[1]	Heiko Herrmann, Wolfgang Muschik, Christina Papenfuß, and Gunnar Rückner. Exploiting the dissipation-inequality in case of constrained state space variables. In Proceedings of the International Symposium on Trends in Continuum Physics TRECOP'98, Singapore, August 17 - 20 1998. World Scientific. [ bib ]
[2]	Heiko Herrmann, Gunnar Rückner, and Wolfgang Muschik. Constitutive theory in general relativity: Basic fields, state spaces and the principle of minimal coupling. Rendiconti del Seminario Matematico dell'Universitá e Politecnico di Torino, 58(2):133-140, 2000. http://www.seminariomatematico.unito.it/rendiconti/58-2.html. [ bib | .ps | .pdf ] A scheme is presented how to describe material properties under the influence of gravitation. The relativistic dissipation inequality is exploited by LIU`s procedure. As an example an ideal spinning fluid is considered in the given frame-work.
[3]	Heiko Herrmann, Gunnar Rückner, and Wolfgang Muschik. Constitutive theory in general relativity: Spin-material in spaces with torsion. Rendiconti del Seminario Matematico dell'Universitá e Politecnico di Torino, 58(2):141-146, 2000. [ bib | .ps | .pdf ] Some of the problems arising in general relativistic constitutive theory can be solved by using the Riemann-Cartan geometry, a generalization of the Riemann geometry containing torsion. As an example the ideal spinning fluid (Weyssenhoff fluid) is discussed and different results for Einstein and Einstein-Cartan theories are compared.
[4]	Heiko Herrmann, Wolfgang Muschik, Christina Papenfuß, and Gunnar Rückner. Liu-technique for exploiting the dissipation-inequality in case of constrained state space variables. In Trends in Application of Mathematics to Mechanics. Chapman & Hall/CRC, 2000. [ bib ]
[5]	Heiko Herrmann, Gunnar Rückner, Wolfgang Muschik, and Horst-Heino von Borzeszkowski. Spin axioms in relativistic continuum physics. Theoretical and Applied Mechanics, 28-29:169-183, 2002. GCM Belgrad. [ bib | DOI | .pdf ]
[6]	Heiko Herrmann, Gunnar Rückner, Wolfgang Muschik, and Horst-Heino von Borzeszkowski. Spin axioms in relativistic continuum physics. arXiv, gr-qc/0208004, 2002. [ bib | arXiv | arXiv | .ps | .pdf | http ] The 24 components of the relativistic spin tensor consist of 3+3 basic spin fields and 9+9 constitutive fields. Empirically only 3 basic spin fields and 9 constitutive fields are known. This empirem can be expressed by two spin axioms, one of them identifying 3 spin fields, and the other one 9 constitutive fields to each other. This identification by the spin axioms is material-independent and does not mix basic spin fields with constitutive properties. The approaches to the Weyssenhoff fluid and the Dirac-electron fluid found in literature are discussed with regard to these spin axioms. The conjecture is formulated, that another reduction from 6 to 3 basic spin fields which does not obey the spin axioms introduces special material properties by not allowed mixing of constitutive and basic fields.
[7]	Heiko Herrmann. Implementation of liu's procedure in mathematica for use in relativistic constitutive theory. arXiv, physics/0206081, 2002. [ bib | arXiv | arXiv | .ps | .pdf | http ] The aim of this article is to show, how computer algebra can be used when applying Liu's procedure. Although Mathematica (a commercial product by Wolfram Research Inc.) is used, it is possible to use other computer algebra systems as well.
[8]	Heiko Herrmann, Gunnar Rückner, and Wolfgang Muschik. Exploiting the second law. In Structured Media (TRECOP'01), Poznan, 2002. Publishing House of Poznan University of Technology. [ bib ]
[9]	Thoralf Chrobok, Heiko Herrmann, and Gunnar Rückner. Spinning fluids in relativistic hydrodynamics. Technische Mechanik, 22(1):1-7, 2002. [ bib | .pdf ] We study the well known propagation and constraint equations in General Relativity for the case where the matter source is an ideal Weyssenhoff fluid. Moreover we derive these equations for the Einstein-Cartan theory of gravitation for the same matter source. We discuss the different couplings of the matter content in detail in both theories and consider especially the behavior of the spin, angular and total angular momentum.
[10]	Heiko Herrmann, Gunnar Rückner, Thoralf Chrobok, and Wolfgang Muschik. Constitutive theory in general relativity and einstein-cartan theory: Spin balances, energy-momentum balances and weyssenhoff-fluid. Technische Mechanik, 22(1):66-73, 2002. [ bib | .pdf ] It is shown, that the usually considered spin balances are too restrictive and only valid for pointlike particles. Furthermore, we will derive the full spin balance and discuss the Weyssenhoff-Fluid.
