## Introduction to mechanics of deformable solids |

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Page 37

In the

elastic element and the stress in the viscous element (recall that forces in the

elements of the model represent stresses in the material), a = a' + a' while the

strains ...

In the

**Kelvin**or Voigt model, the stress at all times is the sum of the stress in theelastic element and the stress in the viscous element (recall that forces in the

elements of the model represent stresses in the material), a = a' + a' while the

strains ...

Page 39

t = tI c - a, 1 a Maxwell model

At time t = 0, (a — <ti and) t = 0. Therefore B = —<ti/Ek, and the

curve for abrupt loading is given by This expression checks the intuitive feeling

that ...

t = tI c - a, 1 a Maxwell model

**Kelvin**model Fig. 3.12 Relaxation at constant strain.At time t = 0, (a — <ti and) t = 0. Therefore B = —<ti/Ek, and the

**Kelvin**creepcurve for abrupt loading is given by This expression checks the intuitive feeling

that ...

Page 42

strain is the sum of the strain of the Maxwell component plus the strain of the

OM = Oft These same conditions on strain and on stress apply at all times and for

all ...

strain is the sum of the strain of the Maxwell component plus the strain of the

**Kelvin**, t = tAf + tK while the stress imposed upon each is the applied stress O —OM = Oft These same conditions on strain and on stress apply at all times and for

all ...

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applied assemblage axial force beam behavior centroid circumferential column compatibility components of stress conditions of deformation constant creep cross section cylinder deflection diameter direction displacement elastic-perfectly plastic elongation equations of equilibrium factor of safety free-body sketch fully plastic homogeneous idealization increase inelastic initial interior pressure isotropic Kelvin Kelvin material limit linear Maxwell linear-elastic response linear-viscoelastic linear-viscous load maximum Maxwell material modulus Mohr's circle neutral axis nonlinear normal stress outer perfectly plastic perpendicular plane plastic deformation plastic-limit Poisson's ratio principal stresses Prob problem pure bending radial radius ratio rectangular residual stress rotation shaft shear strain shear stress shell shown in Fig simple shear solution statically statically determinate steel stress and strain stress-strain curve stress-strain relations Suppose surface symmetry temperature tensile stress thick-walled sphere thickness time-dependent tion torque torsion uniform unloading versus viscous yield curve yield stress zero