[{"data":1,"prerenderedAt":37},["ShallowReactive",2],{"topic-en-strength-of-materials\u002Ftension-and-compression\u002Fmechanical-properties-of-materials\u002Felastic-properties-of-materials":3},{"topic":4,"trail":18,"children":32,"tasks":33,"alternates":34},{"id":5,"name":6,"locale":7,"path":8,"seo_title":9,"seo_description":10,"seo_text":11,"content_html":12,"content_chunks":13},111,"Elastic Properties of Materials","en","strength-of-materials\u002Ftension-and-compression\u002Fmechanical-properties-of-materials\u002Felastic-properties-of-materials","Elastic Properties of Materials — E, G and Poisson's Ratio","Young's modulus E, shear modulus G, Poisson's ratio ν, and their physical meaning in linear-elastic deformation calculations.","This topic summarizes the main elastic constants of an isotropic material: Young's modulus E, shear modulus G, and Poisson's ratio ν. It explains their physical meaning, units, engineering use, and the relation between E, G, and ν for a linearly elastic isotropic material.","\u003Cp>Elastic properties describe a material's resistance to reversible deformation. For a linearly elastic isotropic material, the principal constants include Young's modulus $E$, shear modulus $G$, and Poisson's ratio $\\nu$.\u003C\u002Fp>\u003Cdiv class=\"formula-chunk\">\u003Cp>Within the linear-elastic range, normal stress is proportional to axial strain:\u003C\u002Fp>\u003Cp>$$\\sigma=E\\varepsilon.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>$\\sigma$\u003C\u002Fstrong> — normal stress, Pa or MPa;\u003C\u002Fli>\u003Cli>\u003Cstrong>$E$\u003C\u002Fstrong> — Young's modulus, Pa or MPa;\u003C\u002Fli>\u003Cli>\u003Cstrong>$\\varepsilon$\u003C\u002Fstrong> — axial strain, dimensionless.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>The law applies to the linear portion of the stress–strain curve while $\\sigma$ and $\\varepsilon$ remain proportional.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>\u003C\u002Fdiv>\u003Ch2>Poisson's ratio\u003C\u002Fh2>\u003Cp>Under uniaxial tension, longitudinal elongation is accompanied by transverse contraction. Poisson's ratio is defined as $\\nu=-\\varepsilon_{\\perp}\u002F\\varepsilon_{\\parallel}$, where $\\varepsilon_{\\perp}$ is transverse strain and $\\varepsilon_{\\parallel}$ is longitudinal strain.\u003C\u002Fp>\u003Ch2>Shear modulus\u003C\u002Fh2>\u003Cp>The shear modulus $G$ characterizes material stiffness in shear. For a linearly elastic isotropic material, the elastic constants are related by $G=E\u002F[2(1+\\nu)]$.\u003C\u002Fp>\u003Ch2>Engineering application\u003C\u002Fh2>\u003Cp>$E$ is used in tension, compression, and bending calculations; $G$ is used in shear and torsion; and $\\nu$ is needed to describe the coupling between longitudinal and transverse strains.\u003C\u002Fp>",[14],{"id":15,"code":16,"type":17,"locale":7},68,"uniaxial-hooke-law","formula",[19,23,27,31],{"id":20,"name":21,"path":22},45,"Strength of Materials","strength-of-materials",{"id":24,"name":25,"path":26},46,"Tension and Compression","strength-of-materials\u002Ftension-and-compression",{"id":28,"name":29,"path":30},48,"Mechanical Properties of Materials","strength-of-materials\u002Ftension-and-compression\u002Fmechanical-properties-of-materials",{"id":5,"name":6,"path":8},[],[],{"en":35,"uk":36},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Ftopics\u002Fstrength-of-materials\u002Ftension-and-compression\u002Fmechanical-properties-of-materials\u002Felastic-properties-of-materials","https:\u002F\u002Fmechclassroom.com\u002Ftopics\u002Fopir-materialiv\u002Froztyah-i-stysk\u002Fmekhanichni-vlastyvosti-materialiv\u002Fpruzhni-kharakterystyky-materialiv",1787712539021]