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REFERENCES 1. Ahmed L, Ansell A & Malm R: “Numerical Modelling and Evaluation of Laboratory Tests with Impact Loaded Young Concrete Prisms,” Materials and Structures , Vol. 49, No. 11, November 2016, pp. 4691-4704. 2. Anson M & Newman K: “The Effect of Mix Proportions and Method of Testing on Poisson’s Ratio for Mortars and Concretes,” Magazine of Concrete Research , Vol. 18, No. 56, September 1966, pp. 115-130. 3. Byfors J: “Plain Concrete at Early Ages,” Research Fo 3:80, Swedish Cement and Concrete Institute, Stockholm, 1980, 464 p. 4. Mesbah H A, Lachemi M

aspect) in thickness and in Poisson’s ratio. Here we also calculate the effect of other plate’s parameters to vibrational frequency. The results of the present paper are also compared with published results of [ 10 ] and [ 11 ]. 2 Differential equation of motion The differential equation of motion and time function for visco elastic plate with thickness variation is given by [ 6 ]: (1) [ D 1 ( Φ ,   xxxx + 2 Φ ,   xxyy + Φ , yyyy ) + 2 D 1 , x ( Φ , xxx + Φ , xyy ) + 2 D 1 , y ( Φ , yyy + Φ , yxx ) + D 1 , xx ( Φ , xx + ν   Φ , yy ) + D 1 , yy ( Φ , yy + ν   Φ , xx

Materials, Endeavour , 15(4), 170–174. 5. Grima J., Attard D., Gatt R., Cassar R. (2009), A Novel Process for the Manufacture of Auxetic Foams and for Their re-Conversion to Conventional Form, Advanced Engineering Materials, 11(7), 533-535. 6. Lakes R. S. (1991), Experimental Micro Mechanics Methods for Conventional and Negative Poisson’s Ratio Cellular Solids as Cosserat Continua, Journal of Engineering Materials and Technology , 113, 148-155. 7. Lakes R. S. (2016), Physical Meaning of Elastic Constants in Cosserat, Void, and Microstretch Elasticity, Journal

://dx.doi.org/10.1002/(SICI)1521-4095(200005)12:9<617::AID-ADMA617>3.0.CO;2-3 [62] Argatov I.I., Díaz R.G., Sabina F.J., Int. J. Eng. Sci., 54 (2012), 42. http://dx.doi.org/10.1016/j.ijengsci.2012.01.010 [63] Coenen V.L., Alderson K.L., Phys. Stat. Sol. B, 248 (2011), 66. http://dx.doi.org/10.1002/pssb.201083977 [64] Alderson A., Chem Ind., 10 (1999), 384. [65] Liu Q., Literature Review: Materials with Negative Poisson’s Ratios and Potential Applications to Aerospace and Defense, Defense Science and Technology Organization, Victoria, Australia, 2006 [66] Critchley R., Corni I

References ASTM E132 – 17. Standard Test Method for Poisson’s Ratio at Room Temperature. ASTM E111 – 17. Standard Test Method for Young’s Modulus, Tangent Modulus, and Chord Modulus. Ashikuzzaman, Md., Tarif Uddin, A., Zahidul, A., Altaf Hossain, Md. (2018). Effect of Brick Forming Load on Mechanical Properties of FlyAsh Bricks. Tr Civil Eng & Arch , 3 (2), 1–6. TCEIA.MS.ID.000157. DOI: 10.32474/TCEIA.2018.03.000157 Bednarski, L., Sienko, R., Howiacki, T. (2014). Oszacowanie wartosci i zmiennosci modulu sprezystosci betonu w istniejacej konstrukcji na podstawie

References [1] Alderson A., Alderson K.L., Auxetic materials , Proceedings of the Institution of Mechanical Engineers, Part G, Journal of Aerospace Engineering – Special Issue Paper, 2007, 565–575. [2] Alderson K.L., Alderson A., Evans K.E., The Interpretation of the Strain–dependent Poisson’s Ratio in Auxetic Polyethylene , J. Strain Anal., 1998, 32, 201–212. [3] Danielsson M., Parks D., Boyce M.C., Constitutive modelling of porous hyperelastic materials , Mechanics of Materials, 2004, 36, 347–358. [4] Darijani H., Naghdabadi R., Hyperelastic materials

Abstract

It is widely accepted that failure due to plastic deformation in metals greatly depends on the stress triaxiality factor (TF). This article investigates the variation of stress triaxiality along the yield locus of ductile materials. Von Mises yield criteria and triaxiality factor have been used to determine the critical limits of stress triaxiality for the materials under plane strain condition. A generalized mathematical model for triaxiality factor has been formulated and a constrained optimization has been carried out using genetic algorithm. Finite element analysis of a two dimensional square plate has been carried out to verify the results obtained by the mathematical model. It is found that the set of values of the first and the second principal stresses on the yield locus, which results in maximum stress triaxiality, can be used to determine the location at which crack initiation may occur. Thus, the results indicate that while designing a certain component, such combination of stresses which leads the stress triaxiality to its critical value, should be avoided.

as a structural support for painting in Science and Technology in the Service of Conservation, IIC, London, 139-145. [28] Sun, H., (2005). On the Poisson’s ratios of a woven fabric. Composite Structures 68(4), 505-510. [29] Turinski, Ž. (1976). Slikarska tehnologija. Turistička štampa (Beograd). [30] Warren, W.E., (1990). The elastic properties of woven polymeric fabric. Polymer Engineering Science, 30(20) 1309-1313. [31] Young C. R. T., Hibberd R. D., (1999). Biaxial tensile testing of paintings on canvas. Studies in Conservation, 44, 129-141. [32] Zheng, J

[ 8 ] the first several roots of the dispersion equation were (numerically) obtained and it was revealed that some of the roots were complex relating to attenuating modes. Beside dispersion curves, variation of the displacement magnitudes along radius of the rod for the first three L (0, m ) modes at fixed Poisson’s ratio ν = 0.3317 was analyzed in [ 19 ]. One of the interesting peculiarities of propagating L (0, m ), m > 1 modes at γ → 0, where γ is the wave number ( γ = 2 π/λ , λ is the wavelength), corresponds to the zero slope of the dimensionless

modulus ( E ), crack damage stress (σ cd ), uniaxial compressive strength (σ c ), Poisson’s ratio (ν), crack initiation stress (σ ci ), axial failure strain (ε a, max ), maximum volumetric strain (ε cd ), crack initiation strain (ε ci ) and M R for each of the studied 50 samples. The values of elastic modulus ( E ) and Poisson’s ratio (ν) were calculated by using linear regressions along linear portions of stress–axial strain curves and radial strain–axial strain curves, respectively. The values of crack initiation stress (σ ci ) and crack damage stress (σ cd ) were