Christian Hellmich

• Head of Department at TU Wien

This study addresses a critical gap in the literature by developing a unified analytical model for evaluating the stability and dynamic behavior of cylindrical sandwich shells with functionally graded nanocomposite face sheets and variable-porosity cores. The model incorporates graphene nanoplatelets (GNP) and carbon nanotubes (CNT) as reinforcemen...

State-of-the-art monitoring equipment has been a key element of the New Austrian Tunneling Method (NATM) ever since its establishment and description in the 1960s. In particular so-called hybrid methods combining geodetic displacement measurements with material and structural mechanics modeling have provided access to the ground pressure distributi...

In this article, an exact analytical method for the free vibration analysis of functionally graded (FG) graphene platelet (GPL)-reinforced composite (GPLRC) sector cylindrical shells is presented by considering Levy-type boundary conditions for the first time. The analysis relies on the use of the Halpin–Tsai micro-mechanical model for evaluating t...

High-resolution imaging technologies such as micro-computed tomography (CT) have not only revealed the intricate geometrical properties of biomedical materials and systems such as hard tissue engineering scaffolds, but also provided important data sources for the mechanical integrity of these systems, including implants. For the latter purpose, mec...

Organisms generate shapes across size scales. Whereas patterning and morphogenesis of macroscopic tissues has been extensively studied, the principles underlying the formation of micrometric and submicrometric structures remain largely enigmatic. Individual cells of polychaete annelids, so-called chaetoblasts, are associated with the generation of...

The New Austrian Tunneling Method (NATM) essentially rests on observational information concerning displacements measured in selected positions at the inner surface of shotcrete tunnel shells. The combination of these measurements with advanced material and structural mechanics, in the course of so-called hybrid methods, have successfully delivered...

There is a need to develop an integrated computational platform that will contain both datasets and multiscale models related to bone (modelling), cancer, cardiovascular diseases, and tissue engineering. The SGABU platform is a robust information system capable of data integration, information extraction, and knowledge exchange, with the goal of de...

Hybrid methods, i.e. combinations of deformation measurements with structural and material mechanics have been successfully used, for more than 20 years, for the New Austrian Tunneling Method (NATM), and beyond. This contribution extends these developments with respect to the mechanical behavior of such structures for more efficient evaluation of l...

The Mori-Tanaka-Benveniste scheme is very popular for the homogenization of the elastic stiffness of microheterogeneous composites consisting of one matrix phase and any number of inclusion phases. In addition, the scheme allows for homogenization of eigenstresses/eigenstrains, e.g. in the fields of poroelasticity, thermoelasticity, drying shrinkag...

Falling weight deflectometer (FWD) tests are performed worldwide for assessing the health of pavement structures. Interpretation of FWD-measured surface deflections turns out to be challenging because the behavior of pavement structures is temperature-dependent. In order to investigate the influence of temperature on the overall pavement performanc...

The elastic compliance of cementitious materials increases slightly, and their time-dependent “creep” compliance increases significantly with increasing temperature. The present contribution provides quantitative insight into this topic. Thereby, the focus rests on mature cement paste made from Ordinary Portland cement and distilled water. Macrosco...

The compressive strength evolution of 37 centigrade-cured Biodentine, a cement-based dental material, is quantified experimentally by crushing cylindrical specimens with length-to-diameter ratios amounting to 1.84 and 1.34, respectively, at nine different material ages ranging from 1 h to 28 days. After excluding strength values significantly affec...

The nonlinear Finite Element Method (FEM) is the current gold standard for the thermo-mechanical analysis of reinforced concrete structures. As an alternative, this paper is devoted to a model reduction strategy which reduces the CPU time by a factor of 500. This strategy combines Fourier series-based solutions for the thermal conduction problem, a...

The micromechanics of composites with multiple phases of different shapes embedded into a matrix phase, typically requires symmetrization strategies for their homogenized elasticity tensors, in particular so if the popular Mori–Tanaka estimate is employed. We here explore the implications of such symmetrization techniques, on the concentrations ten...

