Logarithmic Spin, Logarithmic Rate and Material Frame-Indifferent Generalized Plasticity

Soldatos, Dimitris; Triantafyllou, Savvas P.

doi:10.1142/s1758825116500605

Cited by 2 publications

(4 citation statements)

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“…Moreover, Eq. constitutes the underlying equation of a general model of rate‐independent elastic‐plastic behavior called generalized plasticity (see Lubliner ; see also the later works given in ).…”

Section: Elastic and Plastic Processes; Elastic Range And Domainmentioning

confidence: 99%

“…The evolution of plastic flow is considered to be normal to the loading surfaces as per

\begin{matrix} true \\ left L_{v} b_{e} = λ (τ, g, κ, a) \frac{\partial f}{\partial τ} (g^{- 1} \otimes g^{- 1}) (〈〉, r), normali . e ., \\ left {false(L_{v} b_{e} false)}^{i j} = λ (τ^{a b}, g_{a b}, κ, a^{a b}) \frac{\partial f}{\partial τ^{k l}} g^{k i} g^{l j} (〈〉, r), \end{matrix}

where the function λ is assumed to be an isotropic function in all its arguments, so that the principle of material frame‐indifference ‐ see, e.g., [, p. 272], ‐ is satisfied.…”

Section: A Model Problemmentioning

confidence: 99%

“…Remark The idea discussed in Remark is the one appearing within a somewhat different kinematic context in Xiao et al. ; see also example 3.4 in . More specifically these authors determine the function y upon making a shift of emphasis from the quasi‐yield (hyper)surface to a particular loading surface ‐ termed therein as the “bounding surface” ‐ which is defined as

f (τ, κ, a) = g (τ, a) - j (κ) = 0,

where

g false(τ, bolda false) = ‖τ^{'} - a‖, j false(κ false) = \sqrt{\frac{2}{3}} false(K κ + c_{0} false),

and c 0 is identified as a model parameter.…”

Section: A Model Problemmentioning

confidence: 99%

“…The simple shear problem constitutes a standard test within the context of large deformation plasticity ‐ see, e.g. ‐ and is defined (recall Eq. ) ‐ as:

x^{1} = X^{1} + γ X^{2}, x^{2} = X^{2}, x^{3} = X^{3},

where

γ = γ (t)

is the applied shear.…”

Section: One‐component Loadingsmentioning

confidence: 99%

See 3 more Smart Citations

On the quasi‐yield surface concept in plasticity theory

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Section: Elastic and Plastic Processes; Elastic Range And Domainmentioning

confidence: 99%

“…The evolution of plastic flow is considered to be normal to the loading surfaces as per

\begin{matrix} true \\ left L_{v} b_{e} = λ (τ, g, κ, a) \frac{\partial f}{\partial τ} (g^{- 1} \otimes g^{- 1}) (〈〉, r), normali . e ., \\ left {false(L_{v} b_{e} false)}^{i j} = λ (τ^{a b}, g_{a b}, κ, a^{a b}) \frac{\partial f}{\partial τ^{k l}} g^{k i} g^{l j} (〈〉, r), \end{matrix}

where the function λ is assumed to be an isotropic function in all its arguments, so that the principle of material frame‐indifference ‐ see, e.g., [, p. 272], ‐ is satisfied.…”

Section: A Model Problemmentioning

confidence: 99%

f (τ, κ, a) = g (τ, a) - j (κ) = 0,

where

g false(τ, bolda false) = ‖τ^{'} - a‖, j false(κ false) = \sqrt{\frac{2}{3}} false(K κ + c_{0} false),

and c 0 is identified as a model parameter.…”

Section: A Model Problemmentioning

confidence: 99%

“…The simple shear problem constitutes a standard test within the context of large deformation plasticity ‐ see, e.g. ‐ and is defined (recall Eq. ) ‐ as: