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Mechanical Metamaterials


Admission Requirements

BSc in Physics or similar


This course introduces and discusses the physical principles of mechanical metamaterials. Research on these metamaterials, whose properties depend on their geometric structure rather than their composition, has exploded in the last decade. Examples of such metamaterials include patterned elastic media and origami (folding) structures, leading to unusual negative response, programmable mechanics and shape morphing materials.

Using recent literature, we discuss these materials, as well as their underlying principles, which include (tensorial) elasticity and elastic instabilities, mechanisms, frustration and combinatorics: cool physics for new and surprising materials.

Each lecture deals with one or more recently studied mechanical metamaterial, and to understand their physics, the course introduces three more general topics:

  • Introduction to linear elasticity

  • Buckling and nonlinear instabilities

  • Maxwell Counting, Floppy Modes and Self Stresses

After each lecture a set of exercises have to be made and one or two papers have to be read.
Each lecture a presentation is given by one of the students on these papers, followed by a general discussion in which active participation is required. The course is ended by a final short presentation on a student design for a metamaterial.

Specific topics that are covered:

  • Introduction to elasticity, elastic constants, stress and strain, and auxetic metamaterials

  • Elastic tensor, anisotropic elasticity, extremal and pentamode materials, mechanical cloak.

  • Maxwell counting, floppy modes, and self stresses. Disordered metamaterials.

  • Spontaneous symmetry breaking, Bending, buckling, holey sheet metamaterial

  • Controlled symmetry breaking, nonlinear instabilities and programmable mechanical metamaterials

  • Characteristic lengthscales

  • Combinatorial design and metacubes

  • Origami metamaterials, foldability

Course objectives

Main learning objective of MSc course Mechanical Metamaterials: you are able to critically discuss the role of geometry in determining the effective properties of metamaterials.

Specifically, after this course, you are able to:

  • Write down the elastic equations for complex and anisotropic materials and geometries.

  • Perform scaling analysis for elastic constants etc.

  • Analyze basic elastic instabilities.

  • Analyze the degrees of freedom of complex hinged structures.

  • Critically discuss the role of geometry in metamaterials

Moreover, you have acquired an overview of a very recent piece of literature.


Physics Schedule
For detailed information go to Timetable in Brightspace

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

Mode of instruction

See Brightspace

Assessment method

Grading according to a weighted average of exercies and presentations.

Reading list

not applicable


From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.

Extensive FAQ's on MyStudymap can be found here.


Lecturer: Prof.dr. Martin van Hecke


Transferable skills

During this course you will be trained how to

  • critically read research papers

  • to present and discuss research work

  • perform calculations on complex elastic structures