To capture the degree of anisotropy of a class, a universal elastic anisotropy index (AU) was formulated. It replaces the Zener ratio, which is suitable for cubic crystals. Robert Hooke was a brilliant English polymath who discovered the law of elasticity that we now know as Hooke`s law. In physics, Hooke`s law is an empirical law that states that the force (F) required to extend or compress a spring by a certain distance (x) is linearly with respect to that distance – i.e. Fs = kx, where k is a characteristic constant factor of the spring (i.e. its stiffness), and x is small compared to the total possible deformation of the spring. The law is named after the 17th-century British physicist Robert Hooke. He first explained the law as a Latin anagram in 1676. , He published the solution of his anagram in 1678 under the title: ut tensio, sic vis (“like extension, therefore force” or “expansion is proportional to force”). Hooke states in the 1678 article that he had known the law since 1660. The law also applies if a stretched steel wire is twisted by pulling a lever attached to one end. In this case, the tension Fs can be considered as the force exerted on the lever and x as the distance traveled by it on its circular trajectory. Or equivalently, you can let Fs be the applied torque of the lever at the end of the wire, and x is the angle around which that end rotates.
In both cases, Fs is proportional to x (although the constant k is different in each case). Hooke also invested the compound microscope, which he used to look at all kinds of objects, revealing a small world of microorganisms that humans had never seen before. He published a book called Micrographia with drawings of his finds, including a flea and a head louse. It is also believed that he was the first person to use the word “cell”. Due to the inherent symmetries of σ, ε and c, only 21 elastic coefficients of the latter are independent.  This number can be further reduced by the symmetry of the material: 9 for an orthorhombic crystal, 5 for a hexagonal structure and 3 for a cubic symmetry.  For isotropic media (which have the same physical properties in each direction), c can be reduced to only two independent numbers, the mass modulus K and the shear modulus G, which quantify the material`s resistance to volume changes and shear strains, respectively. At relatively large force values, the deformation of the elastic material is often greater than expected by Hooke`s law, although the material remains elastic and returns to its original shape and size after the force is removed. Hooke`s law describes the elastic properties of materials only in the range where force and displacement are proportional. (See Deformation and flow.) Sometimes Hooke`s law is formulated as F = −kx.
F no longer stands for the applied force, but the same opposite restorative force that returns elastic materials to their original dimensions. In the case of a spiral spring stretched or compressed along its axis, the applied (or restorative) force and the resulting deformation or compression have the same direction (i.e. the direction of this axis). Therefore, if Fs and x are defined as vectors, Hooke`s equation is still valid and states that the force vector is the strain vector multiplied by a fixed scalar. Hooke`s law only applies to certain materials under certain loading conditions. Steel exhibits linear-elastic behavior in most engineering applications; Hooke`s law applies to him throughout the yield range (i.e. for stresses below the yield strength). For some other materials, such as aluminum, Hooke`s law only applies to part of the elastic zone. For these materials, a proportional limit stress is defined, below which the errors associated with the linear approximation are negligible. A uniform spring of the force constant $k$ is cut into two pieces, the lengths of which are in the ratio $1: 2$. Ratio of force constants of t. Hooke`s law is the first classic example of an explanation of elasticity – the property of an object or material that allows it to return to its original shape after distortion.
This ability to return to normal shape after distortion can be called “force restoration.” According to Hooke`s law, this restorative force is usually proportional to the amount of “tension” experienced. We must choose the right declaration for whose right. Hook`s law states that the force is equal to K.X. The force exerted by a constrained or compressed spring is proportional to the displacement if it is constant. Do they stretch a string? This force is always in the opposite direction. That`s right, Mhm. The sign indicates that it is a negative sign. The statement is character. Yes, that`s right.
Thank you very much. Modern elasticity theory is a generalized variation of Hooke`s law, which states that the deformation/deformation of an elastic object or material is proportional to the load applied to it. However, since general stresses and deformations can have several independent components, the “proportionality factor” can no longer be a single real number. Like so many other devices invented over the centuries, a basic understanding of mechanics is needed before they can be used so widely. In terms of springs, this means understanding the laws of elasticity, torsion and force that come into play – collectively known as Hooke`s law. Isotropic materials are characterized by properties independent of direction in space. Physical equations with isotropic materials must therefore be independent of the coordinate system chosen to represent them. The strain tensor is a symmetric tensor.
Since the trace of any tensor is independent of any coordinate system, the most complete coordinateless decomposition of a symmetric tensor is to represent it as the sum of a constant tensor and a traceless symmetric tensor.  So, in index notation: Choose the right alternative from the given choices. The expansion of a spring from its resting position is directly proportional to the force. Hooke`s law is a physical principle that states that the force required to extend or compress a spring by a certain distance is proportional to that distance. The law is named after the 17th-century British physicist Robert Hooke. It was named as an attempt to demonstrate the relationship between the forces exerted on a feather and its elasticity. He first explained the law as a Latin anagram in 1660 and published the solution in 1678 as ut tensio, sic vis – which translates as “like expansion, that is, force” or “expansion is proportional to force”. Spring is a marvel of human engineering and creativity. On the one hand, there are many variants – compression spring, extension spring, torsion spring, coil spring, etc. – all of which perform different and specific functions. These functions, in turn, allow for the creation of many man-made objects, most of which were created as part of the scientific revolution of the late 17th and 18th centuries.
Hooke`s equation is true (to some extent) in many other situations where an elastic body is deformed, such as the wind blowing over a tall building and a musician plucking a guitar string. An elastic body or material for which this equation can be assumed is called linear-elastic or hooked. This law had many important practical applications, including the creation of a balance wheel that allowed the creation of the mechanical clock, portable watch, spring scale, and pressure gauge (also known as the pressure gauge). Since this is a close approximation of all solids (as long as the strain forces are small enough), many branches of science and technology are also indebted to Hooke for the development of this law. These include the disciplines of seismology, molecular mechanics and acoustics. Hooke`s law, the law of elasticity discovered in 1660 by English scientist Robert Hooke, states that for relatively small deformations of an object, the displacement or magnitude of the deformation is directly proportional to the force or strain load. Under these conditions, after removing the load, the object returns to its original shape and size. The elastic behavior of solids according to Hooke`s law can be explained by the fact that small shifts of their molecules, atoms or ions from normal positions are also proportional to the force causing the displacement. Imagine a simple spiral spring where one end is attached to a solid object while the free end is pulled by a force of size Fs.
Suppose the spring has reached a state of equilibrium in which its length no longer changes. Let x be the quantity by which the free end of the spring has been moved from its “relaxed” position (if it is not stretched).