6 - Scaling Mechanics of Networks to RBCs 4-fold symmetry...

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1 Scaling Mechanics of Networks to RBCs • 4-fold symmetry uses three moduli, s and p Pure shear Simple shear Stressing Networks • Enthalpy • Non-linear elasticity dependence on stress • Lower Compressive, Higher Shear with increasing tension • At the vertex: • Not always a dilating tension: uniaxial must account for Poisson’s ratio in 2D: Physiologically-Relevant T Thermal contraction •K A and μ are independent of T and stress for Six-fold A and μ are dependent for Four-fold Spring Network w/ Degenerate Ground State Six-fold vs. Four-fold Spring Network 6 4
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2 Constitutive Equations • Relate Tension, Pressure, and Curvature P T A 2 R p 2 L proj 1 R p f - 1 R o T = K A ( A/A o ) Membrane Properties • Consider a small, flat membrane element Areal Modulus, K a 10 nm Membrane Bending Modulus • Force Balance • Simplifies to: = 0 ζ = (r/R P ) sin(n π * In (r/R P )/ln (R o /R P ) * sin m φ Bending Modulus B = K A d 2 /12 Further Simplifications…
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3 Thermo vs. Continuum Approach
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6 - Scaling Mechanics of Networks to RBCs 4-fold symmetry...

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