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With the vector a defining the direction of crack advance, we define the ne...

With the vector a defining the direction of crack advance, we define the new a for |xi − xt | ≤rS xSi = xi for |xi −xt | > rS () where xS i is the shifted position of.

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() 2C 2G Obviously, the dislocation crack extension force for a mixed mode ...

() 2C 2G Obviously, the dislocation crack extension force for a mixed mode I, vector bx situated at x, produces a vertical force — bx by G/2Tra(xt—xt) on.

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degrees of freedom, i.e. e 8va KA = −5: (11) where X is the vector XT * [u-...

degrees of freedom, i.e. e 8va KA = −5: (11) where X is the vector XT * [u-s, V., patch except at a crack tip where it is coupled to a special crack tip element.

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Background — For isotropic linear elastic response, the asymptotic crack ti...

Background — For isotropic linear elastic response, the asymptotic crack tip have a continuously turning tangent vector t(s) = e3, local crack plane normal db{xt) = n(xx) dxu the crack problem is described by the dislocation density, im(x,).

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T 51) (1 0 \((\-$-X!R-xT)-x 0\(\ -XR-l\ ~\-M-lT R-l)\ 0 iy ^0 1)• Thus it s...

T 51) (1 0 \((\-$-X!R-xT)-x 0\(\ -XR-l\ ~\-M-lT R-l)\ 0 iy ^0 1)• Thus it suffices to find ((3A')A) of dimension m by the vector of operators '(Si,, £m) and then to.

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state variable for a point on the crack front, which we can identify as: Γ ...

state variable for a point on the crack front, which we can identify as: Γ Γ A We can define the vector of nodal material resistance forces, as fcracfkmaterialh, = respectively, and defined as follows f t f exftspaceh TRI T spaceh TET XT hPdh.

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These solutions of crack-tip fields for linear strain-hardening materials a...

These solutions of crack-tip fields for linear strain-hardening materials are the stress tensor and the velocity vector, instead of two higher-order equations in the Similarly, let r and i? be polar coordinates corresponding to xt (/ = 1,2) and er.

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which is transformed to the strain vector in the crack directions with the ...

which is transformed to the strain vector in the crack directions with the strain 2cxscxt, 2cyscyt, 2czsczt, cxscyt + cyscxt, cysczt + czscyt, czscxt + cxsczt. 2cxtcxn.

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() i=1 In Eq. (), the displacement vector and coordinate vector in the phys...

() i=1 In Eq. (), the displacement vector and coordinate vector in the physical uT = [u,v] and xT = [x, y]; in three dimensions, uT = [u,v,w] and xT = [x, y,z]. If the nodes closest to the crack tip in the physical element are moved to the.

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