András Árpád Sipos

Budapest University of Technology and Economics · Department of Morphology and Geometric Modeling

Striking shapes in nature have been documented to result from chemical precipitation — such as terraced hot springs and stromatolites — which often proceeds via surface-normal growth. Another studied class of objects is those whose shape evolves by physical abrasion — the primary example being river and beach pebbles — which results in shape-depend...

Abrasion of sedimentary particles in fluvial and eolian environments is widely associated with collisions encountered by the particle. Although the physics of abrasion is complex, purely geometric models recover the course of mass and shape evolution of individual particles in low- and middle-energy environments (in the absence of fragmentation) re...

The shapes of roots exhibit distinctive patterns, which attracted significant attempts at an explanation. We develop a geometrically exact, elastic, three-dimensional morphoelastic rod model of root elongation coupled with control mechanisms representing circumnutation, gravitropism, and thigmotropism. Possible forms of the evolution equations for...

The order of appearance and the position of meridional cracks in brittle domes is a delicate question of mechanics. This paper investigates a dimension-reduced model, a pressurized brittle ring constrained to the plane, to show that a simple, deterministic approach based on the Griffith theory of fracture predicts quasi-equidistant, i.e., close to...

Large granitic boulders resting on steep slopes represent considerable safety hazards that largely depend on the location of the contact surface characterized by the impression d, denoting the parallel distance between the contact surface and the original rock surface. On the other hand, this impression reflecting the often convex nature of the con...

Most techniques of measuring the stress intensity factor (SIF) in the cracking process assume a crack in a planar medium. Currently, there is no effective approach for curved brittle shells, particularly for non-developable cases, i.e., shapes with non-vanishing Gaussian curvature. This paper introduces a novel approach to obtaining material proper...

Land snails exhibit an extraordinary variety of shell shapes. The way shells are constructed underlie biological and mechanical constraints that vary across gastropod clades. Here, we quantify shell geometry of the two largest groups, Stylommatophora and Cyclophoroidea, to assess the potential causes for variation in shell shape and its relative fr...

The collapse of masonry arches under static loads mainly occurs because some voussoir interfaces open and form hinges and eventually transform the structure into a mechanism. There is an interest in the maximum number of concurrent hinges at a given arch geometry and stereotomy, which latter refers to the cutting pattern of the voussoirs. This pape...

The present study investigates the relation between the optimal geometry (quantified via the minimum thickness) and the number of concurrent hinges at the masonry arch’s limit state. The Heymanian assumptions regarding material behavior are adopted, and only constant thickness arches subject to static (i.e., self-weight) loading are considered. Fir...

The evolution of the cracking pattern of an internally pressurized, circular, brittle ring supported with radial elastic springs is investigated. The ill-posed Griffith-type energy functional is regularized via a sequence of boundary value problems (BVPs). We show, that internal bending in the fragments plays an essential role in the position of th...

Crack formation in hemispherical domes is a distinguished problem in structural mechanics. The safety of cracked domes has a long track record; the evolution of the cracking pattern received less attention. Here, we report displacement-controlled loading tests of brittle hemispherical dome specimens, including the evolution of the meridional cracki...

Limit state analysis of masonry arches sets to assess the safety of the structure by determining the minimum thickness that just contains a thrust line. Based on the Heymanian assumptions regarding material qualities and the equilibrium approach to the static theorem it has been explicitly proven for semi-circular arches that both the thrust line a...

Motivated by the grave consequences of an aircraft impact into robust engineering structures like nuclear power plants, we investigate the time-dependent reaction force during the impact of a crushing, elongated elasto{plastic missile into a robust elastic target. We derive a set of partial differential equations on a time-dependent domain to descr...

Friction is much needed for the equilibrium of masonry arches as it transfers load between the voussoirs. In this paper, applying an analytical formulation of the problem, the angle of friction as a geometric constraint on the stereotomy (bricklaying pattern) is investigated to find the possible range of minimum thickness values of circular and ell...

In technical textile engineering, macro-level phenomenological modelling effectively describes the material’s highly nonlinear behaviour. However, existing material laws concentrate on the normal stiffness in the orthotropic yarns and simplify the shear effect because of the two orders of magnitude difference between shear and normal stiffness. Thi...

Abrasion of sedimentary particles in fluvial and aeolian environments is widely associated with collisions encountered by the particle. Although the physics of abrasion is complex, purely geometric models recover the course of mass and shape evolution of individual particles in low and middle energy environments (in the absence of fragmentation) re...

