EN0175-16

# EN0175-16 - EN0175 10 26 06 Plastic material behavior Yield...

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Unformatted text preview: EN0175 10 / 26 / 06 Plastic material behavior Yield condition: Y σ σ = Plastic loading: Y σ σ = , d > σ P ε Y σ σ ε 1 E E ε 1 E Y σ We will now denote the initial yield stress as Y σ and the current yield stress as Y σ ; see above figure. Decompose strain into elastic & plastic parts P E ε ε ε + = In incremental form: E E σ ε d d = ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ > = = otherwise , d , if , d d σ σ σ σ ε Y P h P h ε σ d d = is the tangent modulus of P ε σ − curve (which is obtained from experiments or fitting an assumed mathematical curve to experimental data). 1 EN0175 10 / 26 / 06 Perfectly plastic: = h P ε Y σ Linear work hardening: . const = h P ε Y σ 1 h Power law hardening: N Y P Y Y E ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = 1 σ ε σ σ P ε Y σ How to generalize this idea to 3D? For elastic part, ij kk ij ij kk ij E ij E K E E E δ σ μ σ δ σ ν σ ν ε σ ε 9 2 1 ' + = − + = ⇒ = P ij E ij ij ε ε ε d d d + = kk ij ij E ij K σ δ σ μ ε d...
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EN0175-16 - EN0175 10 26 06 Plastic material behavior Yield...

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