Material StrengthStress vs StrainSpring ConstantInelastic MaterialShear ModulusTwist a LegBulk ModulusUnder PressureMaterial StrengthMaterial StrengthStress vs StrainStress vs StrainA graph of stress versus A graph of stress versus strain is linear for small strain is linear for small stresses.stresses.The slope of stress versus The slope of stress versus strain is a strain is a modulusmodulus that that depends on the type of depends on the type of material.material.For normal stress this is For normal stress this is Young’s modulus Young’s modulus YY..YStress Strain stiff materialelastic materialSpring ConstantSpring ConstantYoung’s modulus is a from a Young’s modulus is a from a linear relation like Hooke’s linear relation like Hooke’s law.law.•Young’s modulus describes Young’s modulus describes a type of material.a type of material.•The spring constant The spring constant describes an object.describes an object.YY and and kk are related. are related.LkLLYAFLAFLLLAFY)(//LFInelastic MaterialInelastic MaterialThe linear behavior of The linear behavior of materials only lasts up to a materials only lasts up to a certain strength – the certain strength – the yield yield strengthstrength..Materials can continue to Materials can continue to deform but they won’t deform but they won’t restore their shape.restore their shape.For very high strain a For very high strain a material will break.material will break.Stress Strain breaking strengthyield strengthShear ModulusShear ModulusMaterials also have a Materials also have a modulus from shear forces.modulus from shear forces.Shear modulus Shear modulus SS also also matches with a spring matches with a spring constant.constant.The angle The angle = = xx//LL is is sometimes used for shear.sometimes used for shear.F xA (goes into screen)LxkxLSAFxAFLLxAFSss)(//Twist a LegTwist a LegOne common fracture is a One common fracture is a torsion fracture. A torque is torsion fracture. A torque is applied to a bone causing a applied to a bone causing a break.break.•The shear modulus of bone The shear modulus of bone is 3.5 GPa.is 3.5 GPa.•The lower leg has a The lower leg has a breaking angle of 3breaking angle of 3. . •It requires 100 Nm of It requires 100 Nm of torque.torque.Torque and angle apply.Torque and angle apply.Angle is Angle is xx//LL = tan = tanApproximately Approximately RR//LL = = Sheer is related to torque.Sheer is related to torque.RLSAFxAFLSssBulk ModulusBulk ModulusPressure changes volume, Pressure changes volume, not length.not length.Bulk modulus Bulk modulus BB relates relates changes in pressure and changes in pressure and volume.volume.The negative sign represents The negative sign represents the decrease in volume with the decrease in volume with increasing pressure.increasing pressure.PVVA (surface area)VVPVVAFBVV///Under PressureUnder PressureSteel has a bulk modulus of Steel has a bulk modulus of BB = 60 GPa. A sphere with a = 60 GPa. A sphere with a volume of 0.50 mvolume of 0.50 m33 is is constructed and lowered into constructed and lowered into the ocean where the ocean where PP = 20 = 20 MPa.MPa.How much does the volume How much does the volume change?change?Use the relation for bulk Use the relation for bulk modulus.modulus.BB = -( = -(PP) / () / (VV//VV))VV= -= -VV P P / / BBSubstitute values:Substitute values:(-0.50 m(-0.50 m33)(2.0 x 10)(2.0 x 1077 Pa) / Pa) / (6.0 x 10(6.0 x 101010 Pa) Pa)VV = -1.6 x 10 = -1.6 x 1044 m
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