).
Advisor / Committee
Each student is required to meet with their advisor prior to registration every semester.
Credits Per Term Allowed
15 credit maximum. Refer to the Graduate School: Maximum Credit Loads and Overload Requests policy.
Time Limits
Qualifying Exam: The written portion of the qualifying exam is offered twice a year, once in August/September and once in January, generally the week before classes start. The associated literature review presentation must be completed within the timing limits stated (see graduate handbook, contact box).
- If you enter the PhD program directly without an MS or equivalent degree, you will first earn 30 graduate credits. Take your qualifying exam either the first or second time that it is offered after the semester in which you earn those 30 credits.
- If you earn a UW–Madison Engineering Mechanics MS and immediately enter the PhD program in the following semester, take your qualifying exam either the first or second time it is offered after the semester in which you earned your MS.
- If you enter the PhD program with an MS degree either from another department or institution, or are returning to UW–Madison with an MS degree after an absence, take the exam at the start of your third PhD semester
Preliminary Exam: PhD students must complete their preliminary exam within five years of passing their qualifying exam.
Dissertation Defense (oral thesis presentation): There must be at least nine (9) months between the preliminary exam and dissertation defense.
A candidate for a doctoral degree who fails to successfully complete the dissertation defense and deposit the dissertation within five years after passing the preliminary examination may be required to take another preliminary examination to be admitted to candidacy a second time.
Average Time to Degree: The average time to degree, beyond the bachelor degree, is 6 years.
Grievances and Appeals
These resources may be helpful in addressing your concerns:
- Bias or Hate Reporting
- Graduate Assistantship Policies and Procedures
- Hostile and Intimidating Behavior Policies and Procedures
- Employee Assistance (for personal counseling and workplace consultation around communication and conflict involving graduate assistants and other employees, post-doctoral students, faculty and staff)
- Employee Disability Resource Office (for qualified employees or applicants with disabilities to have equal employment opportunities)
- Graduate School (for informal advice at any level of review and for official appeals of program/departmental or school/college grievance decisions)
- Office of Compliance (for class harassment and discrimination, including sexual harassment and sexual violence)
- Office Student Assistance and Support (OSAS) (for all students to seek grievance assistance and support)
- Office of Student Conduct and Community Standards (for conflicts involving students)
- Ombuds Office for Faculty and Staff (for employed graduate students and post-docs, as well as faculty and staff)
- Title IX (for concerns about discrimination)
Department of Mechanical Engineering Grievance Procedures
If a student feels unfairly treated or aggrieved by faculty, staff, or another student, the University offers several avenues to resolve the grievance. Students’ concerns about unfair treatment are best handled directly with the person responsible for the objectionable action. If the student is uncomfortable making direct contact with the individual(s) involved, they should contact the advisor or the person in charge of the unit where the action occurred (program or department chair, section chair, lab manager, etc.). Many departments and schools/colleges have established specific procedures for handling such situations; check their web pages and published handbooks for information. If such procedures exist at the local level, these should be investigated first. For more information see the Graduate School Academic Policies & Procedures: https://grad.wisc.edu/acadpolicy/?policy=grievancesandappeals. The Assistant Dean for Graduate Affairs (engr-dean-graduateaffairs@engr.wisc.edu) provides overall leadership for graduate education in the College of Engineering (CoE), and is a point of contact for graduate students who have concerns about education, mentoring, research, or other difficulties.
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The student is encouraged to speak first with the person toward whom the grievance is directed to see if a situation can be resolved at this level.
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Should a satisfactory resolution not be achieved, the student should contact the Associate Chair for Graduate Studies or the John Bollinger Chair of Mechanical Engineering to discuss the grievance. The Associate Chair for Graduate Studies or Department Chair will facilitate problem resolution through informal channels and facilitate any complaints or issues of students. The first attempt is to help students informally address the grievance prior to any formal complaint. Students are also encouraged to talk with their faculty advisors regarding concerns or difficulties if necessary. University resources for sexual harassment, discrimination, disability accommodations, and other related concerns can be found on the UW Office of Compliance website. Other campus resources can be found above.
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If the issue is not resolved to the student’s satisfaction the student can submit the grievance to the Associate Chair for Graduate Studies in writing, within 60 calendar days of the alleged unfair treatment.
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On receipt of a written complaint, a faculty committee will be convened by the Associate Chair for Graduate Studies to manage the grievance. The faculty committee will obtain a written response from the person toward whom the complaint is directed. This response will be shared with the person filing the grievance.
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The faculty committee will determine a decision regarding the grievance. The Associate Chair for Graduate Studies will report on the action taken by the committee in writing to both the student and the party toward whom the complaint was directed within 15 working days from the date the complaint was received.
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At this point, if either party (the student or the person toward whom the grievance is directed) is unsatisfied with the decision of the faculty committee, the party may file a written appeal. Either party has 10 working days to file a written appeal to the School/College.
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Documentation of the grievance will be stored for at least 7 years. Significant grievances that set a precedent will be stored indefinitely.
The Graduate School has procedures for students wishing to appeal a grievance decision made at the school/college level. These policies are described in the Graduate School’s Academic Policies & Procedures: https://grad.wisc.edu/acadpolicy/?policy=grievancesandappeals.
Other
n/a
Professional Development
Graduate School Resources
Take advantage of the Graduate School's professional development resources to build skills, thrive academically, and launch your career.
Learning Outcomes
- Demonstrate an extraordinary, deep understanding of mathematical, scientific, and engineering principles in the field.
- Demonstrate an ability to formulate, analyze, and independently solve advanced engineering problems.
- Apply the relevant scientific and technological advancements, techniques, and engineering tools to address these problems.
- Recognize and apply principles of ethical and professional conduct.
- Demonstrate an ability to synthesize knowledge from a subset of the biological, physical, and/or social sciences to help frame problems critical to the future of their discipline.
- Demonstrate an ability to conduct original research and communicate it to their peers.