The stiffness of cementitious materials decreases with increasing temperature. Herein, macroscopic samples of mature cement pastes are subjected at 20, 30, and 45 °C, respectively, to three-minutes-long creep compression experiments. The test evaluation is based on the linear theory of viscoelasticity and Boltzmann’s superposition principle. This y...

Biological materials and systems are hierarchically organized.The main motivation for hierarchical biomechanics is that the wide variability of mechanical properties encountered at the macroscopic scale may be traced back to just a few universal. i.e. tissue-invariant, mechanical properties of elementary components at a sufficiently small scale (su...

Based on the principle of virtual power, equilibrium conditions are established for the forces within a cross section of a tunnel top heading driven according the New Austrian Tunneling Method (NATM). External forces, namely impost actions and ground pressure distributions following a third-order polynomial, are analytically linked with internal fo...

Stress and strain average rules are the key conceptual pillars of the wide field of continuum micromechanics of materials. The aforementioned rules express that the spatial average of (micro‐)stress and (micro‐)strain fields throughout a microscopically finite representative volume element (RVE) are equal to the (macro‐)stress and (macro‐)strain va...

Calcite-reinforced hydrates provide the superior mechanical properties of Biodentine, a cementitious material used in dentistry. Herein, a self-consistent micromechanics model links two nanoindentation-probed, lognormally distributed microstiffness distributions of infinitely many hydrate phases, to the material’s macrostiffness, quantified from lo...

Countless research contributions reflect two major concepts for modeling the spread of the COVID-19 pandemic: (i) ordinary differential equations for population compartments, such as infected or deceased persons (these approaches often exhibit limited predictive capabilities); and (ii) rules applied to digitally realized agents in the populations (...

Biodentine is a calcium silicate/calcium carbonate/zirconium dioxide/water-based dental replacement biomaterial, significantly outperforming the stiffness and hardness properties of chemically similar construction cement pastes. We here report the first systematic micromechanical Investigation of Biodentine, combining grid nanoindentation with ultr...

It is widely accepted that the nonlinear macroscopic mechanical behavior of soft tissue is governed by fiber straightening and re-orientation. Here, we provide a quantitative assessment of this phenomenon, by means of a continuum micromechanics approach. Given the negligibly small bending stiffness of crimped fibers, the latter are represented thro...

The mechanical interactions of C-(N-)A-S-H (Calcium-sodium-aluminum-silicate-hydrate) gel with slag and fly ash inclusions in alkali-activated materials (AAM) are quantified through image-supported grid nanoindentation. Nonuniform distributions of indent-specific indentation properties reveal that the elasticity-related domain is up to 130 times th...

This paper aims at elucidating which factors are effective in terms of influencing the die swell of unvulcanized rubber upon extrusion. To that end, compression, viscosity, and extrusion tests were performed on two types of ethylene-propylene-diene rubbers, while additional compression tests were performed on natural rubber. First, all three testin...

Nanoindentation, laser ablation inductively coupled plasma mass spectroscopy and weighing ion-spiked organic matrix standards revealed structure-property relations in the microscopic jaw structures of a cosmopolitan bristle worm, Platynereis dumerilii . Hardness and elasticity values in the jaws’ tip region, exceeding those in the center region, ca...

Background Testing standards prescribe dog-bone samples for the determination of clear-wood longitudinal tensile strength. However, the literature reports a high number of invalid tests due to the unexpected failure of the sample outside the gauge length. Motivation The paper aims at understanding the reason for the premature failure of dog-bone s...

This paper addresses the question to which extent the stiffness of an elastic foundation in general, and of a discontinuity occurring in the foundation in particular, affects the stresses to which a beam resting on such a foundation is exposed to. This is particularly relevant for tramway rails, where foundation discontinuities may be generated in...

en Quantification of the level of loading of shotcrete supports from measured displacements of NATM‐driven tunnels is common practice in Austria. At construction sites of the Austrian Federal Railways (OeBB), a hybrid method developed at the TU Wien (Vienna University of Technology) has been successfully applied over the last 15 years. Because OeBB...

