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BouncWen

Bouc-Wen Model

The BoucWen model is a phenomenological model. Compared to the original formulation, the following modifications are applied.

  1. \(A=1\).
  2. \(\gamma+\beta=1\).

Theory

The evolution of internal displacement \(z(t)\) is governed by the differential equation,

\[ \Delta{}z=\dfrac{\Delta{}u}{u_y}\left(1-\left(\gamma+\text{sign}\left(z\cdot\Delta{}u\right)\beta\right) \Big|z\Big|^n\right). \]

Then,

\[ F=aF_y\dfrac{u}{u_y}+\left(1-a\right)F_yz. \]

For state determination, \(z\) is solved by using the Newton method.

Syntax

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material BoucWen (1) (2) (3) (4) (5) (6)
# (1) int, unique material tag
# (2) double, elastic modulus
# (3) double, yield stress
# (4) double, hardening ratio
# (5) double, beta, a positive parameter
# (6) double, n, a positive exponent

Caveat

Since it is a phenomenological model, the non-observable internal "displacement" \(z\) has no physical meaning. For small loops, it violates plasticity postulates.

It is recommended to use a value greater than unity for \(n\).

Example

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material BoucWen 1 2E5 400 .01 1E-1 2
materialTest1D 1 1E-3 10 20 30 40 50 60 30

example one

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material BoucWen 1 2E5 400 .01 2. .6
materialTest1D 1 1E-3 10 20 30 40 50 60 30

example two