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Stresses and Strains
Published in M.S. Rahman, M.B. Can Ülker, Modeling and Computing for Geotechnical Engineering, 2018
Certain other definitions are made at this point to characterize such a material. A homogeneous material is one having identical properties at all points in its volume. With respect to its properties, a material is isotropic if that property is the same in all directions at a point. A soil mass/layer is anisotropic if its physical or engineering properties vary in different directions. The forces, which act on all elements of the volume of a continuum are known as body forces. Some examples are gravity and inertia forces. These forces are represented by the symbol bj (force per unit mass), or as γj (force per unit volume). They are related through the density by the equation, ρbi=γiorρb=γ, $$ \rho b_{i} = \gamma _{i} \,\,or\,\,\rho b = \gamma , $$
A generic stress surface introduced in the customised octahedral plane
Published in G.N. Pande, S. Pietruszczak, H.F. Schweiger, Numerical Models in Geomechanics, 2020
U. Praastrup, B.L. Ibsen, P.V. Lade
That a material behaves isotropically means that the properties of the material are independent of the direction of the chosen coordinate system. Consequently, when loading an isotropic material in the same manner in different directions the material behaves the same. Hence, a formulation in terms of principal stresses is sufficient in cases of isotropy. For an anisotropic material the situation is different as the properties of anisotropic materials depend on the direction considered. Thus, a formulation based exclusively on principal stresses is not adequate for materials that behave anisotropically. For cross-anisotropic materials an axis of symmetry exists for the material properties.
Inhomogeneous Metamaterials: Super Quasicrystals
Published in Tie Jun Cui, Wen Xuan Tang, Xin Mi Yang, Zhong Lei Mei, Wei Xiang Jiang, Metamaterials, 2017
Tie Jun Cui, Wen Xuan Tang, Xin Mi Yang, Zhong Lei Mei, Wei Xiang Jiang
Although homogeneous metamaterials have exhibited many unusual physical properties, such as negative refractions and zero-index refractions, inhomogeneous metamaterials provide a different way to control EM waves. In this chapter, we will mainly focus on the property and applications of inhomogeneous metamaterials. Inhomogeneity means that the EM parameters of the materials (e.g., the permittivity and permeability) vary with space position. The materials can be isotropic or anisotropic. Many novel devices have been proposed using inhomogeneous meta-materials, such as invisibility cloaks, concentrators, high-performance antennas, and illusion devices.
Analytical and numerical investigation of polyvinyl chloride (PVC) confined concrete columns under different loading conditions
Published in Australian Journal of Structural Engineering, 2023
Haytham F. Isleem, Babatunde Olawale Yusuf, Wang Xingchong, Tang Qiong, P. Jagadesh, Daudi Salezi Augustino
The stress-strain response and softening rule of PVC plastic would be different from that of concrete. PVC plastic is a ductile material with large strain. It is regarded as an isotropic material due to its similar properties in all directions. The PVC tube is modelled as a von Mises material with isotropic hardening. For the effective modelling of the material, it is imperative to define the parameters of yield strength, Poisson's ratio, elastic modulus, and inelastic strain for the elastic and plastic material definition. As reported, the test results of PVC employed are presented in Table 4.