A considerably improved, multiscale, continuum-micromechanics-based model for the elasticity and ultimate strength of transversely isotropic paper sheets; reliably reflecting an image-based description of the hierarchical, macroscopic-to-nanoscopic scale organization of such sheets and of their constituents – is presented and thoroughly validated

Profound investigation of the unsurpassed mechanical properties of suspended graphene motivates the link between classical continuum mechanics (where the notions of “mechanical strength”, “mechanical stiffness”, and “elastic energy” have actually been coined) and density functional theory (DFT) rooted in quantum mechanics. Namely, the latter quanti...

The thermal and mechanical properties of bricks are strongly dependent on both the chemical composition and the microstructural features of the used fired clay material. Focussing on the latter, we here identify, in terms of volume fraction, shape, and orientation characteristics, one-to-several micrometer-sized subdomains (“material phases”) withi...

Large deflections relevant for suspended circular graphene sheets with simply supported boundaries are computed by a theory for 2D membranes subjected to several types of vertical axisymmetric forces, based on the principle of virtual power (PVP). Corresponding stress–strain relations are provided in the form of a nonlinear hyperelastic material mo...

The COVID-19 pandemic has world-widely motivated numerous attempts to properly adjust classical epidemiological models, namely those of the SEIR-type, to the spreading characteristics of the novel Corona virus. In this context, the fundamental structure of the differential equations making up the SEIR models has remained largely unaltered—presuming...

It is useful to describe the deformation characteristics of long biological macromolecules, such as deoxyribonucleic acid (DNA), by means of terms such as “bending”, “stretching”, or “twisting”. These terms are borrowed from classical beam theory, a traditional and widely known subfield of continuum mechanics, whereas the standard numerical modelin...

It is very well known that bone is a hierarchically organized material produced by bone cells residing in the fluid environments filling (larger) vascular pores and (smaller) lacunar pores. The extracellular space consists of hydroxyapatite crystals, collagen type I molecules, and water with non-collageneous organics. It is less known to which exte...

Fired clay bricks are employed in increasingly demanding application domains, such as multi-storey buildings and facades allowing only minimal heat loss. The latter requirement is often met by the use of pore forming agents. Then, pore size and morphology, as well as the thermal conductivity of the solid constituents of fired clay, govern the mater...

Tramway rail steel is exposed to extreme temperature conditions both during production (e.g. in terms of heat treatment) and over its decades-to-century-long service life (e.g. in terms of welding operations in the course of maintenance). The question arises whether this induces local stiffness reductions and hence stiffness inhomogeneities at the...

State-of-the-art micromechanical models for cement and concrete typically introduce two types of hydrate gel built up by single nanometer-sized solid calcium-silicate-hydrate (C-S-H) blocks and a constant gel porosity in between, in order to upscale nanoindentation-derived elastic properties of ”low density C-S-H gel” and ”high-density C-S-H gel” u...

The increased incidence of fractures in aging tramway rails has motivated the development of a new, efficient numerical tool for studying structural mechanics problems related to such rails. We introduce virtual velocity fields reflecting axial, bending, shear, and torsional deformations, which are then translated, via the principle of virtual powe...

ISBN: 978-802610876-4 https://www.scopus.com/record/display.uri?eid=2-s2.0-85090751146&origin=resultslist

ISBN: 978-802610876-4 https://www.scopus.com/record/display.uri?eid=2-s2.0-85090717195&origin=resultslist

Climate changes result in an increase of extreme weather events. Concrete pavements e.g. may be subjected more frequently to hail showers, following significant solar heating of their top surface. This scenario is studied by means of multiscale thermoelastic analysis. The semi-analytical solution of the heat conduction problem provides access to th...

