Micromechanics of Materials


Credit Hours:


Learning Objective:

1. Mechanics of multiphase materials such as relevant to the design and the analysis of composites, multiphase alloys, porous solids, foams, honeycomb materials, architecture materials
2. Mechanics of material damage as this emerges from the evolution of microcracks and the growth of voids.
3. Relationships to connect microstructure information to material properties.
4. Implication to design, investigate case studies.


Increasingly mechanical engineering design makes use of advanced materials. These novel materials can only be applied successfully if it is understood that materials fundamentally a of heterogeneous nature. The course introduces the fundamental mechanics aspects required for the analysis of heterogeneous materials, and concepts required for their application in mechanical engineering.
Three major topics are covered:
(1) Mechanics of multiphase materials including composites, multiphase steels and alloys, porous solids
(2) Mechanics of architecture materials, such as foams and honeycomb structures, lattice materials, and topologically interlocked material systems.
(3) Mechanics of damage and failure due to void growth or microcracking. Spring 2017 Syllabus PDF.

Topics Covered:

Introduction to Micromechanics of Materials; Multiphase Materials; Unidirectional Composites, Modeling principles, Unidirectional Composites, Modulus, stress and strain localization, Unidirectional Composites, Shear Modulus, Poisson Ratio, Elastic-Plastic Loading, Unidirectional Composites, Failure, Unidirectional Composites, Thermomechanical Properties, Short Fiber Composites, Shear Lag Model; Homogenization Theory: Representative Volume Element Concept, Averaging, Homogenization II: Basic Equations, Thermal Strains, Eigenstrains, Mechanical Loading, Dilute Approximation, Self-Consistent Model, Mori-Tanaka Method, Further modeling approaches, Finite Element Modeling Aspects; Case study: Multiphase materials; Cellular Solids Introduction, Honeycomb Structures, Elastic Properties - Non-linear Properties Failure, Properties of Foams, Foams - Thermal Shock Properties - Energy Absorption, Biological Materials; Case study: Cellular Solids; Introduction to Damage Mechanics, Damage as Internal Variable, Methods for Determination of Damage, Thermodynamics of Damage, Damage Equivalent Stress, Kinetic of Damage Evolution, Ductile Fracture Models; Case study: Damage Mechanics.


Good standing in the ME graduate program

Applied / Theory:

30 / 70

Web Address:


Web Content:

Syllabus, grades, lecture notes, homework assignments, solutions, chat room, and message board.


Homework will be assigned on a bi-weekly basis. One independent paper. Accepted via email (course email address will be provided - tentatively me559@purdue.edu).


Required - Students are required to work on an independent project related to the course material. A project proposal is due after the first six weeks of the course, and a final report in the form of a short technical paper is due one week before the end of the semester. Project is not job-related.


(2) 1-hour exams and (1) final exam.


None Required.
S. Nemat-Nasser, M. Hori, "Micromechanics: Overall Properties of Heterogeneous Materials", North Holland; 2 edition (Reference)
T.W. Clyne, P.J. Withers, "An Introduction of Metal Matrix Composites, Cambridge Solid State Science Series", (Reference)
L.J. Gibson, M.F. Ashby, "Cellular Solids", Cambridge University Press (Reference)
J. Lemaitre (Author), "A Course in Damage Mechanics", Springer-Verlag (Reference)
M. Ashby, "Material Selection in Mechanical Design", Butterworth-Heineman (Reference)

Computer Requirements:

ProEd Minimum Computer Requirements. Students will need access to a PC for Office applications, MatLab or similar, and potentially to a finite element code (if a student decides to use this for the project, but not required).

ProEd Minimum Requirements:


Tuition & Fees: