Introduction to Mechanics of Deformable Solids |
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Page 37
... Kelvin model = σ " = Εκε de Ск dt independently of the prior history of the stress and the strain . The differential equation governing the behavior of the Kelvin model in tension ( or equally well in compression ) is σ = σe + ov = Еке ...
... Kelvin model = σ " = Εκε de Ск dt independently of the prior history of the stress and the strain . The differential equation governing the behavior of the Kelvin model in tension ( or equally well in compression ) is σ = σe + ov = Еке ...
Page 39
... Kelvin model At time t = = σ1 and ) € = 0 . Therefore B = -σ1 / Ex , and the Kelvin creep curve for abrupt loading is given by € = 01 ( 1 EK ― e- ( Ex / Cx ) ) This expression checks the intuitive feeling that in a Kelvin material the ...
... Kelvin model At time t = = σ1 and ) € = 0 . Therefore B = -σ1 / Ex , and the Kelvin creep curve for abrupt loading is given by € = 01 ( 1 EK ― e- ( Ex / Cx ) ) This expression checks the intuitive feeling that in a Kelvin material the ...
Page 42
... Kelvin , € = EM + EK while the stress imposed upon each is the applied stress σ = σM = σK These same conditions on ... Kelvin component or the Maxwell dashpot imme- diately . A stress of EM1 is imposed . As time goes on , the Maxwell and ...
... Kelvin , € = EM + EK while the stress imposed upon each is the applied stress σ = σM = σK These same conditions on ... Kelvin component or the Maxwell dashpot imme- diately . A stress of EM1 is imposed . As time goes on , the Maxwell and ...
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applied assemblage axes axial force beam behavior cantilever centroid circumferential column compatibility components of stress constant creep cylinder deflection diameter direction displacement elastic-perfectly plastic elongation equations of equilibrium factor of safety free-body sketch homogeneous idealization increase inelastic initial interior pressure isotropic J₂ Kelvin Kelvin material limit linear Maxwell linear-elastic linear-viscoelastic linear-viscous load maximum Maxwell material modulus Mohr's circle neutral axis nonlinear normal stress outer P₁ P₂ perfectly plastic perpendicular plane plastic-limit principal stresses Prob problem pure bending radial radius ratio rectangular residual stress rigid end plates rotation shaft shear strain shear stress shell shown in Fig simple shear solution statically determinate steel stress and strain stress-strain curve stress-strain relations Suppose surface symmetry T₁ T₂ temperature tensile tensile stress thick-walled time-dependent torque torsion uniform unloading versus viscous yield curve yield stress Young's modulus zero ΕΙ σα σο στ