During their lifetimes, tramway networks become increasingly susceptible to mechanical damage in the form of rail fractures. Understanding the underlying reasons, and initiating appropriate countermeasures may be facilitated by (computational) modeling tools. The development of such tools calls for a sound theoretical foundation. The latter is stil...

Serious mandibular diseases such as tumor or osteonecrosis often require segmental or marginal mandibulectomy, the latter with improved outcome thanks to preserved mandibular continuity. Nevertheless, gradual osteolytic and/or osteosclerotic skeletal changes frequently indicate repetitive resections. Based on the fundamental adaptivity of bone to m...

2D materials such as planar fibrous networks exhibit several mechanical peculiarities, which we here decipher through a 3D-to-2D transition in the framework of continuum micromechanics or random mean-field homogenization theory. Network-to-fiber concentration (or “downscaling”) tensors are derived from Eshelby-Laws matrix-inclusion problems, specif...

Micromechanical representation of bone ultrastructure as a composite of aligned mineralized collagen fibrils embedded in a porous polycrystalline matrix has allowed for successfully predicting the (poro/visco-)elastic and strength properties of bone tissues throughout the entire vertebrate animal kingdom, based on the “universal” mechanical propert...

There is growing experimental evidence for non‐affine deformations occurring in different types of fibrous soft tissues; meaning that the fiber orientations do not follow the macroscopic deformation gradient. Suitable mathematical modeling of this phenomenon is an open challenge, which we here tackle in the framework of continuum micromechanics. Fr...

Deflection modes relevant for plates with rigidly supported edges are commonly used as kind of “approximation” for the deformation behavior of plates which are freely swimming on an elastic foundation. However, this approach entails systematic errors at the boundaries. As a remedy to this problem, we here rigorously derive a theory for elastically...

Optimizing thermal and mechanical properties of clay block masonry requires detailed knowledge on the microstructure of fired clays. We here identify the macro- and microporosity stemming from the use of three different pore-forming agents (expanded polystyrene, sawdust, and paper sludge) in different concentrations. Micro-CT measurements provided...

Quasi-instantaneous thermal expansion of cement pastes is governed by the relative humidity (RH) within their air-filled pores and by the decrease/increase of this internal RH resulting from a temperature decrease/increase. The latter effect is traced back to quasi-instantaneous water uptake/release by cement hydrates, using microporomechanics and...

“Universal” organizational patterns in bone are reviewed and presented, in terms of mathematically expressed rules concerning the composition and elasticity of a large variety of tissues. Firstly, experimental data sets gained from dehydration-demineralization tests, dehydration-deorganification tests, and dehydration-ashing tests are thoroughly an...

This contribution highlights recent developments in the analysis and monitoring of tunnel linings based on so‐called hybrid methods. In this context, the word ”hybrid“ refers to a suitable combination of measurement data from geotechnical monitoring, with advanced simulation tools of engineering mechanics. The first part of this contribution refers...

It is widely believed that the activities of bone cells at the tissue scale not only govern the size of the vascular pore spaces (and hence, the amount of bone tissue available for actually carrying the loads), but also the characteristics of the extracellular bone matrix itself. In this context, increased mechanical stimulation (in mediolateral re...

Mandibular pathologies as oral cancer, septic or aseptic osteonecrosis due to radiation or medication therapy, or severe atrophy cause progressing skeletal compromise with the risk of pathological mandibular fracture (PMF). In a recent clinical study, PMF was reported for 4 out of 44 cases after marginal mandibulectomy related to oral cancer. Motiv...

Transfer relations, representing analytical solutions of the linear theory of slender circular arches, have facilitated structural analysis of segmented tunnel linings. This is the motivation to apply such relations to two examples of circular arch bridges in which the bridge deck is held from the arch by equally spaced hangers. First, the number o...

This paper presents the results of the numerical benchmark campaign on modelling of hydration and microstructure development of cementitious materials. This numerical benchmark was performed in the scope of COST Action TU1404 “Towards the next generation of standards for service life of cement-based materials and structures”. Seven modelling groups...

