Doctoral College TU-D Unravelling advanced 2D materials
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Coupled problems in membrane and nanocomposite mechanics

C. Hellmich, Intsitute of Mechanics of Materials and Structures

The CH group develops continuum theories and corresponding analytical and numerical mathematical models for the mechanics of materials and structures. They have pioneered multiscale mechanics formulations, spanning up to eight length scales from the several nanometer to the several centimeter level.
These activities concern both fundamental contributions to homogenization and scale transition theory [CH1], as well as material system-specific model developments, quantifying universal patterns and mechanical design principles for mineralized tissues (including bones and mineralized tendons) [CH2], wood and wood products [CH3], as well as cementitious materials (concrete) [CH4].
This has allowed for integrating engineering mechanics with various experimental microscopic and nanoscopic methods,  such as micro and nanoComputed Tomography, nano and picoindentation, ultrasonics, TEM, and SEM. Very recent acitvities concern also planar mateiral systems such as paper; and in the TU-D DK, these approaches will be further extended towards graphene membranes and graphene-boron-nitride nano-composites.

PhD Project 1: Continuum Nanomechanics of Suspended Graphene Membranes

Co-supervisor:  Florian Libisch

Graphene membranes do not only bridge the traditional divide between soft and hard condensed matter physics, but also exhibit physical properties which are standardly dealt with by cleanly separated disciplines: micro- and nanoelectronics on the one hand, and continuum mechanics on the other. In this context, the application of advanced continuum mechanics theories to graphene is still in its infancy, as is the exploration of corresponding electro-mechanical couplings. This is the focus of the proposed PhD project.

PhD Project 2: Mechanical states of graphene on hexagonal boron nitride

Co-supervisor: Ulrike Diebold

Due to their extreme surface-to-volume ratio, the properties of two-dimensional materials are strongly influenced by substrates: graphene aligned on a hexagonal boron nitride (hBN) substrate features a moiré structure with 13.6 nm periodicity, strongly modifying electronic properties. The lattice mismatch will also result in strain effects, as the lattice locally stretches to accommodate the substrate lattice spacing. For graphene, such strain effects lead to Landau-level like modifications of the density of states, described by a strain-induced pseudo-magnetic field. This project will lead to key insights in exploiting substrate effects in 2D materials.


  1. B. Pichler, and Ch. Hellmich: Estimation of influence tensors for eigenstressed multiphase elastic media with non-aligned inclusion phases of arbitrary ellipsoidal shape. Journal of Engineering Mechanics (ASCE) 136, 1043-1053 (2010)  DOI: 10.1061/(ASCE)EM.1943-7889.0000138
  2. A. Fritsch, Ch. Hellmich, L. Dormieux. Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: experimentally supported micromechanical explanation of bone strength. Journal of Theoretical Biology, 260, 230 – 252 (2009) DOI: 10.1016/j.jtbi.2009.05.021
  3. K. Hofstetter, Ch. Hellmich, J. Eberhardsteiner. Development and experimental validation of a continuum micromechanics model for the elasticity of wood. European Journal of Mechanics A/Solids 24, 1030–1053 (2005) DOI: 10.1016/j.euromechsol.2005.05.006
  4. B. Pichler, Ch. Hellmich. Upscaling quasi-brittle strength of cement paste and mortar: a multiscale engineering mechanics model, Cement and Concrete Research 41, 467 – 476 (2011)DOI: 10.1016/j.cemconres.2011.01.010