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O-K-State BAE 2023 - Lecture 8 – Viscoelasticity and Deformation

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Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 2301/14/19 BAE2023 Physical Properties of Biological Materials Lecture 81HW#5 Due 2/13 (Friday)Lab #1 Due 2/18 (Next Wednesday)For Friday Read: pg 130 – 168 (rest of Chpt. 4)Lecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 82•Poisson’s Ratio, μ (pg. 115)–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:–εz = σz/E, εy = -μ·εz and εx = -μ·εyLecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 83•Poisson’s Ratio–For multi-axial compression –See equations in 4.2 page 117–Maximum Poisson’s = 0.5 for incompressible materials to 0.0 for easily compressed materials–Examples: gelatin gel – 0.50Soft rubber – 0.49Cork – 0.0Potato flesh – 0.45 – 0.49Apple flesh - 0.21 – 0.29 Wood – 0.3 to 0.5More porous means smaller Poisson’sLecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 84•In addition to Normal stresses: Shearing Stresses–Shear stress: force per unit area acting in the direction parallel to the surface of the plane,τ–Shear strain: change in the angle formed between two planes that are orthogonal prior to deformation that results from application of sheer stress, γLecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 85•Shear modulus: ratio of shear stress to shear strain, G = τ/γ•Measured with parallel plate shear test (pg. 119)Lecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 86Lecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 87Lecture 8 – Viscoelasticity and DeformationExample Problem•The bottom surface (8 cm x 12 cm) of a rectangular block of cheese (8 cm wide, 12 cm long, 3 cm thick) is clamped in a cheese grater.•The grating mechanism moving across the top surface of the 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 the upper surface, estimate the latera movement of the upper surface w/respect to the lower surface.01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 88•Stresses and Strains: described as deviatoric or dilitational•Dilitational: causes change in volume•Deviatoric: causes change in shape but negligible changes in volume•Bulk Modulus, K: describes response of solid to dilitational stresses•K = average normal stress/dilatation•Dilatation: (Vf – V0)/V0Lecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 89•K = average normal stress/dilatation•Dilatation: (Vf – V0)/V0•Average normal stress = ΔP, uniform hydrostatic gauge pressure•ΔV = Vf – V0•So: K = ΔP/(ΔV / V0)•Δ V is negative, so K is negative•Example of importance: K (Soybean oil) > K (diesel) •Will effect the timing in an engine burning biodieselLecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 810•Apples compress easier than potatoes so they have a smaller bulk modulus, K (pg. 120) but larger bulk compressibility•K-1 =bulk compressibility•Strain energy density: area under the loading curve of stress-strain diagram•Sharp drop in curve = failureLecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 811•Stress-Strain Diagram, pg. 122•Area under curve until it fails = toughness•Failure point = bioyield point•Resilience: area under the unloading curve•Resilient materials “spring back”…all energy is recovered upon unloading•Hysteresis = strain density – resilience•Figure 4.6, page 124•Figure 4.7, page 125Lecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 812•Factors 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. 4.9Lecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 813•Stress Relaxation: Figure 4.10 pg 129–Material is deformed to a fixed strain and strain is held constant…stress required to hold strain constant decreases with time.•Creep: Figure 4.11 pg. 130–A continual increase in deformation (strain) with time with constant loadLecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 814•Tensile testing–Not as common as compression testing–Harder to do–See figure 4.12 page 132Lecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 815•Tensile testingLecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 816•Bending: E=modulus of elasticityD=deflection, F=force, I = moment of inertia•E=L3(48DI)-1•I=bh3/12Lecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 817•Can be used for testing critical tensile stress at failure•Max tensile stress occurs at bottom surface of beam•σmax=3FL/(2bh2)Lecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 818•Contact Stresses (handout from Mohsenin book)–Hertz Problem of Contact StressesImportance: “In ag products the Hertz method can be used to determine the contact forces and displacements of individual units”Lecture 8 – Viscoelasticity and Deformation01/14/19 BAE2023 Physical Properties of Biological Materials Lecture 819•Assumptions:–Material is homogeneous–Loads applied are static–Hooke’s law holds–Contacting stresses vanish at the opposite ends–Radii of curvature of contacting solid are very large compared to radius of contact surface–Contact surface is smoothLecture 8 –


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O-K-State BAE 2023 - Lecture 8 – Viscoelasticity and Deformation

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