The design of bone tissue engineering materials and scaffold structures made thereof is a delicate task, owing to the various, sometimes contradicting requirements that must be fulfilled. The traditional approach is based on a trial-and-error strategy, which may result in a lengthy and inefficient process. Aiming at improvement of this unsatisfacto...

This paper presents the results of the numerical benchmark campaign on modelling of hydration and microstructure development of cementitious materials. This numerical benchmark was performed in the scope of COST Action TU1404 “Towards the next generation of standards for service life of cement-based materials and structures”. Seven modelling groups...

Nowadays, the assessment of the mechanical competence of tissue engineering scaffolds based on computer simulations is a well-accepted technology. Typically, such simulations are performed by means of the Finite Element (FE) method, with the underlying structural model being created based on micro-computed tomography (microCT). Here, this analysis...

Ever since the early days of Féret (1892) and Abrams (1919), concrete research has targeted at relating concrete composition to uniaxial compressive strength. While these activities were mainly characterized by empirical fitting functions, we here take a more fundamental approach based on continuum micromechanics. The loading applied at the concret...

While bone tissue is a hierarchically organized material, mathematical formulations of bone remodeling are often defined on the level of a millimeter-sized representative volume element (RVE), "smeared" over all types of bone microstructures seen at lower observation scales. Thus, there is no explicit consideration of the fact that the biological c...

Segmented tunnel rings exhibit load-induced interfacial dislocations. In order to facilitate structural analysis, a hybrid method is developed and applied to a real-scale test of a segmented tunnel ring. Point loads, imposed on the tested ring, and measured interfacial discontinuities serve as input for the analysis. Moreover, the method accounts f...

Introduction of infinitely many solid phases in continuum micromechanical representations of hierarchical porous media, in combination with rigorous consideration of free strains and stresses (which arise in the material microstructures as plastic or viscous strains, or as pore pressures) turned out as the major key to providing reliable (“nano-mic...

Chloride ingress into concrete is a major cause for material degradation, such as cracking due to corrosion-induced steel reinforcement expansion. Corresponding transport processes encompass diffusion, convection, and migration, and their mathematical quantification as a function of the concrete composition remains an unrevealed enigma. Approaching...

Despite considerable ongoing efforts, accurate computational simulation of the flow behavior of (unvulcanized) rubber remains an open challenge. There is growing evidence that one of the reasons for that is insufficient consideration of, or knowledge on, the mechanical compressibility of the material. As a contribution to tackle this open question,...

N/A

Since its advent in the 1960s, elastoplastic micromechanics has been confronted by continuous challenges, as the classical incremental elastoplastic tangents are known to deliver unrealistically stiff material responses. As a complement to the various “secant” approximations targeting this challenge, we here develop a theoretical framework based on...

Bone tissue engineering materials must blend in the targeted physiological environment, in terms of both the materials’ biocompatibility and mechanical properties. As for the latter, a well-adjusted stiffness ensures that the biomaterial’s deformation behavior fits well to the deformation behavior of the surrounding biological tissue, whereas an ap...

Creep of cementitious materials results from the viscoelastic behavior of the reaction products of cement and water, called hydrates. In the present paper, a single isochoric creep function characterizing well-saturated portland cement hydrates is identified through downscaling of 500 different nonaging creep functions derived from three-minute-lon...

NMR relaxometry (Muller et al., 2012, 2013) quantifies the mass fractions of differently bound water in cement paste, as functions of hydration degree and water-to-cement ratio. We here reduce these findings to a single explanation: the density of C-S-H gel is solely governed by the specific precipitation space, across three “hydration regimes”: In...

Poster prepared for the 33rd Danubia Adria Symposium on Advances in Experimental Mechanics

We here explore for the very first time how an advanced multiscale mathematical modeling approach may support the design of a provenly successful tissue engineering concept for mandibular bone. The latter employs double-porous, potentially cracked, single millimeter-sized granules packed into an overall conglomerate-type scaffold material, which is...