The master of science and doctor of philosophy degrees in engineering mechanics are 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.

The program is broadly structured into several main areas of instruction and research interests in mechanics of materials and astronautics: continuum mechanics, computational mechanics, dynamics and vibration, fluid mechanics, nanomechanics, solid mechanics, and biomechanics. Related fields in which minor work may be done 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 adhesive-bonded joints; composites; failure criteria; analytical and computational solid mechanics; analytical and computational dynamics; multibody dynamics; analytical and computational active and passive space-structure control systems; dynamic stability; nonlinear fracture mechanics of traditional and advanced materials; continuum mechanics; modal analysis; nanomechanics and nanotribology; fluid-structure interaction; non-Newtonian fluid flow; structural mechanics; viscoelasticity; viscoplasticity; cell mechanics; and biomechanics.

Laboratories are well equipped for experimental testing and research; these include holography, Moire, 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 Materials Science 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.

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.

Graduate Admissions Requirements

Requirements	Detail
Fall Deadline	December 15
Spring Deadline	October 1
Summer Deadline	December 15
GRE (Graduate Record Examinations)	Required.*
English Proficiency Test	Every applicant whose native language is not English or whose undergraduate instruction was not in English must provide an English proficiency test score and meet the Graduate School minimum requirements (https://grad.wisc.edu/apply/requirements/#english-proficiency).
Other Test(s) (e.g., GMAT, MCAT)	n/a
Letters of Recommendation Required	3

*	a) Current UW-Madison NE/EP/EMA undergraduate students are not required to submit GRE scores. b) Due to COVID-19, GRE scores are not required for all applications to Engineering Mechanics graduate programs for the Spring 2022 term.

The Graduate School sets minimum requirements for admissions. Academic program admission requirements are often more rigorous than those set by the Graduate School. Please check the program website for details and admissions deadlines.

Minimum Graduate School Requirements

Review the Graduate School minimum academic progress and degree requirements, in addition to the program requirements listed below.

Major Requirements

MODE OF INSTRUCTION

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 are able to complete a program with minimal disruptions to careers and other commitments. 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

University General Education Requirements

Requirements	Detail
Minimum Credit Requirement	60 credits
Minimum Residence Credit Requirement	32 credits
Minimum Graduate Coursework Requirement	30 of the required 60 credits must be in graduate-level coursework; courses with the Graduate Level Coursework attribute are identified and searchable in the university's Course Guide (https://registrar.wisc.edu/course-guide/). 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.
Other Grade Requirements	Courses in which grades of BC, C, or below are received cannot be counted toward the degree except as follows: 1) Credits of C will be allowed provided they are balanced by twice as many credits of A or by four times as many credits of AB, 2) Credits of BC will be allowed provided they are balanced by twice as many credits of AB or by an equal number of credits of A.
Assessments and Examinations	Ph.D. 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.
Doctoral Minor/Breadth Requirements	There are two minor options available: Minor Option A Students minor in a single department and satisfy the minor requirements of that department. Minor Option B (Distributed Minor) This option requires a minimum of 9 credits in two or more departments outside the major, in related courses selected for their relevance to a particular area of concentration. The following rules apply: 1. Courses typically included on or within the scope of the E M A Qualifying Exam shall not be considered acceptable for the Ph.D. Minor Option B. 2. At least 6 credits must be taken in courses listed in the UW-Madison Guide as "Grad 50%" courses.

Required COURSES

At least 36 of the required 60 credits must be in classes satisfying the following general requirements and mathematics, breadth and depth requirements.

