Orthotropic body

An orthotropic body has material properties that are different in three mutually perpendicular directions at a point in the body and, further, has three mutually perpendicular planes of material property symmetry. Thus, the properties depend on orientation at a point in the body. 

For an orthotropic particle in steady translation through an unbounded viscous fluid, the total drag is given by Eq. (4-5). In principle, it is possible to follow a development similar to that given in Section IT.B.l for axisymmetric particles, to deduce the general behavior of orthotropic bodies in free fall. This is of limited interest, since no analytic results are available for the principal resistances of orthotropic particles which are not bodies of revolution. General conclusions from the analysis were given in TLA. 

Experimental data and numerical results for principal values of the translational tensor for some axisymmetric and orthotropic bodies (cylinders, doubled cones, parallelepipeds) were discussed in [94], It was established that the results are well approximated by the following dependence for the relative coefficient of the axial drag ... 

The physical quantities appearing in Equations (4.21 to 4.26) are si, Sz, G12, V12, and V21. Fiowever, because of Equation (4.25) the number of physical quantities to be measured for a two-dimensional orthotropic body are reduced from 6 to 4. It is important to note that, if the material were transversely isotropic such that the material were isotropic in the 1-2 plane, the physical quantities involved would be Ei=E2, G12 and Vi2=V2i. 

Orthotropic body The mataM properties of an ortholropic material are different in three mutually perpendicular directions (material principal directions). The material properties for any other orientation in an orthotropic mataial can be obtained by appropriate transformation of the material povolies obtained for the principal material directions. Thus, the properties of an orthotropic material are a function of orientation. Planes perpendicular to the principal material directions are called planes of material symmetry. 

A so-called specially orthotropic lamina is an orthotropic lamina whose principal material axes are aligned with the natural body axes ... 

However, as mentioned previously, orthotropic laminae are often constructed in such a manner that the principal material coordinates do not coincide with the natural coordinates of the body. This statement is not to be interpreted as meaning that the material itself is no longer orthotropic instead, we are just looking at an orthotropic material in an unnatural manner, i.e., in a coordinate system that is oriented at some angle to the principal material coordinate system. Then, the basic question is given the stress-strain relations In the principal material coordinates, what are the stress-strain relations in x-y coordinates ... 

Note that the transformed reduced stiffness matrix Qy has terms in all nine positions in contrast to the presence of zeros in the reduced stiffness matrix Qy. However, there are still only four independent material constants because the lamina is orthotropic. In the general case with body coordinates x and y, there is coupling between shear strain and normal stresses and between shear stress and normal strains, i.e., shear-extension coupling exists. Thus, in body coordinates, even an orthotropic lamina appears to be anisotropic. However, because such a lamina does have orthotropic characteristics in principal material coordinates, it is called a generally orthotropic lamina because it can be represented by the stress-strain relations in Equation (2.84). That is, a generally orthotropic lamina is an orthotropic lamina whose principai material axes are not aligned with the natural body axes. 

A body has a plane of symmetry if the shape is unchanged by reflection in the plane. Orthotropic particles have three mutually perpendicular planes of symmetry. An axisymmetric particle is symmetric with respect to all planes containing its axis, so that it is orthotropic if it has a plane of symmetry normal to the axis, i.e., if it has fore-and-aft symmetry. 

The tensor S is symmetric only at a point O unique for each body, this point is called the center of hydrodynamic reaction. This tensor is called the conjugate tensor and characterizes the crossed reaction of the body under translational and rotational motion (the drag moment in the translational motion and the drag force in the rotational motion). For bodies with orthotropic, axial, or spherical symmetry, the conjugate tensor is zero. However, it is necessary to take this tensor into account for bodies with helicoidal symmetry (propeller-like bodies). 

In many fracture mechanics-based approaches, crack advance is taken to occur when K reaches some critical value Kc (equivalent energy-based criteria are also widely used). Kc may then be measured using a pre-cracked specimen, in which a and hence K are well defined. In some cases (PMMA, for example) crack advance is observed to proceed via breakdown of a single craze at the crack tip. By modeling a craze as an orthotropic linear elastic body it has been shown that Kc is given by Eq. (72), where v is Poisson s ratio, a is related to the craze anisotropy, C7c is the draw stress normal to the craze-bulk interface, Vf is the fibril volume fraction in the craze, and oy is the stress to break a craze fibril [33]. 

The bone tissue materials (osteons, cement lines, and interstitial tissues) are all considered as saturated orthotropic poroelastic media. Neglecting the body forces, the linear anisotropic poroelastic equations in low-frequency range are given by [10] ... 

In this section, the mechanical anisotropy of some commercial cellophanes will be discussed quantitatively firstly, on the basis of the theory of infinitesimal deformations of an orthotropic elastic body in bulk, and secondly, in terms of the biaxial orientation of the crystalline and noncrystalline structural units and their mechanical anisotropy. The simple volume additivity concept of the contribution from both phases to the bulk properties will be the primary problem to be addressed for such bulk phenomena as mechanical properties, in contrast to the treatment of Ward et ai, who discussed a monophase system with a rather undefined structural unit. 

---