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Similitude theory helps engineers and scientists to accurately predict the behaviors of real systems through the application of scaling laws to the experimental results of a scale model related to the real system by similarity conditions. The theory was applied when studying the deep drawing process of a bathtub made from cold rolled low carbon aluminum-killed steel from the point of view of material limits. The bathtub model was created on the basis of geometric, physical, and mechanical similarity on a scale of 1:5. Thus, simulations and physical models were created. The simulation model was used to verify the combination yield locus/hardening law on the basis of comparing the thickness change. As a result, Hill 48/Krupkowski showed the minimal deviation by comparing data evaluated from numerical simulations and that measured on the physical model. Additionally, material anisotropy was modelled when virtual materials were defined from experimentally measured values of the plastic strain ratio. As an outcome, extra deep drawing quality steel with an average plastic strain ratio of rm ≥ 1.47 and an average strain hardening exponent of nm ≥ 0.23 must be used for the deep drawing of the bathtub.

The palette of a vertex x of a graph G determined by a proper edge colouring ϕ of G is the set {ϕ(xy) : xy ∈ E(G)} and the diversity of ϕ is the number of different palettes determined by ϕ. The palette index of G is the minimum of diversities of ϕ taken over all proper edge colourings ϕ of G. In the article we determine the palette index of K m,n for m ≤ 5 and pose two conjectures concerning the palette index of complete bipartite graphs.

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The control of biomechanical processes in the tissue-implant interface and thermal changes created by friction or inflammatory processes in the implant and its environment represent the key validating processes of the postimplanting process. It is crucial for a patient and their health to minimize the invasiveness of the temperature measuring processes and the inner mechanical stress in the implant-tissue interface. For the purpose of these measurements, amorphous magnetic glass-coated microwires are the most suitable. Compared with other sensors, such as radio frequency identification sensors, the microwires have a significant advantage due to their dimensions (∼2 cm × 50 µm) (because of which the sensor almost does not interfere with the inner implant structures), their production is relatively cheap, and only ∼20 mm microwire is needed for the functional sensor. This paper is concerned with the testing of more types of microwire fixation in an implant and the impact of the fixation; it deals with necessary magnetic properties of a microwire and their dependence on the temperature. Microwire made of master alloy Fe 78 W 5 B 17 was created and fixed in four ways: 1) on one end; 2) on two ends; 3) in the middle; and 4) along its full length. The results show that the optimal way of fixation is the one along the full length of a microwire; however, the final signal is influenced by both, the type and volume of the applied fixation material. The highest sensitivity of the designed microwire was in the range of 120-140°C with no fixation and only with the full length fixation, this sensitivity decreased to 40-50°C, which is a level close to the level required for biomedical applications (35-42°C).Index Terms-Amorphous magnetic glass-coated microwires, magnetoelasticity, smart implants, switching field.