535.733.81 - Micromechanics of Heterogeneous Materials and Composites
Description
This course introduces core concepts in the micromechanics of heterogeneous materials and composites. Micromechanics is the study of the relationship between macroscopic material behavior and properties of its constituents. The course begins with fundamental concepts in mechanics such as tensor and matrix algebra, stress and strain, balance laws, isotropic and anisotropic linear elasticity, and boundary value problems. The course then focuses heavily on micromechanics topics including representative volume elements, Voigt and Reuss bounds, Eshelby’s equivalent inclusion method, dilute distribution and self-consistent methods, Hashin-Shtrikman bounds, Mori-Tanaka theory, and microstructure characterization and generation. Applications of these topics are provided for particulate and matrix-based composites, fiber-reinforced composites (e.g., laminates), materials with microcracks, and materials with periodic microstructures. Students will leave the course able to make property predictions for a broad range of heterogeneous materials. Prerequisite: A prior course on the mechanics of materials at the advanced undergraduate level or above.
Instructor
Ryan Hurley
Course Structure
The course materials are divided into modules which can be accessed by clicking Modules on the course menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.
Course Topics
- Introduction to Micromechanics, Composites, and Core Mathematics
- Elasticity and Anisotropy
- Representative Volume Elements, Averages
- Voigt and Reuss Bounds
- Eshelby’s Equivalent Inclusion Method, Tensor, and Dilute Distribution Approximations
- The Self-Consistent Method and Mori-Tanaka Mean Field Theory
- Hashin-Shtrikman Bounds and Higher-Order Estimates
- Microstructure Characterization and Reconstruction
- Theory of Homogenization for Cracked Solids
- Macromechanics of Lamina and Laminates
- Micromechanics of Lamina
- Failure and Damage
- Periodic Microstructures
Course Goals
The goals of this course are to empower students with the fundamental mathematical tools and physical insights to analyze the mechanical behavior of heterogeneous materials and composites in academic and industry settings.
Course Learning Outcomes (CLOs)
- Evaluate mathematical expressions involving tensors using tensor notation and matrix algebra.
- Discuss anisotropic linear elasticity and its role in the macroscopic properties of composite materials.
- Explain core concepts in micromechanics such as representative volume elements and average stress and strain.
- Discuss the importance of Eshelby’s inclusion theory in the field of micromechanics and in the prediction of macroscopic properties of composites.
- Predict the effective macroscopic properties of matrix-based composites, fiber-reinforced composites, solids with microcracks, and composites with periodic microstructures.
- Evaluate the relationship between microscopic properties and macroscopic properties of composite materials and their constituent phases.
- Discuss the merits of schemes for estimating macroscopic properties of composite materials.
- Explain microstructure descriptors and reconstruction techniques for heterogeneous materials.
Textbooks
The course relies heavily on two textbooks (not required but highly encouraged):
- Nemat-Nasser, S., Hori, M. (2013). Micromechanics: Overall properties of heterogeneous materials. Elsevier.
- Li, S., Wang, G. (2008). Introduction to micromechanics and nano mechanics. World Scientific Publishing Company.
The course relies on several other textbooks for one to two modules each (also not required):
- Torquato, S. (2002). Random heterogeneous materials: microstructure and macroscopic properties. Springer Science+Business Media, New York.
- Sadd, M. H. (2009). Elasticity: theory, applications, and numerics. Academic Press.
- Jones, R. M. (1999). Mechanics of Composite Materials. Taylor & Francis.
Other Materials & Online Resources
see eReverses link on the course menu
Required Software
In this class, some computer literacy skills you are expected to have include creating and submitting files in a word processing program or as a PDF, downloading and installing software (Matlab), optionally using Excel spreadsheets, using presentation software, and using web conferencing tools and software. Additionally, you will be expected to use online search tools for academic purposes (e.g., Google Scholar), properly cite information sources, and prepare a presentation of such findings.
Student Coursework Requirements
All assignments are due on the dates listed in the course site. They will be graded using the rubric provided there, and grades will be posted within one week of the due date.
Late submissions will be reduced by 15% of the total number of available points for each week they are late (no exceptions without prior coordination with the instructors).
Weekly Assignments: 60% (approximately one per module)
Discussions: 20% (approximately one per module)
Mini-Project: 20% (2% for initial proposal, 2% each for two interim reports, 14% for final report and presentation)
Grading Policy
EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10).
| Score Range | Letter Grade |
|---|---|
| 100-97 | = A+ |
| <97-93 | = A |
| <93-90 | = A− |
| <90-87 | = B+ |
| <87-83 | = B |
| <83-80 | = B− |
| <80-77 | = C+ |
| <77-73 | = C |
| <73-70 | = C− |
| <70-67 | = D+ |
| <67-63 | = D |
| <63 | = F |
Course Evaluation
LLM policy:
Students are permitted to use Large Language Models (LLMs) such as ChatGPT, Claude, or Copilot to clarify equations, review core concepts, or explore alternative solution approaches in this course. These tools can be valuable aids for understanding mechanical engineering fundamentals and verifying reasoning.
However, all problem-solving work must be completed by the student. This means that while you may consult an LLM for conceptual help, you must independently work through and present each step of your solution, including derivations, assumptions, and justifications. Copying or directly reproducing an LLM-generated solution is not acceptable and will be treated as academic misconduct.
Disclosure requirement:
If you use an LLM for any assignment or project, you must include a brief statement at the end of your submission describing:
Which tool you used, and
How it assisted you (e.g., “Used ChatGPT to check my understanding of control volume analysis in the energy balance derivation”).
This policy encourages responsible use of emerging technologies while maintaining academic integrity and ensuring that all students develop the ability to solve engineering problems independently.
Academic Policies
Deadlines for Adding, Dropping and Withdrawing from Courses
Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.
Academic Misconduct Policy
All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students. This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.
Students with Disabilities - Accommodations and Accessibility
Johns Hopkins University is committed to providing welcoming, equitable, and accessible educational experiences for all students. If disability accommodations are needed for this course, students should request accommodations through Student Disability Services (SDS) as early as possible to provide time for effective communication and arrangements. For further information about this process, please refer to the SDS Website.
Student Conduct Code
The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/
Classroom Climate
JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).
Course Auditing
When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.