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Unformatted text preview: EN0175 11 / 02 / 06 Remarks on plastic material behavior 1) Yield surfaces (a surface in the stress space representing the condition/criterion whether the solid responds elastically or plastically to the applied load) The von Mises and Tresca yield conditions are represented by the following yield surfaces in the stress space (view long the ( 1 , 1 , 1 3 1 ) direction). condition Mises von condition Tresca I σ II σ III σ 2) The strain can be decomposed into elastic and plastic parts. In incremental form, P E ε ε ε d d d + = The elastic part is related to stress via the usual linear elastic equations. The plastic part of strain in incremental form can be written as ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ≥ = = otherwise , d , if , d 2 3 d P ' e Y e e ij P ij σ σ σ σ ε σ ε 2 J- flow theory: ' ' 2 2 1 ij ij J σ σ = , ' ' 2 ij ij J σ σ = ∂ ∂ Based on the above relations, the plastic strain can be rewritten in term of as 2 J 1 EN0175 11 / 02 / 06 ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ∂ ∂ = otherwise , loading , d 2 3 d P ' 2 e ij P ij J σ ε σ ε 3) Normality rule Yield stress: ( ) Y ij Y ij ij e f σ σ σ σ σ σ = ⇒ = = ' ' ' 2 3 where ( ) ' ij f σ represents a general yield surface. Differentiate the equation 2 ' ' 2 3 e ij ij σ σ σ = gives ( ) e ij ij e e e ij ij e ij ij σ σ σ σ σ σ σ σ σ σ σ ' ' ' ' 2 ' ' 2 3 d d...
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This note was uploaded on 01/10/2010 for the course EN 0175 taught by Professor Huajiangao during the Spring '06 term at Brown.
- Spring '06