[11]	Gunnar Rückner, Heiko Herrmann, and Wolfgang Muschik. Constitutive theory in general relativity: Possible applications to cosmology and the weyssenhoff-fluid. In Proceedings of the 5th International Seminar on Geometry, Continua and Microstructures 2001, Bukarest, September 26 - 28, 2002. Editura Academiei Romane. [ bib ]
[12]	Heiko Herrmann, Gunnar Rückner, and Wolfgang Muschik. Constitutive theory in grt and ect: Geometrically induced constraints to state spaces and constitutive laws. In Proceedings of the 5th International Seminar on Geometry, Continua and Microstructures 2001, Bukarest, September 26 - 28, 2002. Editura Academiei Romane. [ bib ]
[13]	Heiko Herrmann. Non-equilibrium Thermodynamics in Geometrized Theories of Gravitation with Curvature and Torsion. dissertation.de Verlag im Internet, Dissertation, Fakultät II, TU Berlin, D83, 2003. ISBN 3-89825-662-6. [ bib | http ] In this thesis the constitutive theory - which is well-developed in non-relativistic physics - is formulated for geometrized theories of gravitation with curvature and torsion. In the introduction an overview about the non-relativistic constitutive theory is presented and some problems of constitutive theory in GRT are mentioned. Then the fundamentals of ECT (Einstein-Cartan Theory) are given. In the main part the relativistic balances for particle number density, energy-momentum, spin, and entropy are given as ”ad hoc” equations, motivated by their non-relativistic analoga. A special set of balances is derived as a consequence of the field equations of GRT and ECT. The comparison of both sets of balances shows that some balances cannot be derived from the field equations (and therefore not from a variational principle). Another difference is that the ”balances” which are consequences of the field equations do not allow for the existence of external fields, but have geometrical sources. The complete set of balances can be generated by including the geometrical sources into the ad hoc equations. These complete balances are not compatible with the field equations of GRT and ECT; because of this, a motivation for a possible modification of the field equations is given. This procedure is based on the assumption, that a geometrized theory of gravitation as a frame theory has to allow for the description of complex materials, although these might not be of astrophysical interest (up to now). The balances, motivated by ”lifting”, are assumed to be also valid in geometrized theories of gravitation. Spin and energy-momentum are supposed to couple directly to geometry. The modification of the field equations, introduced in this context, shall denote a possible way to formulate field equations and balances in a consistent way. It is open whether it is possible to derive the balances (including the balance of entropy!) together with the field equations by a variational principle; this is not a topic of this thesis. The balance of spin is investigated. It contains 6 equations for 6 wanted spin fields, but only 3 of them are measurable up to now. The spin tensor consists of 24 independent components, 6 wanted fields, and 18 constitutive functions. As a possible solution for the problem of the additional spin fields, spin axioms are formulated. These spin axioms state, that also in relativity theory only 3+9 spin fields exist. Furthermore the spin axioms identify the additional 3+9 fields with the known 3+9, without introducing a special constitutive relation. As the number of independent components of the spin tensor is reduced, restrictions to geometry arise due to the fields equations. In the consequence of the spin axioms, the spin tensor is self-dual with respect to the first 2 indices. This implies that the modified torsion is also self-dual. The restrictions to geometry provide the possibility for experimental verification of the spin axioms. Using the complete set of balances for extended ECT (Riemann-Cartan geometry plus field equations plus complete balances), Liu's procedure is applied to state spaces that are compatible with a generalized Weyssenhoff fluid. The restrictions for the entropy density, entropy flux, and entropy production are derived for the Weyssenhoff fluid. The remarkable point is: Although the constitutive ansatzes for the Weyssenhoff fluid are very restrictive, there is still some freedom for the entropy density, entropy flux, and entropy production.
[14]	Heiko Herrmann, Gunnar Rückner, Wolfgang Muschik, and Liliana Restuccia. Objectivity and the non-objective part of material frame indifference. In Trends in Continuum Physics. Poznan House of Publishing, 2004. [ bib ]
[15]	Heiko Herrmann, Wolfgang Muschik, Gunnar Rückner, and Horst-Heino von Borzeszkowski. Spin axioms in different geometries of relativistic continuum physics. Foundations of Physics, 34(6):1005-1021, 2004. [ bib | DOI ] The 24 components of the relativistic spin tensor consist of 3 + 3 basic spin fields and 9 + 9 constitutive fields. Empirically only three basic spin fields and nine constitutive fields are known. This empirem can be expressed by two spin axioms, one of them denying purely relativistic spin fields, and the other one relating the three additional basic fields and the nine additional constitutive fields to the known (and measurable) ones. This identification by the spin axioms is material-independent and does not mix basic spin fields with constitutive properties. The approaches to the Weyssenhoff fluid and the Dirac-electron fluid found in literature are discussed with regard to these spin axioms. The conjecture is formulated, that another reduction from six to three basic spin fields which does not obey the spin axioms introduces special material properties by not allowed mixing of constitutive and basic fields.
[16]	Wolfgang Muschik, Jürgen Siebert, Heiko Herrmann, and Gunnar Rückner. Close-to-fourier heat conduction equation of solids of constant mass density. Journal of Non-Equilibrium Thermodynamics, 30(4):375-383, 2005. [ bib | DOI ] Heat conduction close-to-Fourier means that we look for a minimal extension of heat conduction theory using the usual Fourier expression of the heat flux density and modifying that of the internal energy as minimally as possible by choosing the minimal state space. Applying Liu's procedure results in the class of materials and a dierential equation both belonging to the close-to-Fourier case of heat conduction.