We investigate the maximal outreach of soft, elastic robotic arms with controllable intrinsic curvature by using the three-dimensional geometrically exact Cosserat rod theory and a linear elastica model. We compare results with previous predictions for rods without intrinsic curvature based on a planar rod theory. We point out that planar models of...

The result of a minimum thickness analysis of masonry arches based on the principle of thrust line is subject to loading, geometry and stereotomy (brick or stone laying pattern): if the latter is unknown, a range of minimum thickness values becomes available. Present paper applies the Heymanian assumptions regarding the material qualities, notably...

Spherical masonry domes are attractive elements of architectural heritage. The often recognizable development of cracks in the meridional direction challenged master builders and later architects and engineers to understand the structural behavior of domes. Membrane theory of shells suggests, that due to the low tensile capacity of masonry, cracks...

Evolution of planar curves under a nonlocal geometric equation is investigated. It models the simultaneous contraction and growth of carbonate particles called ooids in geosciences. Using classical ODE results and a bijective mapping, we demonstrate that the steady parameters associated with the physical environment determine a unique, time-invaria...

The classical approach to the Couplet-Heyman problem in the literature assumes certain stereotomy conditions (mostly radial) and derives the corresponding unique thrust line and minimum thickness value based on limit state analysis. This problem setup is readily turned to an optimization problem: By considering stereotomies a-priori unknown, a rang...

Recent work demonstrates that finite-deformation nonlinear elasticity is essential in the accurate modeling of wrinkling in highly stretched thin films. Geometrically exact models predict an isola-center bifurcation, indicating that for a bounded interval of aspect ratios only, stable wrinkles appear and then disappear as the macroscopic strain is...

We investigate the quasi-static growth of elastic fibers in the presence of isotropic dry or viscous friction. An unusual form of destabilization beyond a critical length is described. In order to characterize this phenomenon, a new definition of stability against infinitesimal perturbations over finite time intervals is proposed and a semi-analyti...

Markers of brittle faulting are widely used for recovering past deformation phases. Rocks often have oriented magnetic fabrics, which can be interpreted as connected to ductile deformation before cementation of the sediment. This paper reports a novel statistical procedure for simultaneous evaluation of AMS (Anisotropy of Magnetic Susceptibility) a...

We investigate the quasi-static growth of elastic fibers in the presence of dry or viscous friction. An unusual form of destabilization beyond a critical length is described. In order to characterize this phenomenon, a new definition of stability against infinitesimal perturbations over finite time intervals is proposed and a semi-analytical method...

Recent work demonstrates that finite-deformation nonlinear elasticity is essential in the accurate modeling of wrinkling in highly stretched thin films. Geometrically exact models predict an isola-center bifurcation, indicating that for a bounded interval of aspect ratios only, stable wrinkles appear and then disappear as the macroscopic strain is...

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper.

River currents, wind, and waves drive bed-load transport, in which sediment particles collide with each other and Earth’s surface. A generic consequence is impact attrition and rounding of particles as a result of chipping, often referred to in geological literature as abrasion. Recent studies have shown that the rounding of river pebbles can be mo...

In recent years it became apparent that geophysical abrasion can be well characterized by the time evolution $N(t)$ of the number $N$ of static balance points of the abrading particle. Static balance points correspond to the critical points of the particle's surface represented as a scalar distance function $r$, measured from the center of mass, so...

In recent years it became apparent that geophysical abrasion can be well characterized by the time evolution $N(t)$ of the number $N$ of static balance points of the abrading particle. Static balance points correspond to the critical points of the particle's surface represented as a scalar distance function $r$, measured from the center of mass, so...

Markers of brittle faulting are widely used for recovering past deformation phases. Rocks often have oriented magnetic fabrics, which can be interpreted as connected to ductile deformation before cementation of the sediment. This paper reports a novel statistical procedure for simultaneous evaluation of AMS (Anisotropy of Magnetic Susceptibility) a...

Constructing structural systems with the minimal required cross section of its members was a strong motivation for progress whole along the history of building. This article investigates the effect of stereotomy on the minimum thickness value of a semi-circular arch made of masonry: a material with negligible tensile strength. The arch is modeled w...

The photometry of the minor body with extrasolar origin (1I/2017 U1) 'Oumuamua revealed an unprecedented shape: Meech et al. (2017) reported a shape elongation b/a close to 1/10, which calls for theoretical explanation. Here we show that the abrasion of a primordial asteroid by a huge number of tiny particles ultimately leads to such elongated shap...

