Lecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationPoisson’s RatioPoisson’s RatioLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationSlide 13Lecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationSlide 16Lecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationLecture 8 – Viscoelasticity and DeformationHW Assignment Due 2/11HW Assignment Due 2/11HW Assignment Due 2/11HW Assignment Due 2/11Lecture 8 – Viscoelasticity andDeformation2/4/2011BAE2023 Physical Properties of Biological Materials1Deformation due to applied forces varies widely among different biomaterialsDepends on many factors•Rate of applied force•Previous loading•Moisture content•Biomaterial composition2/4/2011BAE2023 Physical Properties of Biological Materials2Lecture 8 – Viscoelasticity andDeformationNormal stress: Force per unit area applied perpendicular to the planeNormal strain: Change in length per unit of length in the direction of the applied normal stress2/4/2011BAE2023 Physical Properties of Biological Materials3Modulus of elasticityLinear region of stress strain curve E = σ/εFor biomaterials: apparent E = σ/ε at any given point (secant method)Tangent method: slope of stress/strain curve at any pointLecture 8 – Viscoelasticity andDeformationLecture 8 – Viscoelasticity andDeformationPoisson’s Ratio, μ•When a material is compressed in one direction, it usually tends to expand in the other two directions perpendicular to the direction of compression•The Poisson ratio is the ratio of the fraction (or percent) of expansion divided by the fraction (or percent) of compression, for small values of these changes.2/4/2011BAE2023 Physical Properties of Biological Materials4Poisson’s Ratio•Ratio of the strain in the direction perpendicular to the applied force to the strain in the direction of the applied force.•For uniaxial compression in Z direction:εz = σz/Eεy = -μ·εz εx = -μ·εz2/4/2011BAE2023 Physical Properties of Biological Materials5Poisson’s RatioMulti-axial CompressionSee equations in 4.2 page 117Maximum Poisson’s = 0.5 for incompressible materials to 0.0 for easily compressed materialsExamples:•Gelatin gel – 0.50•Soft rubber – 0.49•Cork – 0.0•Potato flesh – 0.45 – 0.49•Apple flesh - 0.21 – 0.29•Wood – 0.3 to 0.5More porous means smaller Poisson’s Ratio2/4/2011BAE2023 Physical Properties of Biological Materials6Lecture 8 – Viscoelasticity andDeformationShearing StressesShear Stress: Force per unit area acting in the direction parallel to the surface of the plane, τShear Strain: Change in the angle formed between two planes that are orthogonal prior to deformation that results from application of sheer stress, γ2/4/2011BAE2023 Physical Properties of Biological Materials7Lecture 8 – Viscoelasticity andDeformationShear Modulus:Ratio of shear stress to shear strain G = τ/γMeasured with parallel plate shear test(pg. 119)2/4/2011BAE2023 Physical Properties of Biological Materials8Lecture 8 – Viscoelasticity andDeformationExample ProblemThe bottom surface (8 cm x 12 cm) of a rectangular blockof cheese (8 cm wide, 12 cm long, 3 cm thick) is clampedin a cheese grater.• The grating mechanism moving across the top surface ofthe cheese applies a lateral force of 20N.• The shear modulus, G, of the cheese is 3.7kPa.• Assuming the grater applies the force uniformly to theupper surface, estimate the lateral movement of the uppersurface w/respect to the lower surface2/4/2011BAE2023 Physical Properties of Biological Materials9Lecture 8 – Viscoelasticity andDeformationStresses and Strains: Described as Deviatoric or DilitationalDilitational: Causes change in volumeDeviatoric: Causes change in shape but negligiblechanges in volumeBulk Modulus, K: describes response of solid todilitational stresses2/4/2011BAE2023 Physical Properties of Biological Materials10Lecture 8 – Viscoelasticity andDeformation Dilatation: (Vf – V0)/V0Δ V = Vf – V0K = ΔP/(Δ V / V0)ΔP = Average normal stress, uniform hydrostatic gaugepressureK = average normal stress/dilatationV is negative, so K is negative•Example of importance: K (Soybean oil) > K (diesel)•Will effect the timing in an engine burning biodiesel2/4/2011BAE2023 Physical Properties of Biological Materials11Lecture 8 – Viscoelasticity andDeformationApples compress easier than potatoes so they have a smaller bulk modulus, K (pg. 120) but larger bulk compressibilityK-1 =bulk compressibilityStrain Energy Density: Area under the loading curve of stress-strain diagram•Sharp drop in curve = failure2/4/2011BAE2023 Physical Properties of Biological Materials12Stress strain curve for uniaxial compression of cylindrical sample of food product2/4/2011BAE2023 Physical Properties of Biological Materials13Lecture 8 – Viscoelasticity andDeformationStress-Strain Diagram, pg. 122Toughness: Area under curve until it fails Bio yield point: Failure point Resilience: Area under the unloading curve• Resilient materials “spring back”…all energy isrecovered upon unloadingHysteresis: strain density – resilienceFigure 4.6, page 124Figure 4.7, page 1252/4/2011BAE2023 Physical Properties of Biological Materials14Lecture 8 – Viscoelasticity andDeformationFactors Affecting Force-Deformation Behavior•Moisture Content, Fig. 4.6b•Water Potential, Fig. 4.8•Strain Rate: More stress required for higher strain rate, Fig. 4.8•Repeated Loading, Fig. 4.92/4/2011BAE2023 Physical Properties of Biological Materials15Effect of water potential and strain rate on stress-strain curve of cylindrical Ida Red apple tissue2/4/2011BAE2023 Physical Properties of Biological Materials16Lecture 8 – Viscoelasticity andDeformationStress
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