## 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 = ae + a" while the ...

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 = ae + a" while the ...

Page 39

<1 EkU >

and the

expression checks the intuitive feeling that in a

spring the ...

<1 EkU >

**Kelvin**model At time t = 0, (a = <n and) e = 0. Therefore B = —a-i/Ek,and the

**Kelvin**creep curve for abrupt loading is given by e = IL (i _ rft/wi) Thisexpression checks the intuitive feeling that in a

**Kelvin**material the stiffer thespring the ...

Page 42

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

same conditions on strain and on stress apply at all |,imes and for all 1loadings.

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

**Kelvin**, hile the stress imposed upon each is the applied stress = <tm = ak Thesesame conditions on strain and on stress apply at all |,imes and for all 1loadings.

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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 nonlinear-viscous 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 rigid end plates rotation shaft shear strain shear stress shell 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 torque torsion uniform unloading versus viscous yield curve yield stress zero