30 3 Elastic Constants Based on Micromechanics This function uses the simple rule-of-mixtures 名 formula of equation (3.3) Vm =1-Vf; y Vf*NU12f Vm*NUm; function y E2(Vf,E2f,Em,Eta,NU12f,NU21f,NUm,Eif,p) %E2 This function returns Young's modulus in the % transverse direction.Its input are nine values: % Vf fiber volume fraction 名 E2f- transverse Young's modulus of the fiber ” Em - Young's modulus of the matrix % Eta stress-partitioning factor % NU12f Poisson's ratio NU12 of the fiber % NU21f Poisson's ratio NU21 of the fiber % NUm -Poisson's ratio of the matrix % Eif -longitudinal Young's modulus of the fiber % ? parameter used to determine which equation to use: % p =1 -use equation (3.4) % p =2-use equation (3.9) % p =3 -use equation (3.10) % Use the value zero for any argument not needed % in the calculations. Vm 1-Vf; if p ==1 y 1/(Vf/E2f Vm/Em) elseif p ==2 y 1/((Vf/E2f Eta*Vm/Em)/(Vf Eta*Vm)); elseif p =3 deno Eif*Vf Em*Vm; etaf (E1f*Vf ((1-NU12f*NU21f)*Em NUm*NU21f*E1f)*Vm)/deno; etam =(((1-NUm*NUm)*E1f -(1-NUm*NU12f)*Em)*Vf Em*Vm)/deno; y =1/(etaf*Vf/E2f etam*Vm/Em); end function y =G12(Vf,G12f,Gm,EtaPrime,p) %G12 This function returns the shear modulus G12 Its input are five values: 名 Vf fiber volume fraction % G12f -shear modulus G12 of the fiber % Gm shear modulus of the matrix EtaPrime-shear stress-partitioning factor % P parameter used to determine which equation to use: % p=1-use equation (3.5) % p=2-use equation (3.13) % p=3-use equation (3.14) % Use the value zero for any argument not needed % in the calculations. Vm 1 Vf;30 3 Elastic Constants Based on Micromechanics % This function uses the simple rule-of-mixtures % formula of equation (3.3) Vm = 1 - Vf; y = Vf*NU12f + Vm*NUm; function y = E2(Vf,E2f,Em,Eta,NU12f,NU21f,NUm,E1f,p) %E2 This function returns Young’s modulus in the % transverse direction. Its input are nine values: % Vf - fiber volume fraction % E2f - transverse Young’s modulus of the fiber % Em - Young’s modulus of the matrix % Eta - stress-partitioning factor % NU12f - Poisson’s ratio NU12 of the fiber % NU21f - Poisson’s ratio NU21 of the fiber % NUm - Poisson’s ratio of the matrix % E1f - longitudinal Young’s modulus of the fiber % p - parameter used to determine which equation to use: % p = 1 - use equation (3.4) % p = 2 - use equation (3.9) % p = 3 - use equation (3.10) % Use the value zero for any argument not needed % in the calculations. Vm = 1 - Vf; if p == 1 y = 1/(Vf/E2f + Vm/Em); elseif p == 2 y = 1/((Vf/E2f + Eta*Vm/Em)/(Vf + Eta*Vm)); elseif p == 3 deno = E1f*Vf + Em*Vm; etaf = (E1f*Vf + ((1-NU12f*NU21f)*Em + NUm*NU21f*E1f)*Vm) /deno; etam = (((1-NUm*NUm)*E1f - (1-NUm*NU12f)*Em)*Vf + Em*Vm) /deno; y = 1/(etaf*Vf/E2f + etam*Vm/Em); end function y = G12(Vf,G12f,Gm,EtaPrime,p) %G12 This function returns the shear modulus G12 % Its input are five values: % Vf - fiber volume fraction % G12f - shear modulus G12 of the fiber % Gm - shear modulus of the matrix % EtaPrime - shear stress-partitioning factor % p - parameter used to determine which equation to use: % p = 1 - use equation (3.5) % p = 2 - use equation (3.13) % p = 3 - use equation (3.14) % Use the value zero for any argument not needed % in the calculations. Vm = 1 - Vf;