International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

This article discusses the modern knowledge necessary for materials science. Modern scientific knowledge covers on the basis of the greatest scientific results; complete scientific knowledge: mathematics; mathematical physics; quantum mechanics (not relativistic and relativistic); quantum physics; quantum chemistry. Theory and modern tools for testing and monitoring with increasing resolution. High technologies. A research – type methodology has been obtained, but this methodology is also focused on interactions with business. Business research is not fundamental, but it can be very lengthy

This article discusses the modern knowledge necessary for materials science. Modern scientific knowledge covers on the basis of the greatest scientific results; complete scientific knowledge: mathematics; mathematical physics; quantum mechanics (not relativistic and relativistic); quantum physics; quantum chemistry. Theory and modern tools for testing and monitoring with increasing resolution. High technologies. A research – type methodology has been obtained, but this methodology is also focused on interactions with business. Business research is not fundamental, but it can be very lengthy.

Multiscale mathematical modelling requires cross-cutting work with all areas of mathematics. The simplest proof is the mathematical experiment. An example is the finite element method, which is already used in quantum mechanics. The presented results are interesting for us, such as the 3D printer application and epitaxy.Numerical experiments for micron-sized hardening are shown.

Mathematical methods of quantum mechanics are needed to describe the contact phenomena of the boundary casting/mold. Apart from the macro-level, the contact phenomena are part of the technological processes first order phase transition and second order phase transition. Need for professional software for mathematical simulation at macro- and micro-level in foundry. Education in basic mathematics and mathematical physics is also required for engineers. The branch machine-building infrastructure must develop a mechanism for inclusion in the computing infrastructure of the micro-foundries.

Technological first-order phase transition is obtain base process of material science by numerical experiments at use of finite elements method (FEM). The history of movement and the geometry of the front in the first-order phase transition are investigated. A free first-order phase transition was investigated to estimate the local place of the liquid residue. Mathematical model is Stefan-Schwartz task in 3D case. The corresponding temperature fields of a free and technological first-order phase transition are presented. Engineering information is local phase transition conditions is shown of macro-level with the local transition time and volume at the front is assumed.

A scientific methodology for foundry has been developed in order to have a constant connection between foundry and the continuous development of solid state physics. This is achieved through the continuous expansion of the minimum scientific knowledge based on the historical development of metal physics, solid state physics, and today mathematics is placed in the first place. Metal science is a pure application of metal physics and solid state theory based on foundry, today it is materials science. The natural mathematical theory of foundry is the theory of thermal conductivity describing phase transitions of the first and second kind through Stefan-type problems – solidification together with modern software products for descriptions.

A methodology for analyzing and evaluating macroscopic level of first-order phase transition in 3D printer technology is proposed. A classic Stefan-Schwarz task was used. A 3D mathematical model of the Stefan-Schwarz problem is made. The finite element method for numerical solution is applied.
A numerical experiment was evaluated. A geometric drop (flow) model in 3D printer technology is proposed. The idea of filling a “flow” drop by smaller droplets than a “flow” has been investigated numerically. The temperature field at filling in the flow as hereditary was investigated.