[17]	Heiko Herrmann, Gunnar Rückner, and Wolfgang Muschik. Spin axioms in relativistic continuum theory. In Applied and Industrial Mathematics in Italy, pages 371-380. World Scientific, Singapore, 2005. SIMAI 2004. [ bib | DOI ]
[18]	Heiko Herrmann and Gunnar Rückner. Comparison of two different implementations of a finite-difference-method for first-order pde in mathematica and matlab. arXiv, cs.CE/0506051, 2005. [ bib | arXiv | arXiv | .ps | .pdf | http ] In this article two implementations of a symmetric finite difference algorithm for a first-order partial differential equation are discussed. The considered partial differential equation discribes the time evolution of the crack length distribution of microcracks in brittle materia.
[19]	Heiko Herrmann. daemonic tux: Linux mit pkgsrc. freeX, 2007(5):60-61, 2007. [ bib ]
[20]	Christina Papenfuss, Thomas Böhme, Heiko Herrmann, Wolfgang Muschik, and Josef Verhás. Dynamics of the size and orientation distribution of microcracks and evolution of macroscopic damage parameters. Journal of Non-Equilibrium Thermodynamics, 32(2):1-14, 2007. [ bib | DOI ] We are dealing with damage of brittle materials caused by growth of microcracks. In our model the cracks are penny-shaped. They can only enlarge but not heal. For a single crack a RiceGriffith growth law is assumed: There is crack growth only if tension is applied normally to the crack surface, exceeding a critical value. Our aim is to investigate the effect of crack growth on macroscopic constitutive quantities. A possible approach taking into account such an internal structure within continuum mechanics is the mesoscopic theory. A distribution of crack lengths and crack orientations within the continuum element is introduced. Macroscopic quantities are calculated as averages with the distribution function. A macroscopic measure of the progressing damage, i.e., a damage parameter, is the average crack length. For this scalar damage parameter we derive an evolution equation. Due to the unilateral growth law for the single crack, it turns out that the form of this differential equation depends explicitly on the initial crack length distribution. In order to treat biaxial loading, it is necessary to introduce a tensorial damage parameter. We define a second-order tensor damage parameter in terms of the crack length and orientation distribution function.
[21]	Heiko Herrmann. Linux ohne laufwerkschaos. freeX, 2008(4):52-53, 2008. [ bib ]
[22]	Heiko Herrmann, Hong Gu, Gunnar Rückner, Jürgen Siebert, and Wolfgang Muschik. Close-to-fourier heat conduction equation for solids: Motivation and symbolic-numerical analysis. Atti della Accademia Peloritana Dei Pericolanti, LXXXVI(Supplement 1):1-10, 2008. [ bib | DOI | .pdf ] Heat conduction close-to-Fourier means, that we look for a minimal extension of heat conduction theory using the usual Fourier expression of the heat flux density and modifying that of the internal energy as minimal as possible by choosing the minimal state space. Applying Liu's procedure results in the class of materials and a differential equation both belonging to the close-to-Fourier case of heat conduction. A symbolic-numerical computing method is applied to approximate the numerical solutions of 2 special heat conduction equations belonging to the close-to-Fourier class.
[23]	Heiko Herrmann and Peter Ván, editors. Special issue on continuum physics and engineering applications, volume 57(3) of Proceedings of the Estonian Academy of Sciences, September 2008. Preface by Jüri Engelbrecht, Heiko Herrmann and Peter Ván. [ bib | http ]
[24]	Heiko Herrmann. Discretization of continuum physics - a comparison of numerical methods from a physical point of view. Proceedings of the Estonian Academy of Sciences, 57(3):145-154, September 2008. [ bib | DOI | .pdf ] For numerical calculations in continuum physics partial differential equations and the space-time are discretized. This can be done in different ways. Common approaches are finite difference methods and finite element methods, more rarely finite volume methods are used. Each method has different mathematical properties, which have been discussed in the literature, but they also imply a different physical meaning. This issue is discussed in this article and the connection of finite volume methods to thermodynamics of discrete systems is shown.
[25]	Loreta Kelpsaite, Heiko Herrmann, and Tarmo Soomere. Wave regime differences along the eastern coast of the baltic proper. Proceedings of the Estonian Academy of Sciences, 57(4):225-231, December 2008. [ bib | DOI | .pdf ] An effort is made to identify the basic features of subdecadal and decadal changes in the wave climate at different locations in the eastern sector of the Baltic Proper based on the annual mean wave height. Comparison of Vilsandi and Almagrundet data from the northern Baltic Proper with visual observations from the Lithuanian coast during 1993-2005 shows that short-term variations (13 years) of the annual mean wave height have a similar nature at all sites but trends of decadal and subdecadal variability are very different in different parts of the Baltic Proper.
