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Jan Zeman

Publications and source records attributed to Jan Zeman.

At least 55 records · Page 3Linked to original sources

An Integrated Experimental-Numerical Study of the Performance of Lime-Based Mortars in Masonry Piers Under Eccentric Loading

Architectural conservation and repair are becoming increasingly important issues in many countries due to numerous prior improper interventions, including the use of inappropriate repair materials over time. As a result, the composition of repair masonry mortars is now being more frequently addressed in mortar research. Just recently, for example, it has become apparent that Portland cement mortars, extensively exploited as repair mortars over the past few decades, are not suitable for repair because of their chemical, physical, mechanical, and aesthetic incompatibilities with original materials. This paper focuses on the performance of various lime-based alternative materials intended for application in repairing historic structures when subjected to mechanical loading. Results of basic material tests indicate that the use of metakaolin as a pozzolanic additive produces mortars with superior strength and sufficiently low shrinkage. Moreover, mortar strength can be further enhanced by the addition of crushed brick fragments, which explains the longevity of Roman concretes rich in pozzolans and aggregates from crushed clay products such as tiles, pottery, or bricks. An integrated experimental-numerical approach was used to identify key mortar parameters influencing the load-bearing capacity of masonry piers subjected to a combination of compression and bending. The simulations indicate increased load-bearing capacities for masonry piers containing metakaolin-rich mortars with crushed brick fragments, as a result of their superior compressive strength.

cond-mat.mtrl-sci↗

Micromechanics-Based Simulations of Compressive and Tensile Testing on Lime-Based Mortars

The purpose of this paper is to propose a continuum micromechanics model for the simulation of uniaxial compressive and tensile tests on lime-based mortars, in order to predict their stiffness, compressive and tensile strengths, and tensile fracture energy. In tension, we adopt an incremental strain-controlled form of the Mori-Tanaka scheme with a damageable matrix phase, while a simple $J_2$ yield criterion is employed in compression. To reproduce the behavior of lime-based mortars correctly, the scheme must take into account shrinkage cracking among aggregates. This phenomenon is introduced into the model via penny-shaped cracks, whose density is estimated on the basis of a particle size distribution combined with the results of finite element analyses of a single crack formation between two spherical inclusions. Our predictions show a good agreement with experimental data and explain the advantages of compliant crushed brick fragments, often encountered in ancient mortars, over stiff sand particles. The validated model provides a reliable tool for optimizing the composition of modern lime-based mortars with applications in conservation and restoration of architectural heritage.

cond-mat.mtrl-sci↗

Computational Homogenization of Fresh Concrete Flow Around Reinforcing Bars

Motivated by casting of fresh concrete in reinforced concrete structures, we introduce a numerical model of a steady-state non-Newtonian fluid flow through a porous domain. Our approach combines homogenization techniques to represent the reinforced domain by the Darcy law with an interface coupling of the Stokes and Darcy flows through the Beavers-Joseph-Saffman conditions. The ensuing two-scale problem is solved by the Finite Element Method with consistent linearization and the results obtained from the homogenization approach are verified against fully resolved direct numerical simulations.

cs.CE↗

Localization Analysis of an Energy-Based Fourth-Order Gradient Plasticity Model

The purpose of this paper is to provide analytical and numerical solutions of the formation and evolution of the localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. An energy-based variational approach is employed and the governing equations with appropriate physical boundary conditions, jump conditions, and regularity conditions at evolving elasto-plastic interface are derived for a fourth-order explicit gradient plasticity model with linear isotropic softening. Four examples that differ by regularity of the yield stress and stress distributions are presented. Results for the load level, size of the plastic zone, distribution of plastic strain and its spatial derivatives, plastic elongation, and energy balance are constructed and compared to another, previously discussed non-variational gradient formulation.

cond-mat.mtrl-sci↗

Localization Study of a Regularized Variational Damage Model

The paper presents a detailed analysis and extended formulation of a rate-independent regularized damage model proposed by Mielke and Roubíček (2006). Localization properties are studied in the context of a simple one-dimensional problem, but the results reveal the fundamental features of the basic model and of its modified versions. The initial bifurcation from a uniform solution is described analytically while the complete failure process is studied numerically. Modifications of the regularizing term and of the dissipation distance are introduced and their effect on the global response is investigated. It is shown that, with a proper combination of model parameters, a realistic shape of the load-displacement diagram can be achieved and pathological effects such as extremely brittle response or expansion of the damage zone accompanied by stress locking can be eliminated.

cond-mat.mtrl-sci↗

Guaranteed upper-lower bounds on homogenized properties by FFT-based Galerkin method

