# Jiří Vala's research while affiliated with Brno University of Technology and other places

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## Publications (67)

Development of advanced materials and structures for civil engineering, due to the requirements of green and sustainable building, including the reduction of energy consumption and the balance between occupant comfort and environmental friendliness, needs proper analysis of related physical, chemical, etc. processes, whose mathematical description...

The analysis of dynamic contacts/impacts of several deformable bodies belongs to both theoretically and computationally complicated problems, because of the presence of unpleasant nonlinearities and of the need of effective contact detection. This paper sketches how such difficulties can be overcome, at least for a model problem with several elasti...

The widely used method for solution of impacts of bodies, called the penalty method, is based on the contact force proportional to the length of the interpenetration of bodies. This method is regarded as unsatisfactory by the authors of this contribution, because of an inaccurate fulfillment of the energy conservation law and violation of the natur...

The article focuses on modelling origin damage to heterogeneous materials, especially to the issue of modelling the formation and propagation of cracks in fibre cementitious composites, which leads to total degradation of any structure. This paper studies mathematical models based on the modification of the stress distribution and deformation calcu...

Numerical models for the stress and strain analysis of quasi-brittle composites, such as cement-based ones, supplied by various stiffening particles, under mechanical, thermal, etc. loads should handle i) the creation of certain micro-damaged zones, antecedent to ii) the initiation and propagation of a system of macroscopic cracks. Whereas ii) can...

Computational prediction of damage in cement-based composites, as steel fibre reinforced ones, under mechanical, thermal, etc. loads, manifested as creation of micro-fractured zones, followed by potential initiation and evolution of macroscopic cracks, is a rather delicatematter, due to the necessity of bridging between micro- and macro-scales. Thi...

Proper design of pressure boundary elements for pipes, vessels, etc., taking the risk of service-related material degradation into account, is conditioned by understanding of their thermal behaviour. The approach applied here correlates the probability of failure with the stress distribution in front of the crack front. Although the occurrence of a...

Diffusion equations in multicomponent environments, as parabolic evolutionary systems, have many physical and engineering applications; another their application was accentuated in 2020 due to the Covid19 infection. This short paper demonstrates the possibility of numerical analysis of direct and inverse problems of this type using some algorithms...

Computational analysis of strength of quasi-brittle materials, crucial for the durability of building structures and industrial components, needs typically a smeared damage approach, referring to the Eringen theory of nonlocal elasticity. Unfortunately its ad hoc constitutive relations cannot avoid potential divergence of sequences of approximate s...

Computational prediction damage in cementitious composites, as steel fibre reinforced ones, under mechanical, thermal, etc. loads, manifested as creation of micro-fractured zones, followed by potential initiation and evolution of macroscopic cracks, is a rather delicate matter, due to the necessity of bridging between micro-and macro-scales. This s...

Heuristic computational analysis of quasi-brittle fracture of building composites as fibre reinforced concrete relies on coupling of local elasticity with nonlocal damage and on cohesive behaviour of fibre/matrix interfaces. This paper verifies such approach on a model quasi-static and quasi-linear problem, using the constructive proofs focused on...

For the design and prediction of thermal behaviour of energy piles the reliable computational evaluation of time-dependent temperature distribution is required. Some knowledge of analytical solutions, leading to some numerically feasible integration schemes, is welcome. This paper demonstrates such approach on certain model problems with finite cyl...

Computational modelling of damage in brittle and quasi-brittle materials needs some coupling between micro- and macroscopic crack initiation and evolution, up to their non-negligible softening behaviour. Most such approaches contain ad hoc evaluations, with some physical and engineering motivations, namely those connected with massive application o...

Recent methods of numerical analysis of both direct and inverse heat transfer problems combine the partial knowledge of analytical or semianalytical solutions with advanced computational algorithms. Numerous approaches rely on the engineering experience with linear or ad hoc linearized initial and boundary value formulations, together with their in...

Development of new time integration schemes for problems of structural dynamics reflects the progress both in the numerical mathematics and in the information technology. Some results from the last several years bring the new insights into such schemes and the convergence of related algorithms. This paper pays attention namely to the unified approa...

This paper pays attention to the automation of basic linear analysis of structures compound from brittle or quasi-brittle materials using the extended finite element method (XFEM) with extrinsic enrichment functions in the form of signed distances, useful in the numerical analysis of crack propagation problems. The basic approaches to numerical qua...

Prediction of quasi-brittle behaviour of structural components from fibre reinforced composites under mechanical loads should incorporate such physical processes as elastic, resp. plastic deformation, crack initiation, crack propagation in a matrix, pull out of fibres and rupture of fibres. The computational model for the practically most important...

