Pure bending in non-linear micropolar elasticity

Author(s):  
Gordan Jelenić
2017 ◽  
Vol 4 (1) ◽  
pp. 104-118 ◽  
Author(s):  
V.V. Zozulya

AbstractNew models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors,vectors of displacements and rotation and body force shave been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby all equations of elasticity including Hooke’s law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking in to account micropolar couple stress and rotation effects.


Holzforschung ◽  
2016 ◽  
Vol 70 (6) ◽  
pp. 567-575 ◽  
Author(s):  
Jinghao Li ◽  
John F. Hunt ◽  
Shaoqin Gong ◽  
Zhiyong Cai

Abstract The static and fatigue bending behavior of wood-fiber-based tri-axial engineered sandwich composite panels (ESCP) has been investigated by four-point bending tests. Fatigue panels and weakened panels (wESCP) with an initial interface defect were manufactured for the fatigue tests. Stress σ vs. number of cycles curves (S-N) were recorded under the different stress levels. The primary failure mode in the fatigue tests was observed in the shear zone (epoxy debonding), which was different from face failure in the pure bending zone for the static bending test. For residual bending (RB) test, epoxy debonding failure occurred between the pure bending zone and shear zone. Macro cracks along the core/face interface developed as the number of cycles increased during the fatigue life. The crack propagation or damage for the panels submitted to fatigue test can be described as a three-stage damage process of first non-linear portion, followed by linear damage accumulation, and lastly non-linear accelerated damage. Bending stiffness degradation at the higher load level had faster degradation during fatigue life. The dissipated energy of the panels was small due to the high stiffness of the materials.


2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Victor A. Eremeyev ◽  
Andrzej Skrzat ◽  
Feliks Stachowicz

Within the linear micropolar elasticity we discuss the development of new finite element and its implementation in commercial software. Here we implement the developed 8-node hybrid isoparametric element into ABAQUS and perform solutions of contact problems. We consider the contact of polymeric stamp modelled within the micropolar elasticity with an elastic substrate. The peculiarities of modelling of contact problems with a user defined finite element in ABAQUS are discussed. The provided comparison of solutions obtained within the micropolar and classical elasticity shows the influence of micropolar properties on stress concentration in the vicinity of contact area.


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