Course List

Code	Title	Credits
General
All courses must be at the 500-level or above. At least 21 credits must be 600-level and above OR from the following list:		21
E M A/​CIV ENGR/​M E  508	Composite Materials
E M A 519	Fracture Mechanics
E M A 522	Aerodynamics Lab
E M A 523	Flight Dynamics and Control
E M A/​M E  540	Experimental Vibration and Dynamic System Analysis
E M A/​M S & E  541	Heterogeneous and Multiphase Materials
E M A/​E P  547	Engineering Analysis I
E M A/​E P  548	Engineering Analysis II
E M A/​M E  570	Experimental Mechanics
Mathematics Requirements		6
At least 6 credits (2 courses) must be in applied mathematics from the following list:
E M A/​E P  547	Engineering Analysis I
E M A/​E P  548	Engineering Analysis II
MATH 519	Ordinary Differential Equations
MATH 521	Analysis I
MATH 522	Analysis II
MATH 540	Linear Algebra II
MATH 619	Analysis of Partial Differential Equations
MATH 623	Complex Analysis
MATH 703	Methods of Applied Mathematics 1
MATH 704	Methods of Applied Mathematics-2
MATH/​COMP SCI  714	Methods of Computational Mathematics I
MATH/​COMP SCI  715	Methods of Computational Mathematics II
Breadth Requirement
As part of their M.S. or Ph.D., students must have taken courses from at least 2 of the 3 areas defined below. For each of the 2 areas, the student must have taken at least 2 courses. The courses must be at a similar level to those listed below.
Solid Mechanics
E M A 506	Advanced Mechanics of Materials I	3
E M A/​CIV ENGR/​M E  508	Composite Materials	3
E M A 519	Fracture Mechanics	3
E M A/​M S & E  541	Heterogeneous and Multiphase Materials	3
E M A/​M E  570	Experimental Mechanics	3
E M A 605	Introduction to Finite Elements	3
E M A 611	Advanced Mechanical Testing of Materials	3
E M A/​E P  615	Micro- and Nanoscale Mechanics	3
E M A 622	Mechanics of Continua	3
E M A 630	Viscoelastic Solids	3
E M A 700	Theory of Elasticity	3
E M A/​M E  703	Plasticity Theory and Physics	3
E M A 705	Advanced Topics in Finite Elements	3
E M A/​M E  706	Plates, Shells and Pressure Vessels	3
E M A/​M E  708	Advanced Composite Materials	3
E M A/​M E  722	Introduction to Polymer Rheology	3
M E/​B M E  603	Topics in Bio-Medical Engineering (Topic: FE for Biomechanics)	1-3
M E 753	Friction, Lubrication and Wear	3
Fluid Mechanics
E M A 521	Aerodynamics	3
E M A 622	Mechanics of Continua	3
M E 563	Intermediate Fluid Dynamics	3
M E 572	Intermediate Gas Dynamics	3
M E 573	Computational Fluid Dynamics	3
M E 769	Combustion Processes	3
M E 770	Advanced Experimental Instrumentation	3
M E 774	Chem Kinetics of Combust Systems	3
M E/​CIV ENGR/​E M A  775	Turbulent Heat and Momentum Transfer	3
MATH 705	Mathematical Fluid Dynamics	3
Dynamics
E M A 523	Flight Dynamics and Control	3
E M A/​M E  540	Experimental Vibration and Dynamic System Analysis	3
E M A 542	Advanced Dynamics	3
E M A 545	Mechanical Vibrations	3
E M A/​ASTRON  550	Astrodynamics	3
E M A 610	Structural Finite Element Model Validation	3
E M A 642	Satellite Dynamics	3
E M A 742	Theory and Applications in Advanced Dynamics	3
E M A 745	Advanced Methods in Structural Dynamics	3
E M A 747	Nonlinear and Random Mechanical Vibrations	3
M E/​E C E  577	Automatic Controls Laboratory	4
M E 740	Advanced Vibrations	3
M E 747	Advanced Computer Control of Machines and Processes	3
M E 748	Optimum Design of Mechanical Elements and Systems	3
Depth Requirement		12
At least 4 courses (12 credits) must be 700-level 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.
List 1		6-12
Any E M A course except E M A 790, E M A 890, or E M A 990.
E M A 601 Special Topics courses may only be counted as 700-level if designated as such by the instructor.
CBE 720	Microhydrodynamics, Brownian Motion, and Complex Fluids
CIV ENGR/​G L E  730	Engineering Properties of Soils
CIV ENGR/​G L E  735	Soil Dynamics
MATH 705	Mathematical Fluid Dynamics
M E 740	Advanced Vibrations
M E 746	Dynamics of Controlled Systems
M E 747	Advanced Computer Control of Machines and Processes
M E 748	Optimum Design of Mechanical Elements and Systems
M E 751	Advanced Computational Dynamics
M E 753	Friction, Lubrication and Wear
M E 769	Combustion Processes
M E 770	Advanced Experimental Instrumentation
M E 774	Chem Kinetics of Combust Systems
M E/​CIV ENGR/​E M A  775	Turbulent Heat and Momentum Transfer
List 2		0-6
COMP SCI/​MATH  714	Methods of Computational Mathematics I
COMP SCI/​MATH  715	Methods of Computational Mathematics II
COMP SCI 733	Computational Methods for Large Sparse Systems
COMP SCI 760	Machine Learning
E C E 717	Linear Systems
E C E 719	Optimal Systems
E C E/​COMP SCI  761	Mathematical Foundations of Machine Learning
E C E/​CBE/​MATH  777	Nonlinear Dynamics, Bifurcations and Chaos
E C E/​COMP SCI/​STAT  861	Theoretical Foundations of Machine Learning
MATH 703	Methods of Applied Mathematics 1
MATH 704	Methods of Applied Mathematics-2
M E 714	Advanced Materials Processing and Manufacturing
M E 718	Modeling and Simulation in Polymer Processing
M E/​E C E  739	Advanced Robotics
M E 758	Solid Modeling
M E 761	Topics in Thermodynamics
M E 764	Advanced Heat Transfer I-Conduction
M S & E 748	Structural Analysis of Materials
M S & E 750	Imperfections and Mechanical Properties
M S & E 760	Molecular Dynamics and Monte Carlo Simulations in Materials Science
PHYSICS 711	Theoretical Physics-Dynamics
PHYSICS 715	Statistical Mechanics
PHYSICS 721	Theoretical Physics-Electrodynamics
PHYSICS 731	Quantum Mechanics
PHYSICS 732	Quantum Mechanics
PHYSICS 751	Advanced Solid State Physics
PHYSICS 801	Special Topics in Theoretical Physics (when taught as Nanostructures in Science and Technology)