Computational analysis of thermal transfer in advanced buildings and their components stimulates the development of minimization algorithms for complicated functions, whose evaluation need numerical analysis of rather complicated initial and boundary value problems of differential or integral equations; consequently no effective evaluation of corre...

Design of low-energy buildings, accenting the energy requirements for artificial heating under the Central European climatic conditions, based on non-stationary heat transfer modelling due to classical thermodynamic principles, can be performed using the system approach, the Fourier multiplicative decomposition of series of approximate solutions an...

Identification of effective implicit time integration schemes for the both linear and nonlinear analysis of structures belongs to research priorities of continuum mechanics. Application of the finite element or similar techniques leads typically to the initial problems for large systems of second order ordinary differential equations of evoloution....

Advanced building design is a rather new interdisciplinary research branch, combining knowledge from physics, engineering, art and social science; its support from both theoretical and computational mathematics is needed. This paper shows an example of such collaboration, introducing a model problem of optimal heating in a low-energy house. Since a...

Implementation of high temperature solar reservoirs is associated with problems related to the physical properties of materials, especially with temperature resistance of the material at temperature changes, with high heat capacity, with high thermal conductivity and with material fire resistance. In the case of silicate materials, more specific ma...

Sandwich cladding panels, based on PUR, PIR or similar foams, are frequently used for insulation of all types of assembled industrial, store and sporting halls, as well as of commercial and administrative objects, namely for those with controlled interior temperature, and represent an advanced and modern building element. However, favourable proper...

Evaluation of temperature development and related consumption of energy required for heating, air-conditioning, etc. in low-energy buildings requires the proper physical analysis, covering heat conduction, convection and radiation, including beam and diffusive components of solar radiation, on all building parts and interfaces. The system approach...

The significance of reasonable prediction and control of energy consumption in building structures follows from the natural requirements of the development of new materials, structures and technologies, as well as from the formal ones from European directives. This paper presents the method based on the generalized multiplicative Fourier decomposit...

Modelling and simulation of thermal processes, based on the principles of classical thermodynamics, requires numerical analysis of partial differential equations of evolution of the parabolic type. This paper demonstrates how the generalized Fourier method can be applied to the development of robust and effective computational algorithms, with the...

Fly ash, a by-product of burning pulverized coal in electrical generating stations, is used as a supplementary pozzolanic material in the production of Portland cement concrete. It improves, e.g., workability of a concrete mixture, suppresses bleeding, reduces the rate of production of hydration heat and delays finishing operations. Consequently ex...

High-temperature behaviour of refractory composites needs proper experimental and theoretical analysis, coming from classical thermodynamics. The dependence of usual thermal characteristics, as the thermal conductivity and thermal capacity, on temperature, cannot be neglected in any computational simulation, thus the experimental identification of...

Development and exploitation of advanced materials, structures and technologies in civil engineering, both for buildings with carefully controlled interior temperature and for common residential houses, together with new European and national directives and technical standards, stimulate the development of rather complex and robust, but sufficientl...

Development of advanced materials resistant to high temperature, needed namely for the design of heat storage for low-energy and passive buildings, requires simple, inexpensive and reliable methods of identification of their temperature-sensitive thermal conductivity and diffusivity, covering both well-advised experimental setting and implementatio...

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The paper presents the validation of physical properties of refractory concrete with heavy filling, using the measurements under high temperature, assumed for the construction of a thermal storage. The whole system, consisting of the storage core and of the insulation container, is characterized by non-stationary thermal transfer, supplied from sol...

European directive on energy performance of buildings (2010) and related national technical rules force reduction of energy consumption of both new and reconstructed buildings due to the so-called passive standard. Consequently the thermal design of such buildings, utilizing advanced materials, structures and technologies, requires proper analysis...

Utilization of advanced materials in civil engineering motivates research in both experimental and computational methods of reliable identification of their material characteristics, as e.g. the thermal conductivity and diffusivity in semilinear evolutionary equations of heat conduction, coming from the energy balance in classical thermodynamics, o...

A new test method of set fibre concrete homogeneity in finished steel fibre-concrete structure is described in this contribution. The method is based on measurements of the changes in magnetic field strength of permanent magnets which are induced by a change of wire distribution in steel fibre-concrete structure. It is evident from the method descr...

The optimal design of the heat storage, as a part of the Czech-Swedish project of the development of original equipment for exploiting solar energy using optical fibres, requires a reliable evaluation of thermal conductivity of powdery materials for insulation layers, both under normal air pressure and in vacuum. The standard evaluation of thermal...