The photometry of the minor body with extrasolar origin (1I/2017 U1) 'Oumuamua revealed an unprecedented shape: Meech et al. (2017) reported a shape elongation b/a close to 1/10, which calls for theoretical explanation. Here we show that the abrasion of a primordial asteroid by a huge number of tiny particles ultimately leads to such elongated shap...

Constitutive description of deformations in technical textiles mostly requires some highly nonlinear material law because of the interaction between the orthotropic yarns and the effect of the matrix. Phenomenological models aim to capture the overall (macro level) behaviour needed in engineering applications. This paper introduces a new, two-dimen...

A recent paper (Healey et al., J. Nonlin. Sci., 2013, 23:777-805.) predicted the disappearance of the stretch-induced wrinkled pattern of thin, clamped, elastic sheets by numerical simulation of the F\"oppl-von K\'arm\'an equations extended to the finite in-plane strain regime. It has also been revealed that for some aspect ratios of the rectangula...

A recent paper (Healey et al., J. Nonlin. Sci., 2013, 23:777-805.) predicted the disappearance of the stretch-induced wrinkled pattern of thin, clamped, elastic sheets by numerical simulation of the F\"oppl-von K\'arm\'an equations extended to the finite in-plane strain regime. It has also been revealed that for some aspect ratios of the rectangula...

The shape of fragments generated by the breakup of solids is central to a wide variety of problems ranging from the geomorphic evolution of boulders to the accumulation of space debris orbiting Earth. Although the statistics of the mass of fragments has been found to show a universal scaling behavior, the comprehensive characterization of fragment...

In this paper we investigate the wrinkling of clamped, thin sheets (with a thickness below 100 micrometer) under uniaxial tension. The widely used Föppl-von Kármán theory based on the small strain assumption predicts the unconditional stability of the wrinkled pattern regardless on the further applied tension. Based on numerical simulations the unc...

River-bed sediments display two universal downstream trends: fining, in which particle size decreases; and rounding, where pebble shapes evolve toward ellipsoids. Rounding is known to result from transport-induced abrasion; however many researchers argue that the contribution of abrasion to downstream fining is negligible. This presents a paradox:...

We report on further results for the problem studied in Healey and Miller (2007) [1], concerning stable equilibria for a two-phase model of an elastic solid in anti-plane shear in the presence of small interfacial energy. The existence and computation of global solution branches of equilibria for arbitrarily small interfacial energy is presented in...

Statistical hypothesis testing for the eigenvalues and eigenvectors of a stochastic tensor is not a straightforward process due to the nonlinear dependence involved in the problem. For anisotropic tensors the linearized approaches of the literature are adequate, however, geophysical applications require the analysis of nearly isotropic tensors, too...

We describe a PDE model of bedrock abrasion by impact of moving particles and show that by assuming unidirectional impacts the modification of a geometrical PDE due to Bloore exhibits circular arcs as solitary profiles. We demonstrate the existence and stability of these stationary, travelling shapes by numerical experiments based on finite differe...

We use a simple, collision-based, discrete, random abrasion model to compute the profiles for the stoss faces in a bedrock abrasion process. The model is the discrete equivalent of the generalized version of a classical, collision based model of abrasion. Three control parameters (which describe the average size of the colliding objects, the expect...

Rocking stones, balanced in counter-intuitive positions have always intrigued geologists. In our paper we explain this phenomenon based on high-precision scans of pebbles which exhibit similar behavior. We construct their convex hull and the heteroclinic graph carrying their equilibrium points. By systematic simplification of the arising Morse-Smal...

Tartószerkezeti vizsgálatokat végeztünk az Érd-Ófaluban álló, a barokk korban épült Szent Mihály-templomon. A szerkezetileg rossz állapotban lévõ templom fedélszékét, falait és alapozását is meg kellett erõsíteni. A szerkezeti károknak egyidejûleg több oka is van: kedvezõtlen építési viszonyok, nagyobb sérülések és szakszerûtlen javítások. Jelen ci...

We designed a post-tensioned concrete cantilever with a 6.50 m free span supported by columns for a villa near Pécs. The shape and number of the bonded strands were determined to balance the dead load of the structure by the transversal component of the prestressing force. The deflections measured on finished structure are in good agreement with th...

The shape of sedimentary particles may carry important information on their history. Current approaches to shape classification (e.g. the Zingg or the Sneed and Folk system) rely on shape indices derived from the measurement of the three principal axes of the approximating tri-axial ellipsoid. While these systems have undoubtedly proved to be usefu...