 It is acceptable for students who earned an M.S. degree in Engineering Mechanics at UW-Madison to use coursework completed while in the M.S. degree program to meet the requirements above.

Prior Coursework

Graduate Work from Other Institutions

With permission from their faculty advisor and the department chair, students may use up to 6 credits of graduate work taken at another institution if they meet departmental MS requirements.  Coursework earned ten or more years prior to admission to the PhD program is not allowed to satisfy requirements.

Graduate Coursework from Previous MS¹

With advisor and EP Graduate Studies Committee approval, students may use up to 15 credits of prior MS coursework toward the PhD, provided that all of the following are met: (1) The student has completed an MS degree in a relevant field. (2) The coursework proposed by the student is at the graduate level and was taken as part of the student’s completed MS program. (3) The student’s faculty advisor agrees that the prior coursework proposed by the student satisfies the Engineering Mechanics PhD program requirements in terms of subject area and rigor. (4) A member of the EP Graduate Studies Committee who is familiar with the EM PhD program confirms the advisor’s recommendation.

1	All credits earned toward the EM MS degree at the University of Wisconsin-Madison count toward the EM PhD program.  This policy applies to students who have not completed a previous MS degree in a relevant field.

UW–Madison Undergraduate

With faculty approval, students who have received their undergraduate degree from UW–Madison may apply up to 7 credits numbered 400 or above toward the minimum graduate degree credit requirement.  This work would not be allowed to count toward the 50% graduate coursework minimum unless taken at the 700 level or above. No credits can be counted toward the minimum graduate residence credit requirement. Coursework earned ten years or more prior to admission to a PhD program is not allowed to satisfy requirements.

With faculty approval, students who have received an ABET-accredited undergraduate degree (not including UW–Madison) may be eligible to apply up to 7 credits of their undergraduate coursework toward the Minimum Graduate Degree Credit Requirement.  No credits can be counted toward the Minimum Graduate Residence Credit Requirement, nor the Minimum Graduate Coursework (50%) Requirement.  Coursework earned five or more years prior to admission to a master's degree is not allowed to satisfy requirements.

UW–Madison University Special

With program approval, students are allowed to count up to 15 credits of coursework numbered 400 or above taken as a UW–Madison Special student toward the minimum graduate residence credit requirement, and the minimum graduate degree credit requirement. UW–Madison coursework taken as a University Special student would not be allowed to count toward the 50% graduate coursework minimum unless taken at the 700 level or above. Coursework earned ten years or more prior to admission to a doctoral degree is not allowed to satisfy requirements.

