A theoretical model for porous viscoelastoplastic (VEP) materials under dry conditions is examined based on the principles of mass and energy conservation using rheological-dynamical analogy (RDA). The model provides the expressions for the creep coefficient, Poisson's ratio, modulus of elasticity, damage variable and strength in the function of porosity and/or void volume fraction (VVF). Compared with numerous versions of acoustic emission monitoring developed to analyze the behavior of the total wave propagation in inhomogeneous media with density variation, the RDA model is found to be comprehensive in interpretation and consistent with physical understanding. The reliability of the proposed model is confirmed by the comparison of numerical results with experimental ones on hardened concrete and rocks.
References
1.
Choren JA, Heinrich SM, Silver-Thorn MB. Young’s modulus and volume porosity relationships for additive manufacturing applications. Journal of Materials Science. 2013;48(15):5103-5112,.
2.
Spriggs RM. Expression for Effect of Porosity on Elastic Modulus of Polycrystalline Refractory Materials, Particularly Aluminum Oxide. J Am Ceram Soc. 1961;44(12):628-629,.
3.
Ryshkewitch E. Compression Strength of Porous Sintered Alumina and Zirconia. J Am Ceram Soc. 1953;36(2):65-68,.
4.
Phani KK, Niyogi SK. Young’s modulus of porous brittle solids. J Mater Sci. 1987;22(1):257-263,.
5.
Wang JC. Young’s modulus of porous materials. J Mater Sci. 1984;19(3):801-808,.
6.
Neville AM, Brooks JJ. Concrete technology. 2010.
7.
Chen X, Wu S, Zhou J. Influence of porosity on compressive and tensile strength of cement mortar. Constr Build Mater. 2013;40:869-874,.
8.
Chen X, Shi D, Guo S. Experimental Study on Damage Evaluation, Pore Structure and Impact Tensile Behavior of 10-Year-Old Concrete Cores After Exposure to High Temperatures. Int J Concr Struct Mater. 2020;14(1):1-17,.
9.
Kumar R, Bhattacharjee B. Porosity, pore size distribution and in situ strength of concrete. Cem Concr Res. 2003;33(1):155-164,.
10.
AlShareedah O, Nassiri S. Pervious concrete mixture optimization, physical, and mechanical properties and pavement design: A review. J Clean Prod. 2021;288:125095,.
11.
Zimmerman RW. Compressibility of sandstones. 1991.
12.
Gassmann F. Elastic Waves through a Packing of Spheres. Geophysics. 1951;16(4):673-685,.
13.
Milašinović DD. Modeling of porous-hardened concrete by rheological-dynamical analogy. Eng Comput (Swansea. 2023;40(9/10):2615-2647,.
14.
Milašinović DD. Rheological-dynamical continuum damage model for concrete under uniaxial compression and its experimental verification. Theor Appl Mech. 2015;42(2):73-110,.
15.
Milašinović D, Goleš D, Rožnjik A, Bošnjak NM. Model of porous materials by rheological-dynamical analogy using the principles of mass and energy conservation. Int Conf Contemp Theory Pract Constr / Међународна конференција Савремена теорија и пракса у градитељству. 2022;(15):092-103,.
16.
Lemaitre J. A Course on Damage Mechanics. 1992.
17.
Milašinović DD, Majstorović D, Vukomanović R. Quasi static and dynamic inelastic buckling and failure of folded-plate structures by a full-energy finite strip method. Adv Eng Softw. 2018;117:136-152,.
18.
Milašinović DD. Rheological-dynamical method for prediction of compressive strength and deformation of rocks. Int J Rock Mech Min Sci. 2021;141:104659,.
19.
Murakami S. Continuum Damage Mechanics. 2012;185.
20.
Gurson AL. Continuum theory of ductile rupture by void nucleation and growth - 1. yield criteria and flow rules for porous ductile media. Am Soc Mech Eng. 1976;76-,.
21.
Rousselier G. Ductile fracture models and their potential in local approach of fracture. Nucl Eng Des. 1987;105(1):97-111,.
22.
Goods SH, Brown LM. Overview No. 1: The nucleation of cavities by plastic deformation. Acta Metall. 1979;27(1):1-15,.
23.
Needleman A, Tvergaard V. An analysis of ductile rupture in notched bars. J Mech Phys Solids. 1984;32(6):461-490,.
24.
Lemaitre J, Dufailly J. Damage measurements. Eng Fract Mech. 1987;28(5–6):643-661,.
25.
Milašinović DD. Rheological–dynamical analogy: visco-elasto-plastic behavior of metallic bars. Int J Solids Struct. 2004;41(16–17):4599-4634,.
26.
Yaman IO, Hearn N, Aktan HM. Active and non-active porosity in concrete. Part I: Experimental evidence. Mater Struct Constr. 2002;34(246):102-109,.
27.
Yaman IO, Aktan HM, Hearn N. Active and non-active porosity in concrete Part II: Evaluation of existing models. Mater Struct. 2002;35(2):110-116,.
28.
Zimmerman RW. Elastic moduli of a solid containing spherical inclusions. Mech Mater. 1991;12(1):17-24,.
29.
Xiao JQ, Ding DX, Xu G, Jiang FL. Inverted S-shaped model for nonlinear fatigue damage of rock. Int J Rock Mech Min Sci. 2009;46(3):643-648,.
30.
Xiao JQ, Ding DX, Jiang FL, Xu G. Fatigue damage variable and evolution of rock subjected to cyclic loading. Int J Rock Mech Min Sci. 2010;47(3):461-468,.
31.
Yasar E, Erdogan Y. Correlating sound velocity with the density, compressive strength and Young’s modulus of carbonate rocks. Int J Rock Mech Min Sci. 2004;41(5):871-875,.
32.
Jaeger JC, Cook NGW, Zimmerman RW. Fundamentals of rock mechanics. Vol. 38. 2007. p. 3–4.
33.
Kuster GT, Toksoz MN. Velocity and attenuation of seismic waves in two‐phase media: Part I. Theoretical formulations,” Geophysics. 2012;39(5):587-606,.