TOMOMECH is an Intra-European Marie Curie Fellowship granted to Dirk Müter which ran from 07/2013 to 06/2015.

Title: “Nanomechanics of natural materials from combining tomography and finite element modelling”

Abstract: TOMOMECH’s goal is to connect X-ray tomography and finite element simulation on the nanometre scale to determine structural and mechanical properties of natural materials. In applying this technique to porous rocks and biomineralised shells, TOMOMECH aims at predicting the macroscopic stability of cliffs, defining the pore volume in oil bearing rocks and exploring nature’s solution to mechanical stability in the structure of echinoderms.


  1. D. Müter, H. O. Sørensen, D. Jha, R. Harti, K.N. Dalby, H. Suhonen, R. Feidenhans’l, F. Engstrøm and S. L. S. Stipp
    Appl. Phys. Lett. 105, 043108 (2014)
    “Resolution dependence of petrophysical parameters derived from X-ray tomography of chalk”
  2. D. Müter, H. O. Sørensen, H. Bock and S. L. S. Stipp
    J. Phys. Chem. C 119, 10329-10335 (2015)
    “Particle diffusion in complex nanoscale pore networks”
  3. D. Müter, H. O. Sørensen, J. Oddershede, K. N. Dalby, and S. L. S. Stipp
    Acta Biomaterialia  23, 21-26 (2015)
    “Microstructure and micromechanics of the heart urchin test from X-ray tomography”
  4. M. K. Misztal, A. Hernandez-Garcia, R. Matin, D. Müter, D. Jha, H. O. Sørensen, and J. Mathiesen
    Frontiers in Physics 3, 50 (2015)
    “Simulating anomalous dispersion in porous media using the unstructured Lattice Boltzmann method”

More publications acknowledging TOMOMECH are foreseen for the near future.

Conference contributions:

  1. Conf. on Tomography of Materials and Structures, Québec (Canada) 2015 Poster: “Nanoscale mechanical properties of chalk from X-ray tomography”
  2. InterPore, Padova (Italy) 2015 Talk: “Particle Diffusion in Complex Nanoscale Pore Networks”
  3. X-Ray Microscopy, Melbourne (Australia) 2014 Poster: “Microstructure and micromechanics of sea urchin shells from X-ray tomography”
  4. International Carbon Conference, Reykjavik (Iceland) 2014 Poster: “Nanoscale fluid transport properties of natural porous rocks”
  5. Microscopy and Microanalysis, Hartford (United States) 2014 Poster: “X-Ray Tomography and Finite Elements Simulations of Rock Mechanics”
  6. Liquid Matter Conference, Lisbon (Portugal) 2014 Poster: “Nanoscale fluid transport properties of natural porous rocks”
  7. 3D Materials Science, Annecy (France) 2014 Poster: “Microstructure and mechanical optimisation in sea urchin shells”
  8. DanScatt Meeting, Copenhagen (Denmark) 2014 Poster: “Microstructure and mechanical optimisation in sea urchin shells”

Illustration on top of the page (left to right):
X-ray tomography of sea urchin test (shell) showing ossicles (ball and socket joint for spines) and stereom (fenestrated structure in bulk); Volume mesh of sea urchin stereom ready for finite element simulations; Pore network in a highly compacted chalk sample (green: connected pore network, brown: dead pores).

TOMOMECH’s main objective was to combine X-ray tomographic imaging for natural materials with computer simulations to determine mainly mechanical but also flow properties on the micro- and nanometre scale. Two natural porous materials were chosen to test the validity of this approach, the shell of the heart urchin (microstructured biological material) and chalk (nanostructured geological material).

Tomography, also known as CT, takes 2D projections of the internal structure of a sample using X-rays. These projections are essentially the same as radiographs in medicine. By rotating the sample and taking a large number of projections, it is possible to reconstruct the internal porosity of a sample in three dimensions. Tomography data are usually composed of a stack of grayscale images where the grayscale value corresponds to the local X-ray attenuation factor, i.e. the density of the material. In order to use these data for the computer simulations, it is necessary to segment the data into material and background. At the start of TOMOMECH, I developed an algorithm that uses different filtering steps to enhance the contrast in the images because at very high resolution images can be blurred and thus segmentation becomes difficult. This algorithm proofed itself superior to standard methods and was subsequently used for the rest of the project.

