The equation relating these three elastic constants for isotropic materials is. Simple model of lattice vibrations linear atomic chain. Pdf cauchylike relation between elastic constants in. Elastic constants youngs modulus, modulus of rigidity. The elastic modulus of an object is defined as the slope of its stressstrain curve in the elastic deformation region. Relation between elastic constants free download as pdf file. The constants in the expression for vp differ from those in gardners equation. The relationship between elasticwave velocities and. For isotropic materials, only two independent elastic constants are needed for describing the stressstrain relationship, i.
Different elastic constants and their relationships when an elastic body is subjected to stress, a proportionate amount of strain is produced. Elastic constants and relation among all elastic constants. Young modulus can be expressed using bulk modulus and poissons ratio as \e3k\left 12\mu \right \. Consider a solid cube, subjected to a shear stress on the faces pq and rs and complimentary shear stress on faces qr and ps. Orthotropic materials have 3 planes of material symmetry, and 9 independent elastic constants.
These correspond to elastic moduli in each of the three principal material directions, three poissons ratios that represent the coupling between axial and transverse strains, and three shear moduli that represent the. When an elastic body is subjected to stress, a proportionate amount of strain is produced. Let us establish a relation among the elastic constants e,g and u. This only applies for a uniaxial applied stress, and the component of strain in the direction of the applied stress. Relation between elastic constants stress mechanics. Elastic constants study notes for mechanical engineering. What is the relationship between rigidity modulus and bulk. Relation between elastic constants detailed explanation. Calculator for exploring relations among the elastic constants. Consider a cube of material of side a subjected to the action of the shear and complementary shear stresses as shown in the. The relationship between elasticwave velocities and density in sedimentary rocks. The relation between single crystal elasticity and the.
Elastic constants and their relationship lec5 youtube. Quantify the linear elastic stressstrain response in terms of tensorial quantities and in particular the fourthorder elasticity or sti ness tensor describing hookes law. It is the ratio between compressive stress and compressive strain or tensile stress and tensile strain. Civil engineering mcqs elastic constants and their relationships % civil engineering mcqs elastic constants and their relationships %. This mean strain is the sum of three contributions. There are, however, several equations relating these two entities, all of which involve a third elastic constant. The ratio of the applied stresses to the strains generated will always be constant and is known as elastic constant. If is experimentally measured, often by placing strain gauges on a tensile sample, then this equation is a useful relationship between e and g. Other names are sometimes employed for one or both. An elastic modulus also known as modulus of elasticity is a quantity that measures an object or substances resistance to being deformed elastically i. Elastic constants, relation between elastic constants. In a standard test of tensile properties, a test cylinder or a wire is stretched by an applied force. Elastic constant represents the elastic behaviour of objects. A stiffer material will have a higher elastic modulus.
Derive the relationship between the elastic constants, i. Different elastic constants and their relationships. This lecture includes following topics poissons ratio u youngs modulus or modulus of elasticity e shear modulus or modulus of rigidity c, g or n bulk modulus k relationship between. Relationships between elastic constants from fung, a first course in continuum mechanics although only 2 independent elastic constants are required to completely the properties of an isotropic, elastic medium, there are many different constants from which to choose. Relationship between bulk modulus and elastic constant. How are the value of elastic constants fixed for a given material. From wikiversity optical properties lattice vibrations.
Lindseth 1979 proposed an empirical relation between acoustic impedance and. These are bonded together by interatomic or intermolecular forces and stay in a stable equilibrium position. An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substances tendency to be deformed elastically i. How are the value of elastic constants fixed for a given. Different types of stresses and their corresponding strains within elastic limit are related which are referred to as elastic constants. The relationship between the bulk modulus and the elastic constants is. The relation between the stress and the strain for a given material under tensile stress can be found experimentally.
The fractional change in length the strain and the applied force needed to. Module 3 constitutive equations learning objectives understand basic stressstrain response of engineering materials. Elastic constants and relation among all elastic constants, learn relationship among all elastic constants. The youngs modulus, e, is defined as the constant of proportionality between a uniaxial applied stress and the resulting axial strain, i. The relation between single crystal elasticity and the effective elastic behaviour of polycrystalline materials. Stress produces a strain, but how much strain is produced depends on the solid itself. E, k and v consider the total strain e, for any one direction under hydrostatic stressing in fig. Theres no equation containing only the terms for shear rigidity modulus and bulk modulus. Relation between elastic constants youngs modulus, bulk modulus, and rigidity modulus of any elastic solid are together called as elastic constants. This calculator computes the interrelations among the 5 commonly used elastic constants.
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