Probation

A semester GPA below 3.0 will result in the student being placed on academic probation. If a semester GPA of 3.0 is not attained during the subsequent semester of full time enrollment (or 12 credits of enrollment if enrolled part-time) the student may be dismissed from the program or allowed to continue for one additional semester based on advisor appeal to the Graduate School.

ADVISOR / COMMITTEE

Each student is required to meet with their advisor prior to registration every semester.

CREDITS PER TERM ALLOWED

15 credits

Time Constraints

The Ph.D. qualifying examination should be first taken no later than completion of the M.S. requirements, or the beginning of the fifth semester of graduate study, whichever comes first. Students entering the program with a master’s degree in EMA, EP or NE from another institution, and taking the qualifying exam in that same major, must take the exam by the beginning of their third semester.

Students must submit the doctoral plan of study one month before the end of the semester following the one in which the qualifying exam is passed.

Candidates are expected to pass the Ph.D. preliminary examination no later than the end of the third year of graduate study, or by the end of the second regular semester following the one in which the Ph.D. qualifying examination was passed, whichever is later. A candidate who fails to take the preliminary examination within four years of passing the qualifying examination must retake the qualifying examination.

An oral examination on the findings of the Ph.D. research is required at the end of the thesis work. The candidate must apply for a warrant from the Graduate School through the student services office at least three weeks prior to the exam. The final oral examination must be taken within five years of passing the preliminary examination.

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
  • Office of the Provost for Faculty and Staff Affairs
• Dean of Students Office (for all students to seek grievance assistance and support)
• 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 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)

Engineering Mechanics Grievance Procedures

Students who feel that they have been treated unfairly have the right to a prompt hearing of their grievance.  Such complaints may involve course grades, classroom treatment, advising, various forms of harassment, or other issues. Any student or potential student may use these procedures.

• The student should speak first with the person toward whom the grievance is directed. In most cases, grievances can be resolved at this level.

• Should a satisfactory resolution not be achieved, the student should contact the program’s Grievance Advisor to discuss the grievance. The Graduate Student Coordinator can provide students with the name of this faculty member, who facilitates problem resolution through informal channels. The Grievance Advisor is responsible for facilitating any complaints or issues of students. The Grievance Advisor first attempts 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 concerns can be found on the UW Office of Equity and Diversity website.

• If the issue is not resolved to the student’s satisfaction, the student can submit the grievance to the Grievance Advisor in writing, within 60 calendar days of the alleged unfair treatment.

• On receipt of a written complaint, a faculty committee will be convened by the Grievance Advisor to manage the grievance.  The program faculty committee will obtain a written response from the person toward whom the complaint is directed. The response will be shared with the person filing the grievance.

• The faculty committee will determine a decision regarding the grievance. The Grievance Advisor 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.

• 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 College of Engineering.

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.

The Graduate School has procedures for students wishing to appeal a grievance decision made at the college level. These policies are described in the Academic Policies and Procedures at https://grad.wisc.edu/academic-policies/.

OTHER

n/a

Graduate School Resources

Take advantage of the Graduate School's professional development resources to build skills, thrive academically, and launch your career. 

1. Demonstrate an extraordinary, deep understanding of mathematical, scientific, and engineering principles in the field.
2. Demonstrate an ability to formulate, analyze, and independently solve advanced engineering problems.
3. Apply the relevant scientific and technological advancements, techniques, and engineering tools to address these problems.
4. Recognize and apply principles of ethical and professional conduct.
5. 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.
6. Demonstrate an ability to conduct original research and communicate it to their peers.

FACULTY

PROFESSORS

Paul Wilson (Chair)
Matt Allen
Riccardo Bonazza
Curt A. Bronkhorst
Wendy Crone
Chris Hegna
Douglass Henderson
Roderic Lakes
Oliver Schmitz
Carl Sovinec
Kumar Sridharan
Fabian Waleffe

ASSISTANT PROFESSORS

Jennifer Choy
Adrien Couet
Stephanie Diem
Jennifer Franck
Benedikt Geiger
Ben Lindley
Jacob Notbohm
Ramathasan Thevamaran
Yongfeng Zhang

See also Engineering Physics Faculty Directory.