Zenerov model viskoelastičnosti za ortotropno čvrsto telo i njegova primena u mehanici drveta

Abstract

Pri proračunu elemenata načinjenih od ortotropnih i transverzalno izotropnih polimera potrebno je uzeti u obzir i elastičnu i viskoznu deformaciju, ne samo u glavnom, već i u sporednim anatomskim pravcima. Vremenski zavistan matematički model koji je formulisan u ovom radu važi za prostorno naprezanje. Model opisuje pojavu viskoznog tečenja i relaksacije napona u konstrukcijama od viskoelastičnog ortotropnog čvrstog materijala. Pri izboru modela vodilo se računa da model dovoljno dobro prikazuje stvarno ponašanje takvih materijala i da je istovremeno primenljiv u inženjerskoj praksi. Uzeta su u obzir i elastična i viskozna svojstva materijala (model zavisi i od vremena i od prethodne istorije razvoja deformacija – tzv. memorije materijala). Pri matematičkom modeliranju je korišćena linearna teorija viskoelastičnosti ortotropnih tela. Ta teorija formuliše osnovne vremenske veze napona i deformacija za viskoelastičan materijal izražene preko tenzora napona i deformacija. Linearna teorija se koristi jer je tenzorski račun veoma složen a ipak je omogućeno dobijanje približnog rešenja postavljenog zadatka. Za uspostavljanje veze napona i deformacija korišćen je Zenerov model (standardni linearni model čvrstog tela) jer dobro opisuje i viskozno tečenje pri konstantnom naponu i relaksaciju napona pri konstantnoj deformaciji. Tako se mogu odrediti partikularna rešenja za nosače od ortotropnih materijala, kao što je drvo, izložene linearnom naprezanju u glavnom anatomskom pravcu. Model je primenjen na grede i ploče od bukovine u izotermskim uslovima. Prodiskutovana je primenljivost dobijenog rešenja u praksi.

The calculation of elements made of orthotropic and transversely - isotropic polymers it is necessary to take into account the elastic and viscous strain, not only in the principal, but also in secondary anatomical directions. Time-dependent mathematical model is formulated in this paper applies to the spatial stress. The model describes the occurrence of viscous flow – creep and stress relaxation in the structure of viscoelastic orthotropic solids. The choice of model was taken into account that the model well enough to really show the behavior of such materials and that is also applicable in engineering practice. Were taken into account the elastic and viscous properties of materials (model depends on the time and the previous history of development of deformation - the memory material). The mathematical modeling is used for linear viscoelasticity theory orthotropic body. This theory formulates the basic weather links stress and deformation of the material viscoelastic expressed through stress and strain tensor. Linear theory is used because the tensor account very complex and it is possible to obtain an approximate solution given task. To make the connection of stress and strain was used Zener model (standard linear solid) as well described and viscous flow at a constant stress and relaxation at constant deformation. The model allows the determination of particular solutions for carriers of wood, exposed to linear strain in the "principal" anatomical direction. The model is applied to beams and plates made of beachwood in isothermal conditions. Discussed the applicability of solutions obtained in practice.