Course Description

Increasingly mechanical engineering design makes use of advanced materials. These novel materials can only be applied successfully if it is understood that materials fundamentally are 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. Typically offered in the spring semester. 3 credit hours.

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 2019 Details

Offered MWF / 12:30/1:20 PM

Also available online through the ProEd program

Prof. Thomas Siegmund

ME 2186


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


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, "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).

Detailed Topic List

  • Mechanics of multiphase materials
  • Mechanics of Architectured Materials
  • Mechanics of Materials with Evolving Microstructures
  • Microstructure – property relationships
  • Implication to design


  • Unit 1: Introduction to Micromechanics of Materials
  • Unit 2: Introduction to Micromechanics of Materials

Basic Composite Mechanics

  • Unit 3: Unidirectional Composites, Elastic Properties
  • Unit 4: Unidirectional Composites, Elastic Properties
  • Unit 5: Unidirectional Composites, Shear Modulus, Poisson Ratio, Elastic- Plastic Loading
  • Unit 6: Unidirectional Composites, Failure
  • Unit 7: Unidirectional Composites, Thermomechanical Properties
  • Unit 8: Shear Lag Model
  • Unit 9: Shear Lag Model

Micromechanics of Multiphase Materials

  • Unit 10: Homogenization I: Representative Volume Element Concept, Averaging Schemes
  • Unit 11: Homogenization II: Basic Equations
  • Unit 12: Eigenstrains
  • Unit 13: Eigenstrains – Thermal Strains
  • Unit 14: Eigenstrains – Mechanical Loading
  • Unit 15: Dilute Approximation
  • Unit 16: Dilute Approximation
  • Unit 17: Self Consistent Model
  • Unit 18: Mori-Tanaka Method
  • Unit 19: Mori-Tanaka Method
  • Unit 20: Composite Sphere Model, Generalized Self Consistent Model, Differential Scheme
  • Unit 21: Size Effects in Composites

Architectured Material Systems

  • Unit 22: Cellular Solids – Introduction
  • Unit 23: Honeycomb Structures – Elastic Properties
  • Unit 24: Honeycomb Structures – Non-linear Properties
  • Unit 25: Honeycomb Structures – Non-linear Properties
  • Unit 26: Honeycomb Structures – Failure
  • Unit 27: Properties of Foams
  • Unit 28: Foams, Thermal Shock Properties
  • Unit 29: Foams, Energy Absorption
  • Unit 30: Generalization to Lattice Materials
  • Unit 31: Mechanics of Lattice Materials
  • Unit 32: Segmentation and Assembly as a Material Design Concept
  • Unit 33: Mechanics of Topologically Interlocked Material Systems
  • Unit 34: Mechanics of Topologically Interlocked Material Systems
  • Unit 35: Bioinspiration

Damage Mechanics as an Example of Mechanics with Evolving Microstructure

  • Unit 35: Introduction to Damage Mechanics
  • Unit 36: Introduction to Damage Mechanics
  • Unit 37: Damage as Internal Variable
  • Unit 38: Methods for Determination of Damage
  • Unit 39: Thermodynamics of Damage
  • Unit 40: Damage Equivalent Stress
  • Unit 41: Kinetic of Damage Evolution
  • Unit 42: Ductile Fracture Models

Unifying Concepts

  • Unit 43: Material Design Combining Composition, Shape, Assembly
  • Unit 44: Material Design Combining Composition, Shape, Assembly