Modris Dobelis

A Transversely Isotropic Hyperelastic Constitutive Model of the PDL. Analytical and Computational Aspects

This study describes the development of a constitutive law for the modelling of the periodontal ligament (PDL) and its practical implementation into a commercial finite element code. The constitutive equations encompass the essential mechanical features of this biological soft tissue: non-linear behaviour, large deformations, anisotropy, distinct behaviour in tension and compression and the fibrous characteristics. The approach is based on the theory of continuum fibre-reinforced composites at finite strain where a compressible transversely isotropic hyperelastic strain energy function is defined. This strain energy density function is further split into volumetric and deviatoric contributions separating the bulk and shear responses of the material. Explicit expressions of the stress tensors in the material and spatial configurations are first established followed by original expressions of the elasticity tensors in the material and spatial configurations. As a simple application of the constitutive model, two finite element analyses simulating the mechanical behaviour of the PDL are performed. The results highlight the significance of integrating the fibrous architecture of the PDL as this feature is shown to be responsible for the complex strain distribution observed.

The Spatial Lattice Design from a Tetrapod-Shaped Element

The Spatial Lattice Design from a Tetrapod-Shaped Element Two discoveries demonstrate that hexagon-type spatial rigid bar structures built of tetrapod-shaped superelements are the best for solving of optimal lattice and optimal two dimensional multiscale tessellation problems. Unexplored, however, remain the topological transformations and multiscale tessellation possibilities of regular spatial lattices space in analogy to the 2-dimensional transformations considered so far. Therefore this article concentrates specifically on derivation of hexagon-type spatial lattices and the multiscale tessellation compatibility possibilities of the spatial lattice cells obtained. In order to determine the shapes of the regular spatial hexagonal lattices, two choices are available. The first one is to apply topological transformations to spheres, placed at regular points in space. The second one is to search for all unique combinations of the superelements. However, both of the approaches ask for proof that all possible lattice configurations have been found. A combined approach is to use the 2-dimensional hexagonal lattice as a starting point for expanding to three dimensions. This yields two unique spatial hexagon-type cell analogues and, consequently, two lattice variants. Considering multiscale tessellation possibility of the lattices, an examination of multiscaled lattice cell vertex coincidence reveals that repeating patterns do exist for the second lattice variant.

Is the Constructional Drawing an International Language for Engineers

Drawing is the language of communication between engineers. Using of the language requires learning of the vocabulary, rules of grammar and syntax. The rules of Polish grammar are different from the rules of English, German, Lithuanian or Slovak. The vocabulary of these languages is also different. Implementation of the international project under the Erasmus + Programme, “Development of Interactive and Animated Drawing Teaching Tools”—DIAD-tools No2017-1-LT01-KA202-035177, which was started at 1st of October 2017 and is realized by partners from Estonia, Latvia, Lithuania, Slovakia and Poland, has become an inspiration to ask the authors themselves—is the constructional drawing an universal, international language? The main goal of the project DIAD-tools is to create interactive tools to support the learning of technical drawing. These tools will be available on the online platform available for university’s students, college’s students, school’s and universities’ teachers from different countries. Developed interactive and animated drawing’s materials should be universal, in order to constitute a genuine teaching aid. Therefore, the question about the universal nature of the constructional drawing used in different countries is so important. The authors compare the adopted standard designations of a constructional drawing in force in partner countries implementing the DIAD-tools project. The comparative analysis carried out will enable the development of a maximum universal illustrative material for learning the principles of constructional drawing. At the same time, it will enable the development of illustrative supplemental materials that will contain information about possible differences in the drawing’s symbols or rules that are used in countries of the project’s partners.