[26]	Heiko Herrmann. Towards a description of twist waves in mesoscopic continuum physics. In Ewald Quak and Tarmo Soomere, editors, Applied Wave Mathematics - Selected Topics in Solids, Fluids and Mathematical Methods, pages 127-145. Springer, 2009. [ bib | DOI ] An introduction to Mesoscopic Continuum Physics is given with a focus on Liquid Crystals. Mesoscopic Continuum Physics introduces variables describing the microstructure - like orientation of crystals - into the domain of the fields, thus treating them equivalently to space. The theory of Mesoscopic Continuum Physics has been reformulated, resulting in more compact equations. In this formulation the balance of spin shows up naturally as component equations of the balance of momentum, this is an advantage over the standard formulation, in which it seems to be postulated separately. Starting from this, a wave equation for twist waves has been derived on the mesoscopic space. Twist waves are one of the fundamental modes of orientation waves in liquid crystals. A short repetition of twist-waves of liquid crystals in the Ericksen-Leslie theory is given and compared to a description using the mesoscopic theory.
[27]	Heiko Herrmann and Karl Heinz Hoffmann. Remarks around additional 56 lines of matlab: short parallel finite element implementation using pmatlab. Research Report 296/10, CENS, Institute of Cybernetics at TUT, October 2010. [ bib ] Following Alberty/Carstensen/Funke a parallel Matlab implementation for P1-Q1 finite elements is provided for the numerical solution of elliptic problems on unstructured grids. In this article pMatlab will be used for parallelization and distribution of matrices over the compute cluster.
[28]	Heiko Herrmann and Jüri Engelbrecht. The balance of spin from the point of view of mesoscopic continuum physics for liquid crystals. Journal of Non-Equilibrium Thermodynamics, 35(3):337-346, October 2010. [ bib | DOI ] In this article mesoscopic continuum physics is reviewed using generalized coordinates in the context of liquid crystals. A special focus is put on the balance of spin (internal angular momentum). Mesoscopic continuum physics introduces variables describing the micro-structure - like the orientation of crystals - into the domain of the fields, thus treating them equivalently to space. The theory of mesoscopic continuum physics has been reformulated, resulting in more compact equations. In this formulation the balance of spin shows up naturally as component equations of the balance of momentum, this is an advantage over the standard formulation of mesoscopic continuum physics.
[29]	Heiko Herrmann and Marika Eik. Some comments on the theory of short fibre reinforced material. Proceedings of the Estonian Academy of Sciences, 60(3):179-183, July 2011. [ bib | DOI | .pdf ] The orientation of fibres in short fibre reinforced materials is essential for the properties of the composite. It is state of the art to use an orientation number to estimate how many fibres are aligned in stress direction. This, however, is a very crude approach, as the orientation number is defined by use of the average of the projected length of the fibres. Therefore, the orientation number is not a material property - it depends also on the projection direction. Additionally, a simple number cannot be used to describe anisotropic properties. In this paper we introduce a tensorial approach, which is objective and consists of real material properties.
[30]	Heiko Herrmann. Tex im team. freeX, 2012(1):58-61, 2012. [ bib ]
[31]	Heiko Herrmann and Jüri Engelbrecht. Comments on mesoscopic continuum physics: Evolution equation for the distribution function and open questions. Proceedings of the Estonian Academy of Sciences, 61(1):71-74, January 2012. [ bib | DOI | .pdf ] In mesocopic continuum physics it is common to introduce a mesoscopic distribution function, and also often an evolution equation is derived for this distribution function. The mesoscopic balance equations for mass and the evolution equation for the distribution function, however, are not independent. In this paper different usage cases of mesocopic balances in connection with the evolution equation are discussed. Furthermore the problem of virtual boundaries is discovered, this refers to cases, where the domain in the mesoscopic description becomes non-contiguous despite the macroscopic domain being contiguous.
[32]	Heiko Herrmann. Software tools for science and engineering. Lecture Notes 9/2012, CENS, Institute of Cybernetics at TUT, March 2012. [ bib ] In science and engineering many different software tools are needed and available. But which one is to be used for which purpose? Often a combination of differen small tools proofs to be more useful than a fully integrated suite. This article shall give an overview what software is available, give some examples, some introductions, but also mention some limitations.
[33]	Marika Eik and Heiko Herrmann. Raytraced images for testing the reconstruction of fibre orientation distributions. Proceedings of the Estonian Academy of Sciences, 61:128-136, May 2012. [ bib | DOI | .pdf ] The orientation distribution of fibres is relevant for the properties of many different kinds of materials from many fields, like biology and engineering. In short fibre reinforced composites it is essential for the properties of these materials. PoV-Ray - the Persistence of Vision Raytracer - is a program to create photorealistic images using raytracing. Here we present a sort of “creative misuse” of this program in science, as it was originally developed as an artistic software. However the ability to create virtual images of virtual parts, to test the image recognition software, that is used to measure the fibre orientation distribution, and to be able to compare the result with the known distibution is a huge step forward. In this article the focus is on slicing/photometry, but also CT-like images or microscope images could be produced and used to test segmentation and skeletonization algorithms.