Guaranteed upper-lower bounds on homogenized coefficients, arising from the periodic cell problem, are calculated in a scalar elliptic setting. Our approach builds on the recent variational reformulation of the Moulinec-Suquet (1994) Fast Fourier Transform (FFT) homogenization scheme by Vondřejc et al. (2014), which is based on the conforming Galerkin approximation with trigonometric polynomials. Upper-lower bounds are obtained by adjusting the primal-dual finite element framework developed independently by Dvořák (1993) and Wieckowski (1995) to the FFT-based Galerkin setting. We show that the discretization procedure differs for odd and non-odd number of grid points. Thanks to the Helmholtz decomposition inherited from the continuous formulation, the duality structure is fully preserved for the odd discretizations. In the latter case, a more complex primal-dual structure is observed due to presence of the trigonometric polynomials associated with the Nyquist frequencies. These theoretical findings are confirmed with numerical examples. To conclude, the main advantage of the FFT-based approach over conventional finite-element schemes is that the primal and the dual problems are treated on the same basis, and this property can be extended beyond the scalar elliptic setting.

math.NA↗

Aperiodic compression and reconstruction of real world material systems based on Wang tiles

The paper presents a concept/technique to compress and synthesize complex material morphologies that is based on Wang tilings. Specifically, a microstructure is stored in a set of Wang tiles and its reconstruction is performed by means of a stochastic tiling algorithm. A substantial part of the study is devoted to the setup of optimal parameters of the automatic tile design by means of parametric studies with statistical descriptors at heart. The performance of the method is demonstrated on four two-dimensional two-phase target systems, monodisperse media with hard and soft discs, sandstone, and high porosity metallic foam.

cond-mat.mtrl-sci↗

An FFT-based Galerkin Method for Homogenization of Periodic Media

In 1994, Moulinec and Suquet introduced an efficient technique for the numerical resolution of the cell problem arising in homogenization of periodic media. The scheme is based on a fixed-point iterative solution to an integral equation of the Lippmann-Schwinger type, with action of its kernel efficiently evaluated by the Fast Fourier Transform techniques. The aim of this work is to demonstrate that the Moulinec-Suquet setting is actually equivalent to a Galerkin discretization of the cell problem, based on approximation spaces spanned by trigonometric polynomials and a suitable numerical integration scheme. For the latter framework and scalar elliptic setting, we prove convergence of the approximate solution to the weak solution, including a-priori estimates for the rate of convergence for sufficiently regular data and the effects of numerical integration. Moreover, we also show that the variational structure implies that the resulting non-symmetric system of linear equations can be solved by the conjugate gradient method. Apart from providing a theoretical support to Fast Fourier Transform-based methods for numerical homogenization, these findings significantly improve on the performance of the original solver and pave the way to similar developments for its many generalizations proposed in the literature.

math.NA↗

Finite element model based on refined plate theories for laminated glass units

Laminated glass units exhibit complex response as a result of different mechanical behavior and properties of glass and polymer foil. We aim to develop a finite element model for elastic laminated glass plates based on the refined plate theory by Mau. For a geometrically nonlinear description of the behavior of units, each layer behaves according to the Reissner-Mindlin kinematics, complemented with membrane effects and the von Kármán assumptions. Nodal Lagrange multipliers enforce the compatibility of independent layers in this approach. We have derived the discretized model by the energy-minimization arguments, assuming that the unknown fields are approximated by bi-linear functions at the element level, and solved the resulting system by the Newton method with consistent linearization. We have demonstrated through verification and validation examples that the proposed formulation is reliable and accurately reproduces the behavior of laminated glass units. This study represents a first step to the development of a comprehensive, mechanics-based model for laminated glass systems that is suitable for implementation in common engineering finite element solvers.

cs.CE↗

Existence results for incompressible magnetoelasticity

We investigate a variational theory for magnetoelastic solids under the incompressibility constraint. The state of the system is described by deformation and magnetization. While the former is classically related to the reference configuration, magnetization is defined in the deformed configuration instead. We discuss the existence of energy minimizers without relying on higher-order deformation gradient terms. Then, by introducing a suitable positively $1$-homogeneous dissipation, a quasistatic evolution model is proposed and analyzed within the frame of energetic solvability.

math.AP↗

Numerical model of elastic laminated glass beams under finite strain

Laminated glass structures are formed by stiff layers of glass connected with a compliant plastic interlayer. Due to their slenderness and heterogeneity, they exhibit a complex mechanical response that is difficult to capture by single-layer models even in the elastic range. The purpose of this paper is to introduce an efficient and reliable finite element approach to the simulation of the immediate response of laminated glass beams. It proceeds from a refined plate theory due to Mau (1973), as we treat each layer independently and enforce the compatibility by the Lagrange multipliers. At the layer level, we adopt the finite-strain shear deformable formulation of Reissner (1972) and the numerical framework by Ibrahimbegović and Frey (1993). The resulting system is solved by the Newton method with consistent linearization. By comparing the model predictions against available experimental data, analytical methods and two-dimensional finite element simulations, we demonstrate that the proposed formulation is reliable and provides accuracy comparable to the detailed two-dimensional finite element analyzes. As such, it offers a convenient basis to incorporate more refined constitutive description of the interlayer.

