Standard linear solid model ( $G^{*} = G_{L} + (G_{H} - G_{L}) iω τ / (1 + iω τ)$ )

. It includes immediate and delayed recoverable strain, but no unbounded viscous flow. Large strain, damage or anisotropy require additional constitutive structure.

Recovery after a finite-duration stress load ( $ε (t) = \frac{σ _{0}}{E _{1}} (1 - e^{- t_{h} / τ}) e^{- (t - t_{h}) / τ}, t > t_{h}$ )

 0  0

Apply constant stress

σ_{0}

t = 0

and remove it at

t = t_{h}

. For series spring and Voigt-branch creep, the series spring recovers its strain

σ_{0} / E_{0}

immediately on unloading. The Kelvin-Voigt model branch has retardation time

τ = η / E_{1}

and must keep continuous strain because an instantaneous dashpot displacement would require an impulse. Its post-unloading equation is

η \overset{ε}{˙} + E_{1} ε = 0

. Solving with the branch's strain at

t_{h}

gives the title formula. Thus all remaining strain eventually recovers: this standard linear solid model has no permanent set.

Peak frequencies in a standard linear solid ( $ω_{G^{''}} τ = 1, ω_{t a n δ} τ = G_{R} / G_{U}$ )

 0  0

For a standard linear solid model with

0 < G_{R} < G_{U}

, put

x = ω τ

. Its storage modulus is

G^{'} = G_{R} + (G_{U} - G_{R}) x^{2} / (1 + x^{2})

and its loss modulus is

G^{''} = (G_{U} - G_{R}) x / (1 + x^{2})

. The latter peaks at

x = 1

, whereas its loss tangent is

tan δ = \frac{( G _{U} - G _{R} ) x}{G _{R} + G _{U} x ^{2}} .

(1)

Differentiation puts the loss-tangent peak at

x = G_{R} / G_{U}

, with height

(G_{U} - G_{R}) / (2 G_{R} G_{U})

. A loss-modulus peak and a loss-tangent peak therefore need not occur at the same frequency. For weak relaxation,

G_{U} / G_{R}

is close to one and their frequencies are approximately equal.

 Synonyms (1)

codex/standard-linear-solid

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (1)

Standard linear solid model by

Wikipedia Bot  1

 View more

The Standard Linear Solid (SLS) model is a mathematical model used to describe the viscoelastic behavior of materials. It is particularly effective in capturing the time-dependent strain response of materials that exhibit both elastic (instantaneous) and viscous (time-dependent) behaviors when subjected to stress. ### Components of the SLS Model The SLS model combines two main elements: 1. **Spring Element (Elastic Component):** This represents the elastic behavior of the material.

 Read the full article

  See all articles in the same topic Create my own version

Standard linear solid model ( $G^{*} = G_{L} + (G_{H} - G_{L}) iω τ / (1 + iω τ)$ )

Series spring and Voigt-branch creep ( $J (t) = 1/ E_{0} + (1/ E_{1}) (1 - e^{- E_{1} t / η})$ )

Recovery after a finite-duration stress load ( $ε (t) = \frac{σ _{0}}{E _{1}} (1 - e^{- t_{h} / τ}) e^{- (t - t_{h}) / τ}, t > t_{h}$ )

Peak frequencies in a standard linear solid ( $ω_{G^{''}} τ = 1, ω_{t a n δ} τ = G_{R} / G_{U}$ )

 Ancestors (7)

 Incoming links (10)

 Synonyms (1)

 Discussion (0) New discussion

 Articles by others on the same topic (1)

 Discussion (0)  Subscribe (1) New discussion

 Discussion (0) New discussion