On the walls and vaults of the Roman Catholic Parish Church of Zsámbék cracks have long been observed. According to the parishioners, the crack widths have widened recently and new cracks have also appeared. This may have happened due to the increased traffic of the road beside the church. In this paper we report on the structural analysis, includi...

The origin of the shapes of stones and other particles formed by water or wind has always attracted the attention of geologists and mathematicians. A classical model of abrasion due to W. J. Firey leads to a geometric partial di erential equation repre- senting the continuum limit of the process. This model predicts convergence to spheres from an a...

Saleve is a generic framework for making the development of Parameter Study tasks easy for scientists and engineers not familiar with distributed technologies. In this paper we present our lightweight authentication procedure for Saleve to delegate user credentials towards the grid. Then we present a detailed statistics of abrasion of pebbles gaine...

While the number of asteroids with known shapes has drastically increased over the past few years, little is known on the the time-evolution of shapes and the underlying physical processes. Here we propose an averaged abrasion model based on micro-collisons, accounting for asteroids not necessarily evolving toward regular spheroids, rather (dependi...

A NYOMOTT ZÓNÁBAN NEMLINEÁRIS ANYAGTÖRVÉNYŰ, VASBETON KERESZTMETSZET SEMLEGES TENGELYÉNEK SZÁMÍTÁSA Calculation of the neutral axis of reinforced concrete cross section with non-linear material law in the compressed zone Rechnung die Null-Linie von Stahlbeton Querschnitt mit nonlinear Spannungs-Dehnungslinie in der gedrückten Zone SIPOS ANDRÁS ÁRPÁ...

In our paper we introduce a new method for determining the neutral axis of an arbitrary reinforced concrete cross section under biaxial bending and compression with a nonlinear stress-strain relation in the compressed zone. The method is based on the fact, that the neutral axis of the non-linear problem is a solution of a linear problem with a typi...

We demonstrate examples of beams with symmetric cross sections, loading and boundary conditions where, contrary to the engineer's intuition, slight perturbation of the symmetry (either in the cross section's geometry, or in the loading or boundary conditions) improves the overall structural response. We apply the classical Euler–Bernoulli beam mode...

In this paper we apply a previously developed algorithm to predict unfavourable lateral deformations of precast concrete beams. The algorithm is robust, i.e. there is no danger of false solutions or divergent behaviour, however this reliability requires a high computational effort. This latest is partially compansated by the parallel implementation...

Cikkunkben egy GRID technologiara epulő szamitasi eljarast mutatunk be feszitett, berepedt vasbeton gerendak terbeli elmozdulasainak szamitasara. Az eljarast egy korabbi parhuzamos modszer alapjan fejlesztettuk ki, melyet szinten bemutatunk roviden, bővitve egy ujabb algoritmikus gyorsitasi lehetőseggel. A GRID technologia lenyege, hogy a felhaszna...

A globally convergent iterative algorithm for computing the spatial deformations of elastic beams without tensile strength is presented. The core of the algorithm is an iterative scheme (consistent with the classical Kirchhoff rod theo ry) for locating the neutral axis and thus for determining the curvature. We prove uniqueness and local stability...

In our paper we show a fast, robustly convergent algorithm for the calculation of spatial deformations of cracked, elastic RC bars. The algorithm is fully consistent with the Euler-Bernoulli beam model. Elastic deflections of RC beams can be computed by integrating the curvature along the bar axis, in each step the neutral axis of each (cracked) se...

Deflections of concrete structures are commonly investigated under service loads. For calculating the position of the neutral axis non-linear equations must be solved. There is not an accepted general method, because the functions, which have been used, are sophisticated and their convergence features are not known. This article presents a method...

A kutatás átfogó területet jelölt meg, ezen belül azonban nyolc igen konkrét kutatási célt tűzött ki. A felemelkedő kihajlás vizsgálatával sikerült egy elméleti és gyakorlati szempontból is érdekes témában eredményeket elérnünk: modellünk a tengerfenéken húzódó kábelek geometriailag nemlineáris viselkedését segít megérteni. Növényi indák komplex té...

A projekt keretében a szimmetria és optimális viselkedés viszonyát vizsgáltuk mechanikai, adaptív dinamikai (evolúciós) és populáció-dinamikai feladatokban. Tartószerkezetek esetén megállapítottuk, hogy a szimmetrikus elrendezés gyakran javítható kis aszimmetria bevezetésével és pontos kritériumot határoztunk meg annak eldöntésére, hogy egy adott s...