[34]	Jussi-Petteri Suuronen, Aki Kallonen, Marika Eik, Jari Puttonen, Ritva Serimaa, and Heiko Herrmann. Analysis of short fibres orientation in steel fibre reinforced concrete (SFRC) using x-ray tomography. Journal of Materials Science, 48(3):1358-1367, February 2013. [ bib | DOI ] The mechanical properties of fibre composite materials are largely determined by the orientation of fibres within the matrix. Which orientation distribution short fibres follow in different parts of a structural element is still a subject for research and discussions in the scientific community. In this article, we present a modern and advanced method for measuring the orientation of short fibres in steel fibre-reinforced concrete (SFRC) by X-ray microtomography. With this method, a voxel image of the fibres is obtained directly in 3D, and the orientation of each individual fibre is calculated based on a skeletonized representation of this image. Scans of 12 SFRC samples, taken from the central height region of real-size floor slabs, reveal the fibres to be mostly horizontally oriented near the centre of a floor slab and more vertically oriented near the edge; here the alignment with the formwork dominates. The fibre orientation distributions are characterized by several orientation parameters as quantitative measures for the alignment. On the practical side, this method has the potential to be incorporated into the development and production process of SFRC structures to verify how the fibres contribute to capacity.
[35]	Marika Eik, Karl Lõhmus, Martin Tigasson, Madis Listak, Jari Puttonen, and Heiko Herrmann. DC-conductivity testing combined with photometry for measuring fibre orientations in SFRC. Journal of Materials Science, 48(10):3745-3759, May 2013. [ bib | DOI ] The orientation distribution of fibres has an important impact on the properties of short-fibre reinforced composites. This article introduces a methodology for defining fibre orientations in steel fibre reinforced concrete (SFRC). The main method under consideration is the slicing, where two approaches are introduced, i.e. the photometric analysis and DC-conductivity measurements by a special robot. The advantage of presented slicing method is the fact, that a combined analysing approach is utilized, DC-conductivity testing is joined together with the image analysis. As a result, significant benefits are achieved, e.g. the ability of measuring the orientation of an individual fibre, the measuring of the in-plane angle in the interval [0°, 360°]. An additional important aspect in the presented slicing method is the possible usage of the structural parts extracted from the full-size floor-slabs as specimens, as it is done here. The authors present the statistics of fibre orientations, which are based on the experimental data received by the application of the mentioned analysing approaches. The presented slicing method with its possible extensions offers possibilities to improve the quality control while producing SFRC products.
[36]	Marika Eik, Jari Puttonen, and Heiko Herrmann. Fibre orientation phenomenon in concrete composites: measuring and theoretical modelling. In Fibre Concrete 2013. Faculty of Civil Engineering CTU in Prague, September 2013. [ bib ]
[37]	Emiliano Pastorelli and Heiko Herrmann. A small-scale, low-budget semi-immersive virtual environment for scientific visualization and research. Procedia Computer Science, 25(iii-iv):14-22, September 2013. [ bib | DOI ] This paper describes the design concepts, the making of and some applications of the first Estonian Virtual Reality Environment. Using hardware only slightly above the threshold of consumer level, we built a virtual environment (VE) aimed at scientific visualization with the lowest possible space requirements (smaller than a cube with 2 m edge length in total) and budget (approximately below 30.000 Euro). The system is a fully functional visualization environment that replicates most of the features and properties of a real-sized CAVE-like System, therefore allowing further prototyping and research in the field of Virtual Reality.
[38]	Rene Haber, Janett Prehl, Heiko Herrmann, and Karl Heinz Hoffmann. Diffusion of oriented particles in porous media. Physics Letters A, 377(40):2840-2845, November 2013. [ bib | DOI ] Diffusion of particles in porous media often shows subdiffusive behavior. Here, we analyze the dynamics of particles exhibiting an orientation. The features we focus on are geometrical restrictions and the dynamical consequences of the interactions between the local surrounding structure and the particle orientation. This interaction can lead to particles getting temporarily stuck in parts of the structure. Modeling this interaction by a particular random walk dynamics on fractal structures we find that the random walk dimension is not affected while the diffusion constant shows a variety of interesting and surprising features.
[39]	Renè Haber, Janett Prehl, Karl Heinz Hoffmann, and Heiko Herrmann. Random walks of oriented particles on fractals. Journal of Physics A: Mathematical and Theoretical, 47(15):155001, April 2014. cover picture. [ bib | DOI ] Random walks of point particles on fractals exhibit subdiffusive behavior, where the anomalous diffusion exponent is smaller than one, and the corresponding random walk dimension is larger than two. This is due to the limited space available in fractal structures. Here, we endow the particles with an orientation and analyze their dynamics on fractal structures. In particular, we focus on the dynamical consequences of the interactions between the local surrounding fractal structure and the particle orientation, which are modeled using an appropriate move class. These interactions can lead to particles becoming temporarily or permanently stuck in parts of the structure. A surprising finding is that the random walk dimension is not affected by the orientation while the diffusion constant shows a variety of interesting and surprising features.
