Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


3.032 Mechanical Behavior of Materials


In this subject, we review the structure and mechanical behavior of honeycombs and foams and apply models for their behavior to applications in engineering and medicine and to natural materials. Cellular solids are widespread in nature and in engineering. Natural cellular solids include wood, cork, plant leaves and stems, trabecular bone and the extracellular matrix to which biological cells attach in the body. Engineering honeycombs and foams can be made from polymers, metals, ceramics, glasses and composites. Their unique properties are exploited in applications such as lightweight structural panels, energy absorption devices and thermal insulation. In medicine, their behavior is of interest in understanding increased fracture risk due to trabecular bone loss in patients with osteoporosis, in the development of metal foam coatings for orthopedic implants and in designing porous scaffolds for tissue engineering that mimic the extracellular matrix.


Buy at Amazon Gibson, L. J., and M. F. Ashby. Cellular Solids: Structure and Properties. 2nd ed. Cambridge University Press, 1997. ISBN: 9780521495608. [Preview with Google Books]

Additional Reference

Buy at Amazon Gibson, L. J., M. F. Ashby, and B. A. Harley. Cellular Materials in Nature and Medicine. Cambridge University Press, 2010. ISBN: 9780521195447. [Preview with Google Books]


5 Problem Sets 10%
Project 30%
2 Tests 60%

Academic Integrity

You may discuss problem sets with other students but the work you submit must be your own. For more information, see the MIT website on academic integrity, which has the Handbook on Academic Integrity.



  • Examples, images
  • Overview of properties: Density, mechanical, thermal
  • Examples of applications
  • Selection of cellular materials in engineering design


  • Relative density, open vs closed cells, anisotropy
  • Topological laws: Euler, Aboav-Weaire


  • Honeycombs
  • Foams
  • Lattice materials

Mechanics of honeycombs

  • Stress strain behavior; mechanisms of deformation
  • Linear elasticity: Beam bending
  • Compressive collapse stress: Column buckling, plastic hinges, modulus of rupture
  • Fracture
  • Application of models to natural honeycombs: wood, cork

Mechanics and thermal properties of foams

  • Stress strain behavior; mechanisms of deformation; dimensional analysis
  • Linear elasticity
  • Compressive collapse stress
  • Densification
  • Fracture
  • Microstructural design, lattice materials and property charts
  • Thermal properties
  • Nanofoams (guest lecture, Prof. Demkowicz)

Trabecular bone and osteoporosis

  • Structure of trabecular bone
  • Application of foam models to trabecular bone
  • Modelling of bone loss in osteoporosis

Tissue engineering scaffolds

  • Processing and properties
  • Application of foam models to tissue engineering scaffolds
  • Case study: Osteochondral scaffold
  • Cell-scaffold interactions: cell adhesion, contraction, migration in scaffolds

Applications: Energy absorption devices

  • Energy absorption devices: bicycle helmet case study; fluid-filled foams

Applications: Structural sandwich panels

  • Stresses in sandwich panels; analogy with I beams
  • Minimum weight design of sandwich panels
  • Case study: Downhill skis
  • Sandwich structures in nature: monocotyledon leaves, skulls, shells

Mechanically efficient cellular structures in plants

  • Radial density gradient structures (palm stems, bamboo culms)
  • Cylindrical shells with compliant cores (grass stems, animal quills)
  • Hierarchical structure and mechanics of plants