Mechanics of Soft Materials Tuesday and Thursday L13, 2:00-3:30 PM - PowerPoint PPT Presentation

Mechanics of Soft Materials Tuesday and Thursday L13, 2:00-3:30 PM

What Are Soft Materials? Rubber Skin Tissue Paper Modulus < 10 MPa Gel … Tissue scafold Deformation when subjected to load Type of load Geometry: micro-nano structures Rheological properties Interfacial properties

Shear Modulus (10 9 N/m 2 , GPa ) Material Acrylic 3.2 Soft Materials have modulus of Aluminum 69 the order of few Pa to few MPa Bone 9 Brasses 100 - 125 Gaskets Bronzes 100 - 125 Reinforced Plastic 150 Sealants Concrete 30 Adhesives Diamond 1,050 - 1,200 Glass 50 - 90 Skin Elastic Magnesium 45 Soft Patterning grain) 11 Viscoelastic Polycarbonate 2.6 Solid lubricants Poroelastic Polyethylene HDPE 0.8 Prosthetic devices Terephthalate PET 2 - 2.7 Ductile Drug delivery devices Polyimide 2.5 Viscoplastic Polypropylene 1.5 - 2 Packaging Materials Polystyrene 3 - 3.5 Components of automobile Silicon Carbide 450 Titanium Alloy 105 - 120 Soft robotic components Tungsten 400 - 410 Artificial Tissue Tungsten Carbide 450 - 650 Wrought Iron 190 - 210 Functional surfaces Nylon 2 - 4 Extracellular Matrix Rubber 0.01 - 0.1 10 -6 - 10 -3 Gels

Bio-inspired Patterned Adhesives:  Hierarchical structure  Strong and reusable adhesion  Adheres to almost all surfaces  Self-cleaning  Does not leave any residue  Easy release during locomotion Gorb et al , J. Micromech. Microeng . 2000, 10, 359–364 Patterned adhesive Smooth adhesive Crack arrest, crack initiation Enhancement of adhesion by ~10 times Ghatak et al, Proc. Roy. Soc. London , A, 460, 2725 (2004)

Adhesive suitable for dry and wet adhesion and delivery of drugs and nutrients Tissue Scar Transdermal Patches Cosmetic patches Tissue adhesive • Reversible adhesion: Clean adhesion • Good mechanical strength: ability to sustain large deformation • Multi-functionality: adhesion and drug delivery • Biocompatibility and biodegradability • Resistance against particulate contamination • Amenable for easy wash or cleaning

Inspiration from naturally occurring Adhesives Under water adhesion of mussel Gecko inspired Adhesive • Release of water repellent protein • Adhesion on dry and wet substrate • van der Waals interaction in dry state molecules at interface • Crosslinking of these molecules leading • Swelling of keratin protein of setae to a sticky glue in moist environment 300 c 24 hr 24 hr 24 hr 24 hr 250 24 hr 200 24 hr Rate of 24 hr A novel adhesive 150 Vitamin C release 4 days patch satisfies these 100 ( μ g/cm 2 /day) requirements 50 70 gm 0 1:5 2:5 3:5 Vitamin C solution-gelatin volume ratio

Blood Vessels in Climbing Organ of I nsects: Climbing organ Rhodnius Prolixus (kissing bug) Adult Rhodnius could climb the glass walls of the jars … ability to climb smooth surfaces was due to the existence in the adult insects of a flashy pad situated at the lower end of tibia of the first two pair of legs. Blood filled vessels Wigglesworth, et al, Proc. R. Soc. Lond. B 111, 364-376 ( 1932 ).

Air Pockets at the Adhesive Pads of I nsects Attachment pad of Tettigonia viridissima AS: Air sack CL: Epidermal cell layer EXO: Rod containing exo- cuticle of the pad HM: Haemolymph TD: Tendon of the claw flexor mussle TK: Tanned cuticle J. Comp. Physiology A , 2006 , 186 , 821-831

Peeling off a Microfluidic Adhesive a Majumder et al, Science, 318, 258-261, 2007

25-30 times enhanceme Peeling Torque: nt in adhesion 1.8 a (X 10 - 25 1.5 2 ) 7 20 1.2 6 15 M, 0.9 G , Nm/m 10 J/m 2 0.6 5 5 0.3 0 0.0 0 1 2 3 4 1 2 3 4 5 6 7 8 9 10 ∆ , mm h µ d µ , m , m 1: smooth adhesive 5 : 570 530 2: 120 cp 530 6 : 600 G ∫ h = 300 µ m = ∆ . 7 : 750 710 3: 1000 cp F d A d = 50 µ m peeled 710 8 : 800 4: 5000 cp 800 9 : 1200 5-10: 380 cp 1090 10 : 1200

Asymmetry I nduced by Pair of Embedded Channels: Differently filled with wetting liquid Flexible contacting plate Adhesive film F Substrate t s s h 1 1 d d d d 1 2 1 2 s Majumder et al Soft Mat. , 2012 t = 50 μ m, s 1 = 15 μ m, d = 550 μ m air air oil oil oil air 200 μ m

Dynamic Change in Surface Profile During Separation of Adherent: 20 10 0 0 200 400 600 800 1000 1200 20 10 δ 0 ( ) 0 200 400 600 800 1000 1200 μm 10 0 0 200 400 600 800 1000 1200 20 10 0 0 200 400 600 800 1000 1200 ( ) μm x