3D imaging of the heart urchin, which is burrow dwelling cousin of the more commonly known sea urchins (Fig. 1 left), was performed using a laboratory X-ray tomography instrument with a resolution of about 1 µm. Macroscopically, the shell appears solid but tomography revealed an airy network of struts (Fig. 1 middle). Using image processing software, I was able to determine the thickness and spacing of the struts which showed that there are two distinct regions in the shell, two finely structured regions with strut thickness of about 10 µm on the outer and inner side of the shell and a coarser region (strut thickness ~25 µm) in the middle. Porosity in both regions varies between 30-70% and is achieved by varying the spacing of the struts not their thickness. This demonstrates an intricate biomineralisation process because the shell is entirely composed of magnesium enriched calcite (CaCO3).

In order to study the relation between the microstructure and its mechanical function, I imported the 3D structure into a finite element (FE) simulation (Fig. 1 right). In FE simulations, an arbitrarily shaped object is approximate by larger number of small symmetric elements. The mechanical deformation of the object under external load can then be approximated numerically by evaluating the stresses and strains on the finite elements. Simulating loading along different axes for small subvolumes of the tomographic data, I determined the Young’s modulus (stiffness) of the heart urchin shell for different positions. Around the mouth of the animal, the material is stiffer into the direction parallel to the mouth whereas on less differentiated positions, Young’s modulus is isotropic. This clearly shows evolutionary adaptions to the expected loading direction but without changing the underlying building principle. On average, the shell performs mechanically close to an ideal foam, even at porosities of 70%. This part of TOMOMECH not only elucidated the evolutionary adaptions in this marine organism and demonstrated the validity of the approach, but also gives us a template to improved synthetic materials (biotemplating).


Figure 1: Work flow in TOMOMECH for deriving mechanical properties on the micro- and nanoscale: The sample (here: a heart urchin shell) is imaged using X-ray tomography. From the tomography data, a 3D model is derived and imported into finite element software.

Chalk (Fig. 2 left) is a biogenic limestone that serves as both aquifer and hydrocarbon reservoir. Thus, learning more about the mechanical properties on the pore scale can help study the impact of drilling or chalk cliff stability. Chalk is formed from the remains of ancient algae, the coccolithosphore, and depending on the degree of compaction, a great deal of the original biological structures has survived. The pores and grains in chalk are thus often less than a micrometre in size which necessitates higher resolution which can only be found at synchrotron radiation facility. My host group had already recorded data for chalk (Fig. 2 middle) from both outcrops and drill cuttings provided by an oil company at different resolution. I used these data to derive simple petrophysical parameters, e.g. porosity and surface area, directly from the data and studied their dependence on porosity. I found that better than 25 nm voxel size is needed and accordingly I chose this data set to perform mechanical simulation following the same approach as for the heart urchin shell. The results of these simulations clearly showed than chalk is much weaker than the heart urchin shell at the same porosity and that chalk’s elastic properties drop rapidly with increasing porosity. However, subvolumes in which more intact fossils could be found performed better than regions consisting only calcite crystals. Later on in the project, my host group acquired new data at even higher resolution. Using these data, I could also study the influence of nanometre sized fracture, which leads to a further decrease in mechanical strength. Comparing my results to macroscopical core plug measurements on chalk, I found very good agreement. Therefore, combining tomography and finite element simulations can deliver sensible results and is especially helpful when macroscopic testing is not possible.

In addition to the main objective of studying mechanical properties, I also employed a technique called dissipative particle dynamics (DPD) to simulate diffusion of particles in the nanoscale pore network of chalk. In this technique (Fig. 2 right), particles are simulated using classical equations of motions and force fields to described interactions between particles and the pore wall as well as particles with each other. Comparing the mean-square displacement for particles in the pores and in free diffusion, I was able to determine the tortuosity of the chalk samples. Tortuosity measured how twisted a pore system is and is itself needed to properly determine permeability. Permeability is an important material constant relating hydraulic pressure to fluid flow and thus describes the capability of a rock to promote fluid flow, i.e. in oil production or groundwater flow. The results of the DPD simulations showed that the size of the particles, i.e. molecules or larger aggregates, becomes important because of the very narrow pore throats in chalks. Thus, bigger oil components could be significantly slowed down. Furthermore, attraction of the particles to the surface causes a further decrease in mean square displacement up to the point where particles are basically trapped.


Figure 2: Work flow in TOMOME CH for simulating particle diffusion: The sample (chalk from outcrop or drill cuttings) is imaged using synchrotron radiation X-ray tomography. The pore surface is extracted from the tomography data and diffusing particle are filled into the pores in a dissipative particle simulation.

Other work done in TOMOMECH include 3D X-ray diffraction measurements on spines of the heart urchin showing that the whole spine behave much like a single crystal as well as processing of tomography data for lattice Boltzmann simulations to derive permeability done by colleagues. In summary, TOMOMECH has achieved its goal of combining tomography and finite element simulations and its results have provided a method to derive material properties for industrial application but also insight into structure-function relationships in biomineralised materials.