Response for Classical Extremes Spring Purely Elastic Dashpo p Purely Viscous Response Response Hookean Solid Newtonian Liquid o ny In the case of the classical extremes,all that matters is the values of stress,strain,strain rate.The response is independent of the loading
Response for Classical Extremes Purely Elastic Response Hookean Solid s = G In the case of the classical extremes, all that matters is the values of stress, strain, strain rate. The response is independent of the loading. Spring Dashpo t Purely Viscous Response Newtonian Liquid s =
y=08G r2-e8 where where is called G the relaxation time Maxwell Kelvin-Voigt is called the complaince
s 1 G + t h æ è ç ö ø ÷ where h G is called the relaxation time s G 1- e - t æ t è ç ö ø ÷ where t = h G J = g s is called the complaince
Mechanical analogs of viscoelastic liquids o <Gy Maxwell Kelvin-Voigt Burgers The Maxwell,Kelvin-Voigt and Burgers models
s s G Mechanical analogs of viscoelastic liquids
Dynamic Mechanical Testing -An oscillatory (sinusoidal) Deformation deformation (stress or strain) is applied to a sample. -The material response Response (strain or stress)is measured. -The phase angleδ，or phase shift,between the deformation -Phase angleδ and response is measured
Dynamic Mechanical Testing Deformation Response Phase angle –An oscillatory (sinusoidal) deformation (stress or strain) is applied to a sample. –The material response (strain or stress) is measured. –The phase angle , or phase shift, between the deformation and response is measured
Given y-y ovwt F0r∑o入1δG ΦopM0U1δG o=Gy=Gy。ovwt o=㎡=ndM =nc.oNo0 o=70Y。X00t o=GVy。X0a0t
G t t t dt d dt d G G t For t Given o o o s s s s s s s s s s s