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The properties involving multiplication, division, and exponentiation generally require that a and n are integers. Identity: (a mod n) mod n = a mod n. nx mod n = 0 for all positive integer values of x. If p is a prime number which is not a divisor of b, then abp−1 mod p = a mod p, due to Fermat's little theorem.
Young's modulus is defined as the ratio of the stress (force per unit area) applied to the object and the resulting axial strain (displacement or deformation) in the linear elastic region of the material. Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler.
Elastic modulus. Physical property that measures stiffness of material. An elastic modulus (also known as modulus of elasticity) is the unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it.
Calculations. The stiffness, of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as where, F {\displaystyle F} is the force on the body.
t. e. In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, Fs = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation ...
Margin of Safety is the common method for design criteria. It is defined MS = P u /P − 1. For example, to achieve a factor of safety of 4, the allowable stress in an AISI 1018 steel component can be calculated to be = / = 440/4 = 110 MPa, or = 110×10 6 N/m 2. Such allowable stresses are also known as "design stresses" or "working stresses".
Modulus of resilience (U r) is measured in a unit of joule per cubic meter (J·m −3) in the SI system, i.e. elastical deformation energy per surface of test specimen (merely for gauge-length part). Like the unit of tensile toughness ( U T ), the unit of resilience can be easily calculated by using area underneath the stress–strain ( σ ...
Lamé parameters. In continuum mechanics, Lamé parameters (also called the Lamé coefficients, Lamé constants or Lamé moduli) are two material-dependent quantities denoted by λ and μ that arise in strain - stress relationships. [1] In general, λ and μ are individually referred to as Lamé's first parameter and Lamé's second parameter ...