Crack and Contact Problems for Viscoelastic Bodies (CISM by G.A.C. Graham, J.R. Walton

By G.A.C. Graham, J.R. Walton

The most emphasis of those Lecture Notes is on developing suggestions to express viscoelastic boundary price difficulties; although homes of the equations of viscoelasticity that offer the theoretical underpinnings for developing such suggestions also are coated. specific consciousness is paid to the answer of crack and make contact with difficulties. This paintings is of curiosity within the context of polymer fracture, modelling of fabric behaviour, rebound trying out of polymers and the phenomenon of hysteretic friction.

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Extra resources for Crack and Contact Problems for Viscoelastic Bodies (CISM International Centre for Mechanical Sciences)

Example text

6) and the Cauchy-Riemann equations gives along H, the relation B as where s measured -f (s) an anticlockwise and n the Furthermore since the crack is stress free so is constant on the crack. 14) 2 inward normal to the hole. 13) takes known values on the periphery of the hole. These values being assumed known for all times up to the present. We assume further that the displacement 1/J(x,y) tends to zero as Iz I -7 oo. 17) where C is real and is to be determined by the solution method. See Atkinson and Aparicio (1994) for a fuller discussion of this issue.

S )+IJ. 22) s z[IJ. (s )+fJ. (s ))(cos(zrr)-b) I I I 2 I where ll (s ) - 11. 23) ll (s ) + ll (s ) I I 2 I The real time behaviour of the displacement and stress fields will follow on inverting the above transforms, and each is characterised by solutions to the eigenequation cos(zrr) Explicit solutions are available establishes the roots as . 2 =b to (3. 24) 1 z = ± .!.. 24) and one particular n = 0,±1,±2, ... 25) where the choice of branch of (b -1) 2 is made so that the root to be taken has positive imaginary part and where it is understood that the principal branch of the logarithm has been taken.

23) ll (s ) + ll (s ) I I 2 I The real time behaviour of the displacement and stress fields will follow on inverting the above transforms, and each is characterised by solutions to the eigenequation cos(zrr) Explicit solutions are available establishes the roots as . 2 =b to (3. 24) 1 z = ± .!.. 24) and one particular n = 0,±1,±2, ... 25) where the choice of branch of (b -1) 2 is made so that the root to be taken has positive imaginary part and where it is understood that the principal branch of the logarithm has been taken.

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