[40]	Heiko Herrmann, Marika Eik, Viktoria Berg, and Jari Puttonen. Phenomenological and numerical modelling of short fibre reinforced cementitious composites. Meccanica, 49(8):1985-2000, August 2014. [ bib | DOI ] In this paper, a constitutive model for short fibre reinforced cementitious composites will be presented. This model is based on the St. Venant-Kirchhoff model, which is a special case of a hyperelastic material. This model is refined to include the fibre orientation distribution. Numerical FEM simulations with the developed constitutive model and fracture simulations using the discrete element method are presented. The outcomes of these numerical methods demonstrate how important it is to monitor and further to control the fibre orientation distribution during the manufacturing process. As the manufacturing process might involve casting, as, e.g., in the case of steel fibre reinforced concrete, an outlook on simulations of the manufacturing process in order to predict and to control the fibre orientation distribution is given.
[41]	Emiliano Pastorelli and Heiko Herrmann. Virtual reality visualization for short fibre orientation analysis. In 2014 14th Biennial Baltic Electronic Conference (BEC), pages 201-204, October 2014. [ bib | DOI ] The paper investigates the beneficial contribution of visual feedback in the development of an algorithm for the automatized analysis of fibre orientations in short fibre reinforced composites. Of special interest was steel fibre reinforced concrete (SFRC), a multi-disciplinary research area involving material sciences, physics and civil engineering. More in detail, this paper explains how scientific visualization techniques, employed on a Virtual Reality environment, contribute to the understanding of the SFRC properties, both for research and educational aims. Furthermore, the analysis algorithm to obtain fibre orientation distributions from noisy tomography scans is presented.
[42]	Emiliano Pastorelli and Heiko Herrmann. Complex materials analysis and visualization through virtual reality environments. In Proceedings of the 8th Annual Conference of the Estonian National Doctoral School in Information and Communication Technologies, pages 99-102. Tallinn University of Technology, December 2014. December 5-6, 2014, Rakvere. [ bib ] The paper depicts the development of a series of analysis and visualization tools aimed at supporting scientific research in the field of complex materials. This paper specifically focuses on steel fibre reinforced concrete (SFRC), a multi-disciplinary research area involving material sciences, physics and civil engineering. More in detail, it is explained how scientific visualization techniques, employed on a Virtual Reality environment, contribute to the understanding of the SFRC properties, both for research and educational aims.
[43]	Heiko Herrmann, Marcel Padilla, and Emiliano Pastorelli. A.C.T.I.V.E.: A Scalable Superellipsoid-based CFD Visualization for Virtual and Desktop Environments. In Jerome Perret, Valter Basso, Francesco Ferrise, Kaj Helin, Vincent Lepetit, James Ritchie, Christoph Runde, Mascha van der Voort, and Gabriel Zachmann, editors, EuroVR 2014 - Conference and Exhibition of the European Association of Virtual and Augmented Reality. The Eurographics Association, December 2014. [ bib | DOI ] The paper presents a flexible software (A.C.T.I.V.E.) able to visualize the superellipsoidal glyphs describing the orientation of short fibres during the dynamic process of casting a short fibre reinforced composite in a container. The software is designed to run on the VRUI framework and it features an optional face-tracking to grant a more natural interaction also on standard non-3D displays. Due to its flexibility it can be used on a wide range of environments, from desktop computer to multi-screen CAVE-like systems.
[44]	Heiko Herrmann and Emiliano Pastorelli. Virtual reality visualization for photogrammetric 3d reconstructions of cultural heritage. In Lucio Tommaso De Paolis and Antonio Mongelli, editors, Augmented and Virtual Reality, volume 8853 of Lecture Notes in Computer Science, pages 283-295. Springer International Publishing, December 2014. [ bib | DOI ] In this paper the authors review the design of a self-build general-purpose Virtual Reality environment, which presents all relevant features of a full-size CAVE-like system, yet at a fraction of the financial and space requirements. Further, the application of this system to the development of a virtual museum is presented. The objects in the museum are models, reconstructed via photogrammetry from a set of pictures. For this process cost-free software is used. The presentation of the 3D models in the Virtual Environment is done using BlenderCAVE, a multi-screen extension of the Blender game engine. The main contributions of this paper are the discussion of the design choices for a small and low-budget but feature-rich virtual reality environment and the application of the system for cultural heritage. In this area tools for creation of 3D models and their presentation in a VR environment are presented.
[45]	Marika Eik, Jari Puttonen, and Heiko Herrmann. An orthotropic material model for steel fibre reinforced concrete based on the orientation distribution of fibres. Composite Structures, 121(0):324-336, March 2015. [ bib | DOI ] In the present paper the authors focus on constitutive mappings for steel fibre reinforced concrete, SFRC. The anisotropic properties of this composite are caused by the orientation distribution of fibres. The constitutive relation is developed for one meso-volume element of {SFRC} as a combination of isotropic and orthotropic St. Venant–Kirchhoff material models, which are applied to concrete matrix and to steel fibres, respectively. The alignment tensors and orientation distribution function adopted from the mesoscopic continuum theory are utilised to identify the material meso-symmetry axes and to asses the contribution of fibres in the symmetry axes defined. While assessing the orthotropic meso-elasticity for fibres, the elasticity of an individual fibre in its local coordinates is transformed into the material meso-symmetry axes and weighted with the orientation distribution function of fibres. The advantage of the material model developed for {SFRC} is that it uses complete orientation information of fibres (two angles in spherical coordinates) and utilises tensor quantities complying with material objectivity.