Mechanical behaviour of concrete structures and their durability are conditioned by the reduction of cracking due to plastic and drying shrinkage and of permeability of concrete. This can be done using small metal particles, typically short steel fibres, randomly distributed in the concrete matrix. Since the technological requirements to the prepar...

The quality of computational modelling of thermomechanical behaviour of building structures and their components is conditioned by the reliable design and evaluation of all constitutive relations, included in the model. The identification of corresponding material characteristics is usually much more complicated then the standard analysis of respon...

Final user properties of concrete and other silicate composite structures are conditioned by their early-age history. Bulk deformation in early-age cement-based material system, not subjected to external forces, but generating significant stresses and temperature and humidity redistributions, is associated with the internal volume reduction of ceme...

An extremal principle is formulated for thermodynamic systems near equilibrium subjected to various external conditions. It is shown that the principle describes unambiguously the kinetics of the thermodynamic system and replaces classical phenomenological equations. Thus the principle can be considered as an effective tool for the treatment of non...

Modelling of building heat transfer needs two basic material characteristics: heat con-duction factor and thermal capacity. Under some simplifications these two factors can be determined from a rather simple equipment, generating heat from one of two aluminium plates into the material sample and recording temperature on the contacts between the sam...

Based on the application of the Onsager's thermodynamic extremal principle a new model for the diffusive phase transformation in substitutional alloys is developed. The model assumes the interface of finite thickness with finite mobility and solute segregation and drag in the migrating interface. The model is applied to Fe rich Fe-Cr-Ni system.

Modelling of macroscopic behaviour of materials, consisting of several layers or components, cannot avoid their microstructural properties. This article demonstrates how the method of Rothe, described in the book of K. Rektorys The Method of Discretization in Time, together with the two-scale homogenization technique can be applied to the existence...

Most non-trivial existence and convergence results for systems of partial differential equations of evolution exclude or avoid the case of a non-symmetrical parabolic part. Therefore such systems, generated by the physical analysis of the processes of transfer of heat and moisture in porous media, cannot be analyzed easily using the standard result...

The Kiessl model of moisture and heat transfer in generally nonhomogeneous porous materials is analyzed. A weak formulation of the problem of propagation of the state parameters of this model, which are so-called moisture potential and temperature, is derived. An application of the method of discretization in time leads to a system of boundary-valu...

The aim of this paper is to demonstrate how the variational equations from [11] can be formulated and solved in some abstract Banach spaces without any a priori construction of special linearization schemes. This should be useful e.g. in the analysis of heat conduction problems and modelling of flows in porous media.

Diffusion in multi-component alloys can be characterized (a) by the vacancy mechanism for substitutional components, (b) by
the existence of sources and sinks for vacancies, and (c) by the motion of atoms of interstitial components. The description
of diffusive and massive phase transformation of a multi-component system is based on the principle o...

Abstract The paper gives an overview of methods of the analysis of gray-scaled photographi- cal images for circular domains, motivated by the need of suciently precise and cheap monitoring of displacements of parts of building constructions in time. The overview of methods applied in the literature is followed by the geometrical analysis of the pro...

The reliable analysis of heat transfer in real materials cannot avoid the information about their microstructure. The global computational modelling, covering both the microstruc-tural material properties and the macrostructural behaviour of the whole specimen or even of the complete construction, is usually very expensive or even impossible in pra...

One of principal research directions in computational mechanics is to describe and analyze multi-scale systems and phenomena where at least one macro-and one microscale has to be distinguished. Since such scales in realistic problems differ dramatically (often as meters and micrometers), the standard mesh refinement technique, well-known from the f...

Nonlocal analysis in continuum mechanics typically require numerical treatment of integro-differential problems. This paper demonstrates a model stationary prob-lem of this type, taken (after a sequence of simplifications) from the physical thick-interface model for diffusive and massive phase transformation in substitutional alloys. For certain su...

The aim of this paper is to demonstrate the mathematical problems of modelling the physical process of heat and moisture transfer in porous materials. The method of discretization in time is applied to derive a discretized (generally non-potential) system of PDEs of elliptic type from the original variational problem of evolution. The convergence o...

## Citations

... For real engineering applications the next research step should be the careful revision of physical formulations in the scope of classical thermomechanics, together with the analysis of related mathematical and numerical problems, namely the proper study of energy dissipation on contacts, independently introduced by [28] and [31]. Such dissipation can be accompanied by the formation of plastic or microscopic damage zones, followed by the initiation and development of macroscopic cracks and further phenomena, dangerous for the bearing ability and durability of materials and structures. ...