4.2 peel direction 3.6 3.0 G 2.4 ( ) Case 1 2 J/m 1.8 Case 2 1.2 Case 3 0.6 Case 4 0.0 ( ) = μm 120 150 s 60 s 1 1

Adhesion Between a Flexible Plate on a Layer of Adhesive Bonded to a Rigid Substrate: Flexible plate Spacer Elastic film Contact line z x ∆ Rigid substrate a Adhesive: Elastic, Incompressible, Thin Adherent: Thin, Flexible & Rigid Plate

Stress Equilibrium Relations: = µ + + ( ) p u u u x xx yy zz = µ + + p ( v v v ) y xx yy zz = µ + + p ( w w w ) z xx yy zz u , v , w are displacements in the x , y and z direction respectively I ncompressibility relation: + + = u v w 0 x y z

Plane Strain Approximation: = = = e e e 0 yy xy zy Stress equilibrium relation   ∂ ∂ ∂ 2 2 p u u   = µ +   ∂ ∂ ∂ 2 2   x x z   ∂ ∂ ∂ 2 2 p w w   = µ +   ∂ ∂ ∂ 2 2   z x z Incompressibility relation ∂ ∂ u w + = 0 ∂ ∂ x z

= = = = Dimensionless x X . L , z Z . h , u U . L , w W . h Quantities: ε = h L = µ ε 2 p   µ ∂ ∂ ∂ 2 2 1 P 1 U L U   = µ +   ( ) ∂ ∂ ∂ Dimensionless 2 2 2 2   L X L X h Z h L Stress-Equilibrium   µ ∂ ∂ ∂ 2 2 1 P h W 1 W relation:   = µ +   ( ) ∂ ∂ ∂ 2 2 2 2   h Z L X h Z h L ∂ ∂ ∂ ∂ 2 2 2 P U U U = ε + ≈ 2 Lubrication ∂ ∂ ∂ ∂ 2 2 2 X X Z Z Approximation: ∂ ∂ ∂ 2 2 ε << P W W 1 = ε + ε ≈ 4 2 0 ∂ ∂ ∂ 2 2 Z X Z

Boundary Conditions for Film: = = = = u ( z 0 ) w ( z 0 ) 0 = = = = ψ ( ) 0 , ( ) u z h w z h σ = σ = 0 at 0 < x < a = = xz zz z h z h ψ 4 d = = p ( z h ) D at x<0 4 dx z = h ( ) w , x z Elastic film z ( ) u x , z = x z 0

Integration ∂ ∂ ∂ 2 2 1 p z p u = + + = µ Boundary Condition u Az B ∂ ( ) ∂ ∂ µ ∂ 2 1 p x 2 x z = − 2 u z zh ∂ µ ∂ ∂ p 2 x h p = = = − 0 B 0 , A ∂ µ ∂ z 2 x Incompressibility relation Integration   ∂ ∂ ∂ ∂ ( ) 2 2 3 2 w u 1 p 1 p z z h   = − = − − = − − + 2 z zh w C   ∂ ∂ µ ∂ µ ∂ 2 2   z x 2 x 2 x 3 2 Boundary Condition ∂ ψ 3 6 Dh ψ = µ ∂ 6 12 x

Equation for Plate: ∂ ψ 3 6 Dh ψ = < x 0 µ ∂ 6 12 x ∂ ψ 4 < x < = 0 a 0 ∂ 4 x

Boundary Conditions for Plate: ∂ ψ ∂ ψ = ψ = ψ (i) (ii) ∂ ∂ = − = + x 0 x 0 x x = − = + x 0 x 0 ∂ ψ ∂ ψ ∂ ψ ∂ ψ 2 2 3 3 = = (iii) (iv) ∂ ∂ ∂ ∂ 2 2 3 3 x x x x = − = + = − = + x 0 x 0 x 0 x 0 ∂ ∂ ψ p 2 = = 0 0 (v) (vi) ∂ ∂ 2 x x = = a x 0 x 3 ψ d ψ = ∆ − = or D F (vii) = a x 3 dx = x a ψ = ψ = ψ = 0 (viii-x) = −∞ = −∞ = −∞ x xx x x x

Displacement Field in Adhesive Film: ( ) − ( ) 6 z z h F ' ( ) = φ u x , z x 1 3 kh ( ) − 2 ( ) z 3 h 2 z F ' ( ) = φ w x , z x 2 3 h       + ( ) 3 4 3 3 ak kx kx       φ = + − 2 2 kx kx x e ak e sin ak cos       1 2 2      3        + ( ) ( ) 3 ak 2 3 kx 3 kx       φ = + + + kx 2 kx 2 x e ak e sin ak 2 cos       2 2 2     3   − 1 and have dimension of length and are constants F ' k

Displacement of Plate and Normal Stress at I nterface: ψ ' F ( )       ψ + ( ) x 3 ak 2 3 kx 3 kx       = + + + kx 2 kx 2 e ak e sin ak 2 cos       F '  2   2  3   ∆ 1 6   3 3 Dh =   − = F ' , 1 k ( ) ( )   + + + µ 2 3 6 12 ak 9 ak 2 ak   12