[46]	Marika Eik, Heiko Herrmann, and Jari Puttonen. Orthotropic constitutive model for steel fibre reinforced concrete: linear-elastic state and bases for the failure. In R. Kouhia, J. Mäkinen, S. Pajunen, and T. Saksala, editors, Proceedings of the XII Finnish Mechanics Days : [4-5 June 2015, Tampere, Finland], pages 255-260, June 2015. [ bib | .pdf ] Steel fibre reinforced concrete (SFRC) is a highly promising building material offering durable structures alongside with the minimisation of steel consumption and construction time. Though, its reliable application in civil engineering requires a deeper study due to complex material properties defining its failure and related to volumetric dispersion of fibres, and a bond between the fibres and concrete. The different fibre alignments in concrete matrix lead to anisotropic behaviour, which specifies the tensile strength and the crack intensity of the composite. SFRC crack initiation and development, and failure depend on the strength of the bond and interaction between the steel fibres and concrete. The present paper focuses on the modelling of SFRC linear-elastic state considering and evaluating the orientation distribution of fibres. In addition, the bases of SFRC failure are introduced.
[47]	Tomas Torsvik, Heiko Herrmann, Ira Didenkulova, and Artem Rodin. Analysis of ship wake transformation in the coastal zone by use of timefrequency methods. Proceedings of the Estonian Academy of Sciences, 64(3S):379-388, July 2015. [ bib | DOI ] Ship wake transformation in the coastal zone is analysed based on field measurements of wave conditions at two measurement sites located about 20 m and 100 m from the shore. Analysis of single wake events recorded at both sites is carried out by transforming the time series of the wave amplitude into the time-frequency domain, using both a short-time Fourier transform and a wavelet transform. Analysis reveals that signature features of individual wake components can be tracked as the wake approaches the shore, but the wave amplitude and associated wave energy is transformed differently for different wake components. The wake energy is reduced as the waves propagate through the surf zone, which can be attributed mainly to wave breaking of the leading wave system and a significant reduction of the divergent wave system. However, the energy of transverse waves is stable or increasing, indicating that these waves undergo a non-breaking shoaling process.
[48]	Francesco Ricciardi, Emiliano Pastorelli, Lucio Tommaso De Paolis, and Heiko Herrmann. Scalable medical viewer for virtual reality environments. In Lucio Tommaso De Paolis and Antoni Mongelli, editors, Augmented and Virtual Reality, volume 9254 of Lecture Notes in Computer Science, pages 233-243. Springer International Publishing, August 2015. [ bib | DOI ] This paper presents a scalable virtual reality-based software for medical visualization. Usable on a desktop, on a head-mounted display or on a CAVE-like system, the application allows the full inspection of CT or MRI images superimposed to the 3D models of the organs built from these images. Additionally full volume rendering functionalities and several interaction tools as transparencies, choice of the CT slice to display, hiding and showing of meshes and additional information on the scanning procedure are available. The tool aims at offering an in-depth inspection of the body organs for medical, education and surgical preoperative planning.
[49]	Heiko Herrmann, Kadi Kasepõld, Inga Zaitseva-Pärnaste, Emiliano Pastorelli, and Ira Didenkulova. Photogrammetry based methodology for construction of a first reference 3D model of Pakri cliff for future monitoring of coastal changes and hazard assessment for Pakri lighthouse. Baltic Horizons, 23:57-63, September 2015. [ bib ] This paper reviews the use of photo-based surface reconstruction technique to reveal its potential to monitor and suvey vulnerable parts of the Estonian coast. The aim of the study is to outline the general approach to data acquisition and processing using images acquired from unmanned aerial Vehicles (UAVs) in producing a 3D model for Pakri cliff, north-western Estonia. It is shown that an adequate 3D model of the area can be acquired at high resolution and in much shorter time interval than would norally be achieved through alternative methods. We provide some examples for the use of such technique while pointing to free software packages for data processing, visualization and 3D interpretation. Photogrammetric models serve to act as a cheap alternative to laser scannin or aircraft-based photographic surveys and can be used as a rough estimation of the evolution of the coast due to the action of the sea and other natural and human-induced hazards.
[50]	Heiko Herrmann. Varjatud maailma nähtavaks tegemine: Visualiseerimine. kyb3. raudbetooni sisu. In Jüri Engelbrecht and Tiit Kändler, editors, Keeruka maailma võlu, pages 31-34, Tallinn, Estonia, October 2015. Tallinna Tehnikaülikooli Küberneetika Instituut. [ bib ]
[51]	Heiko Herrmann. A constitutive function for the heat flux in short fibre reinforced composites. Journal of Non-Equilibrium Thermodynamics, 40(4):257-263, December 2015. [ bib | DOI ] A constitutive function for the heat flux in short fiber reinforced compostes is developed. The fiber orientation distribution is considered by means of the second order orientation tensor, therefore the constitutive function for the heat flux will depend on the orientation tensor. The resulting orthotropic equation is discussed also in the context of energy efficiency of buildings.
