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

... 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. ...