Question

roblem Macroscopic mechanical properties of 2-D networks with 6-fold symmetry Consider the network made of linear spring filaments depicted in A to the right, each with (microscopic) spring constant Ksp A shows the un-deformed state of the network. The free energy density of deformation for the network is given by the following expression undeformed where Ka is the area compression modulus and μ the shear modulus of the network, both macroscopic properties (a) Derive the stress-strain relationships for ơxx and ơyy- (b) Prove that the Poisson ratio is given by the relationship v (Oxx 0,0yy-0) as shown in B above. Poisson ratio is defined as v -w. Use the results of (a) (c) Connect the Poisson ratio to Ksp. Hint: Use the relationships K3and 3Asz . Hint: Consider uniaxial stress Exx

Answer 1