cs.CE↗

A framework for integrated design of algorithmic architectural forms

This paper presents a methodology and software tools for parametric design of complex architectural objects, called digital or algorithmic forms. In order to provide a flexible tool, the proposed design philosophy involves two open source utilities Donkey and MIDAS written in Grasshopper algorithm editor and C++, respectively, that are to be linked with a scripting-based architectural modellers Rhinoceros, IntelliCAD and the open source Finite Element solver OOFEM. The emphasis is put on the mechanical response in order to provide architects with a consistent learning framework and an insight into structural behaviour of designed objects. As demonstrated on three case studies, the proposed modular solution is capable of handling objects of considerable structural complexity, thereby accelerating the process of finding procedural design parameters from orders of weeks to days or hours.

cs.CE↗

A micromechanics-based model for stiffness and strength estimation of cocciopesto mortars

The purpose of this paper is to propose an inexpensive micromechanics-based scheme for stiffness homogenization and strength estimation of mortars containing crushed bricks, known as cocciopesto. The model utilizes the Mori-Tanaka method to determine the effective stiffness, combined with estimates of quadratic invariants of the deviatoric stresses inside phases to predict the compressive strength. Special attention is paid to the representation of C-S-H gel layer around bricks and interfacial transition zone around sand aggregates, which renders the predictions sensitive to particle sizes. Several parametric studies are performed to demonstrate that the method correctly reproduces data and trends reported in available literature. Moreover, the model is based exclusively on parameters with clear physical or geometrical meaning and as such it provides a convenient framework for its further experimental validation.

cond-mat.mtrl-sci↗

Compressing Random Microstructures via Stochastic Wang Tilings

This paper presents a stochastic Wang tiling based technique to compress or reconstruct disordered microstructures on the basis of given spatial statistics. Unlike the existing approaches based on a single unit cell, it utilizes a finite set of tiles assembled by a stochastic tiling algorithm, thereby allowing to accurately reproduce long-range orientation orders in a computationally efficient manner. Although the basic features of the method are demonstrated for a two-dimensional particulate suspension, the present framework is fully extensible to generic multi-dimensional media.

cond-mat.mtrl-sci↗

Localization analysis of variationally based gradient plasticity model

The paper presents analytical or semi-analytical solutions for the formation and evolution of localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. A variationally based formulation of explicit gradient plasticity with linear softening is used, and the ensuing jump conditions and boundary conditions are discussed. Three cases with different regularity of the stress distribution are considered, and the problem is converted to a dimensionless form. Relations linking the load level, size of the plastic zone, distribution of plastic strain and plastic elongation of the bar are derived and compared to another, previously analyzed gradient formulation.

cond-mat.mtrl-sci↗

Selected topics in homogenization of transport processes in historical masonry structures

The paper reviews several topics associated with the homogenization of transport processed in historical masonry structures. Since these often experience an irregular or random pattern, we open the subject by summarizing essential steps in the formulation of a suitable computational model in the form of Statistically Equivalent Periodic Unit Cell (SEPUC). Accepting SEPUC as a reliable representative volume element is supported by application of the Fast Fourier Transform to both the SEPUC and large binary sample of real masonry in search for effective thermal conductivities limited here to a steady state heat conduction problem. Fully coupled non-stationary heat and moisture transport is addressed next in the framework of two-scale first-order homogenization approach with emphases on the application of boundary and initial conditions on the meso-scale.

cond-mat.mtrl-sci↗

Homogenization of plain weave composites with imperfect microstructure: Part II--Analysis of real-world materials

A two-layer statistically equivalent periodic unit cell is offered to predict a macroscopic response of plain weave multilayer carbon-carbon textile composites. Falling-short in describing the most typical geometrical imperfections of these material systems the original formulation presented in (Zeman and Šejnoha, International Journal of Solids and Structures, 41 (2004), pp. 6549--6571) is substantially modified, now allowing for nesting and mutual shift of individual layers of textile fabric in all three directions. Yet, the most valuable asset of the present formulation is seen in the possibility of reflecting the influence of negligible meso-scale porosity through a system of oblate spheroidal voids introduced in between the two layers of the unit cell. Numerical predictions of both the effective thermal conductivities and elastic stiffnesses and their comparison with available laboratory data and the results derived using the Mori-Tanaka averaging scheme support credibility of the present approach, about as much as the reliability of local mechanical properties found from nanoindentation tests performed directly on the analyzed composite samples.

cond-mat.mtrl-sci↗

Simple Numerical Model of Laminated Glass Beams

This contribution presents a simple Finite Element model aimed at efficient simulation of layered glass units. The adopted approach is based on considering independent kinematics of each layer, tied together via Lagrange multipliers. Validation and verification of the resulting model against independent data demonstrate its accuracy, showing its potential for generalization towards more complex problems.

cs.CE↗