Theres no equation containing only the terms for shear rigidity modulus and bulk modulus. How are the value of elastic constants fixed for a given material. The equation relating these three elastic constants for isotropic materials is. Different elastic constants and their relationships when an elastic body is subjected to stress, a proportionate amount of strain is produced. How are the value of elastic constants fixed for a given. Elastic constants and relation among all elastic constants. Lindseth 1979 proposed an empirical relation between acoustic impedance and. The ratio of the applied stresses to the strains generated will always be constant and is known as elastic constant. 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. What is the relationship between rigidity modulus and bulk. The relation between single crystal elasticity and the. Relation between elastic constants stress mechanics. Module 3 constitutive equations learning objectives understand basic stressstrain response of engineering materials.
Relation between elastic constants detailed explanation. Different types of stresses and their corresponding strains within elastic limit are related which are referred to as elastic constants. Elastic constants and their relationship lec5 youtube. 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. 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. These are bonded together by interatomic or intermolecular forces and stay in a stable equilibrium position. The relation between the stress and the strain for a given material under tensile stress can be found experimentally. Elastic constants, relation between elastic constants.
The relationship between elasticwave velocities and. Stress produces a strain, but how much strain is produced depends on the solid itself. From wikiversity optical properties lattice vibrations. The constants in the expression for vp differ from those in gardners equation. This only applies for a uniaxial applied stress, and the component of strain in the direction of the applied stress. Quantify the linear elastic stressstrain response in terms of tensorial quantities and in particular the fourthorder elasticity or sti ness tensor describing hookes law. E, k and v consider the total strain e, for any one direction under hydrostatic stressing in fig. Consider a cube of material of side a subjected to the action of the shear and complementary shear stresses as shown in the. 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 and relation among all elastic constants, learn relationship among all elastic constants. The elastic modulus of an object is defined as the slope of its stressstrain curve in the elastic deformation region. For isotropic materials, only two independent elastic constants are needed for describing the stressstrain relationship, i.
If is experimentally measured, often by placing strain gauges on a tensile sample, then this equation is a useful relationship between e and g. The relationship between the bulk modulus and the elastic constants is. Derive the relationship between the elastic constants, i. The relationship between elasticwave velocities and density in sedimentary rocks.
Simple model of lattice vibrations linear atomic chain. We will also discuss about the difference between youngs. The fractional change in length the strain and the applied force needed to. The distortion of the cube, is represented by the dotted lines. Elastic constants youngs modulus, modulus of rigidity. Pdf cauchylike relation between elastic constants in. This calculator computes the interrelations among the 5 commonly used elastic constants. A stiffer material will have a higher elastic modulus. An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substances tendency to be deformed elastically i. Elastic constant represents the elastic behaviour of objects. Relation between elastic constants youngs modulus, bulk modulus, and rigidity modulus of any elastic solid are together called as elastic constants.
When an elastic body is subjected to stress, a proportionate amount of strain is produced. Elastic constants study notes for mechanical engineering. Thermal, acoustic, and optical properties fall 2015 2. Hello, i am talking about the elastic constants like modulus of elasticity, modulus of rigidity, bulk modulus, poisons ratio etc. Civil engineering mcqs elastic constants and their relationships % civil engineering mcqs elastic constants and their relationships %.
Different elastic constants and their relationships. In this article you will learn about the elastic constant youngs modulus, modulus of rigidity and bulk modulus. Introduction elastic constants in the science of materials, numbers that quantify the response of a particular material to elastic or nonelastic deformation when a stress load is applied to that material, are known as elastic constants. The relation between single crystal elasticity and the effective elastic behaviour of polycrystalline materials. Consider a solid cube, subjected to a shear stress on the faces pq and rs and complimentary shear stress on faces qr and ps. Let us establish a relation among the elastic constants e,g and u.
Young modulus can be expressed using bulk modulus and poissons ratio as \e3k\left 12\mu \right \. We can derive the elastic constants relation by combining the mathematical expressions relating terms individually. This mean strain is the sum of three contributions. Elastic constants materials engineering reference with. The youngs modulus, e, is defined as the constant of proportionality between a uniaxial applied stress and the resulting axial strain, i. It is the ratio between compressive stress and compressive strain or tensile stress and tensile strain. Relationship between bulk modulus and elastic constant. There are, however, several equations relating these two entities, all of which involve a third elastic constant.
62 309 1415 249 861 1331 1485 1415 164 224 1360 1240 775 777 1021 1257 636 760 524 1564 534 796 556 1553 85 556 621 120 1455 1286 1489 849 998 461