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Tel, et al.: Journal of Hazardous Materials, vol. 112(2004), p. 225 [10] L.
Rodrigues, et al.: Journal of Hazardous Materials, vol. 173(2010), p. 630 [11] S.
Álvarez-Ayuso, et al.: Journal of Hazardous Materials, vol. 142(2007), p. 191 [17] V.
Hu, et al.: Journal of Hazardous Materials, vol. 162(2009), p. 1542 [19] L.
Wei, et al: Journal of Hazardous Materials, vol. 164(2009), p. 1159 [20] J.

Nakhaev, Composite Binders with the Use of Fine Raw Materials of Volcanic Origin, International journal of environmental & science education. 11 (18) (2016) 12711-12716
Suleymanov, Energy-efficient concretes for green construction, Research journal of applied sciences. 9 (12) (2014) 1087-1090
Klyuev, A.V.Olisov, A.Taskin, Ali Mosaberpanah M., Effect of ash-slag mix and polypropylene fiber on the performances of concrete composite, Materials Science Forum. 1017 (2021) 1–17 [9] R.V.
Mugahed, Enhancing performances of clay masonry materials based on nanosize mine waste, Construction and Building Materials. 269 (2021) 121333
Bogusevich, Energy saving raw materials for the production of new generation silicate materials, International Journal of Pharmacy and Technology. 8 (4) (2016) 22673–22686.

Asphalt modified using nanoscale materials can be defined as complex material of asphalt.
Applied Mechanics and Materials, 2011, Vols.99-100, 1243-1246
JOURNAL OF WUHAN UNIVERSITY OF TECHNOLOGY (TRANSPORTATION SCIENCE & ENGINEERING), 2007, 31(1): 88~91
JOURNAL OF SHANDONG JIAOTONG UNIVERSITY, 2004（4）: 10~14
JOURNAL OF JIANGSU UNIVERSITY (NATURAL SCIENCE EDITION), 2006（6） 548~551.

Guan Institute of Numerical Simulation in Science and Engineering, Department of Computer Science, Tianjin University of Technology and Education, Tianjin 300222, China E-mail: xuanzc@tute.edu.cn Key words: Verification; J-integral; Functionally graded materials; Finite elements Abstract.
Introduction J-integral in functionally graded material (FGM) is an important quantity of interest in material science.
Numerical simulation method has been developed for calculating the J-integral, for example, finite element method is a widely used to compute the J-integral in both homogeneous and nonhomogeneous materials.
By expanding the second integrand, (3) leads to . (4) Using equilibrium () and strain-displacement () conditions and noting that in homogeneous materials, the second integrand of Eq. (4) vanishes, yielding , (5) which is the classical domain form of the J-integral in homogeneous materials.
For nonhomogeous materials, even though the equilibrium and strain-displacement conditions are satisfied, the material gradient term of the second intgrand of (4) dose not vanish.

Nanometer materials and their application technology as an important part of nano science and technology, is considered to has a decisive role to the development of contemporary science and technology.
In order to promote the development of nano science and technology, in July 1990 in the United States in Baltimore held the first international conference of nanotechnology, and announced that "nanotechnology" the international journal.
Nanometer materials.
Countries engaged in materials science experts and scholars are desire to develop new nano materials (especially the nano composite material), seeking for new technology of the preparation of new nano materials, to further explore the particle size of nanometer material, the amount of phase interface, the interface phase relationship between atomic structure and nanometer material performance, and the diffusion process of nanometer materials, the formation mechanism of nanocrystalline ceramics (especially the reticular formation) for further research.
Advanced materials, 1992; 4 (7-8) : 474-481

Mixed-Mode Crack Propagation in Functionally Graded Materials Jeong-Ho Kim 1,a and Glaucio H.
These materials have been introduced to take advantage of ideal behavior of material constituents.
Tina Panontin), and the National Science Foundation (NSF) under grant CMS0115954 (Mechanics and Materials Program).
Shemilt: Journal of Materials Science Vol. 36 (2001), p. 1077
Kim: Mixed-mode crack propagation in functionally graded materials, Ph.D.

It is thus of some interest to understand the dynamic behavior of masonry materials under dynamic loading.
Based on the constitutive relations of the brick and the mortar materials, the equivalent stress-strain relations of the RVE are homogenized by applying various compatible displacement conditions on the RVE surfaces.
They are defined as and (3) in which and are damage parameters that control postfailure stress-strain relations of materials in tension and compression.
Niu: International Journal of Solids and Structures, Vol. 29(5) (1992), p.531-546
Gusella: International Journal of Solids and Structures, Vol. 41 (2004), p.1911-1923

Materials and methods Materials The sample for analysis were commercial dehydrated carrots cube (1 mm diameter and 0.5 mm thickness, 7 ～ 9 % moisture content), they were purchased from Shandong province in China.
Klaus: International Journal of Food Science and Technology, Vol. 44 (2007), p. 1245 [5] S.N.
Resnik and G.Wetzler: Journal of Food Science, Vol. 52 (1987), p. 1063 [9] K.
Chang: Journal of Food Science, Vol. 60 (1995), p. 324 [11] P.S.
Warthesen: Journal of Food Science, Vol. 60 (1995), p. 1048

Introduction Granular materials are encountered widely in nature and engineering.
The parameter can express the stability of granular materials at particle scale.
Critical state and evolution of coordination numberin simulated granular materials.
Journal of Tongji University (Natural Science), 2007, 35, 1299-1304
Microscopic theoretical model of critical state for granular materials.

The rapid development of science and technology and the constant emergence of new materials make the product structure tend to be scientific and reasonable.
With the development of science and technology, new materials and new technologies are emerging in an endless stream.
International Journal of Plasticity.
Art Science and Technology.
Journal of the graduates.