[52]	Heiko Herrmann. Generalized Continua as Models for Classical and Advanced Materials, chapter An Improved Constitutive Model for Short Fibre Reinforced Cementitious Composites (SFRC) Based on the Orientation Tensor, pages 213-227. Springer International Publishing, Cham, 2016. [ bib | DOI ] Short fibre composites are becoming increasingly popular in many applications. This is also true for civil engineering, where short fibre cementitious composites are used more often. For the use in load bearing structures, a constitutive mapping is necessary to calculate the design load and to predict cracking behaviour. Here a constitutive mapping based on the use of isotropic tensor functions of the strain tensor and the orientation tensor is proposed. The model solves some issues of other approaches. A comparison with other constitutive mappings based on tensors is provided.
[53]	Emiliano Pastorelli and Heiko Herrmann. Time-efficient automated analysis for fibre orientations in steel fibre reinforced concrete. Proceedings of the Estonian Academy of Sciences, 65(1):28-36, March 2016. [ bib | DOI | .pdf ] One of the most important factors to determine the mechanical properties of a fibre composite material is the orientation of the fibres in the matrix. Their orientation might differ in distinct parts of the structural element as dependent from the casting techniques and mould materials. This paper presents an algorithm to retrieve the single fibre's orientation information out of SFRC samples scanned through a μCT scanner. The software implemented with the algorithm includes a data filtering component to remove the noise from the datasets and prepare them correctly for the analysis. Due to its short computational times and its almost complete lack of need for external user intervention, the software is able to process and analyse large batches of data in short periods by providing results in a variety of visual and numerical formats.
[54]	Heiko Herrmann, Emiliano Pastorelli, Aki Kallonen, and Jussi-Petteri Suuronen. Methods for fibre orientation analysis of x-ray tomography images of steel fibre reinforced concrete (sfrc). Journal of Materials Science, 51(8):3772-3783, April 2016. [ bib | DOI ] One of the most important factors to determine the mechanical properties of a fibre composite material is the orientation of the fibres in the matrix. This paper presents Hessian matrix-based algorithms to retrieve the orientation of individual fibres out of steel fibre reinforced cementitious composites samples scanned with an X-ray computed tomography scanner. The software implemented with the algorithms includes a massive data filtering component to remove noise from the data-sets and prepare them correctly for the analysis. Due to its short computational times and limited need for user intervention, the software is able to process and analyse large batches of data in short periods and provide results in a variety of visual and numerical formats. The application and comparison of these algorithms lead to further insight into the material behaviour. In contrast to the usual assumption that the fibres act only along their main axis, it is shown that the contribution of hooked-end fibres in other directions may be noticeable. This means that fibres, depending on their shape, should act as orthotropic inclusions. The methods can be used by research laboratories and companies on an everyday basis to obtain fibre orientations from samples, which in turn can be used in research, to study stress-strain behaviour, as input to constitutive models or for quality assurance.
[55]	Marika Eik, Jari Puttonen, and Heiko Herrmann. The effect of approximation accuracy of the orientation distribution function on the elastic properties of short fibre reinforced composites. Composite Structures, 148:12-18, July 2016. [ bib | DOI | http ] In present paper the authors are focusing on the features of the orientation distribution function (ODF), used to give a probabilistic assessment to the orientation of fibres in fibre reinforced composites. The ODF can be approximated using experimental data and used to evaluate the anisotropic effect of fibres in considered directions. The hardened orthotropic elastic properties of steel fibre reinforced concrete (SFRC), evaluated based on the approximated ODF with different orders of accuracy are used as a case study. Input data for the approximation of the ODF are individual orientations of fibres measured by X-ray micro-tomography method. The study outcomes revealed that the orthotropic elastic properties of SFRC may not be estimated accurately enough by using only the second order terms in the reconstruction of the ODF. The accuracy of the stiffness matrix components is sensitive for the orientation distribution type and the approximation of the ODF, and this should be considered in all FE applications using the ODF approach. Besides, within the study the relation between the values of the scalar-order parameter S, evaluating how well the fibres are aligned with each other, and the approximation orders of the ODF is established.
[56]	Heiko Herrmann and Aarne Lees. On the influence of the rheological boundary conditions on the fibre orientations in the production of steel fibre reinforced concrete elements. Proceedings of the Estonian Academy of Sciences, 65(4):408-413, December 2016. Open-Access CC-BY-NC 4.0. [ bib | DOI | .pdf ] In this paper the influence of the boundary conditions on the fibre orientation distribution in rheology simulations of the casting of steel fibre reinforced concrete is discussed. The slip-length of the boundary condition can have a significant influence on the orientation of the fibres. This means that the material and surface properties of the formwork need to be taken into account when designing casting technology for elements made of steel fibre reinforced concrete. This also implies, that there is a chance to influence the fibre orientations by choosing appropriate surface properties of the formwork.
[57]	Heiko Herrmann and Jürgen Schnell, editors. Colloquium 582: Short Fibre Reinforced Cementitious Composites and Ceramics - Book of Abstracts. Tallinn University of Technology, Department of Cybernetics, March 2017. [ bib ]

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