... Such approach has been applied in [32] to the quasi-static version of (2.2) and in [33] to certain dynamical simplification of (2.2), relying on [13] in both cases; its limitation, excluding any realistic description of iv), has been discussed by [31] in details. However, this limitation might be not crucial for engineering applications because most practical numerical simulations are expected to detect the risk of material destruction in advance, whereas the detailed quantitative description of its subsequent disintegration is less interesting. ...

... The formulation and analysis of a model problem, supplied by the main ideas of proofs, in this paper was intended as the demonstration of numerical considerations for a class of initial and boundary value problems for partial differential equations of evolution, connected with extraordinarily significant tasks of modelling and simulation of behaviour of advanced materials, building end structures. Some preliminary computational results, referring namely to [32] and [33], for i), ii) and iii) have been presented (with numerous illustrative figures) and discussed in [34]. The much more detailed analysis is under development, including e. g. such processes as dynamics of multiple contacts / impacts of deformable bodies with potential micro-and macro-cracking by [26], requiring an explicit time integration scheme like [4], as well as an appropriate parallel / distributed computing platform. ...

... Such approach has been applied in [32] to the quasi-static version of (2.2) and in [33] to certain dynamical simplification of (2.2), relying on [13] in both cases; its limitation, excluding any realistic description of iv), has been discussed by [31] in details. However, this limitation might be not crucial for engineering applications because most practical numerical simulations are expected to detect the risk of material destruction in advance, whereas the detailed quantitative description of its subsequent disintegration is less interesting. ...

... Two basic variants of XFEM can be distinguished: the singularity-based approach and the phantom node one. For their better understanding (23) some special parameters a nm js and b nm kls , unlike those well-known from the standard FEM techniques, can be separated from u nm is to enable the presentation of (23) in the form of [54] u nm ...

... Avanzini et al. [11] researched the fatigue strength and crack propagation of short carbon fiber reinforced polyetheretherketone and neat matrix with a small blind hole, which indicates that a lower fiber content and inclusion of additive particles will lower the fatigue strength and resistance to crack propagation. Jiří Vala and Vladislav Kozák [12] conducted a computational analysis of crack formation and propagation in quasi-brittle fiber reinforced composites, and a model based on the properties of fiber cementitious composites was presented. Toshiki Watanabe et al. [13] achieved the observation of crack initiation and propagation in carbon fiber reinforced epoxy resin laminates (CFRPs) by used nanoscopic SR X-CT. ...

... The remedy is to seek for u ∈ W 1,2,2 (I, V, V ), instead of u ∈ W 1,2,2 (I, V, H). As demonstrated by [26] and [49], some convergence properties must be studied in dual spaces exploiting selected results of [50], instead of estimates like (19). Both propositions P5) and P6) are applicable here. ...

... We collect data from around the world due to the somewhat limited frequency of collapsed buildings (about one every two weeks). Most of the literature analyzes the causes of building collapses by studying building failure cases from the perspective of technology and engineering (Jones et al., 2016;Lee, 2014;N emec et al., 2018;Peraza, 2017). The reasons for building collapse are numerous and physical reasons include: earthquake, flooding, bombing, explosions, fire, heavy rain or wind, structural failure caused by poor workmanship and substandard materials of the original build, errors in design and construction, elevator failure, excessive water in the soil beneath the building, soil erosion and landslides, water penetration and corrosion of the reinforcing steel, and weak foundations (Beitel & Iwankiw, 2005;Cuoco et al., 1992;Hadipriono, 1985;Li & Li 2006;Opara, 2007). ...

... The strong motivation for this study comes from the engineering analysis of i) the direct problem of thermal design of a residential building, [15], [16], and ii) the inverse problem of identification of material characteristics as thermal conductivity and diffusivity from well-advised laboratory experiments, [17], [18]. Parallel to the development of special software packages for i) and ii), some convergence properties of ad hoc modifications of the original Nelder-Mead simplex algorithm, [16], have been studied by the authors of this paper, with the concluding requirement of their deeper analysis. ...

... In particular, the above included Robin boundary (or interface) condition is able to handle surface convection, whereas the case of surface radiation seems to be invincible because θ 4 * − θ 4 (and a still more complicated term containing u) is imposed into (1) instead of (or in addition to) θ * − θ from the physical Stefan -Boltzmann law typically, which is not supported by any reasonable trace theorem. However, this difficulty can be overcome, introducing V = {v ∈ W 1,2 (Ω) : v ∈ L 5 (Γ)} by Roubíček [13], p. 64, instead of the usual V, as discussed by Vala [28]. Even W 1,2 (Ω) here can be replaced by a reflexive Banach space W 1,l (Ω) with some finite real l > 1, as demonstrated by Roubíček [13], p. 204. ...