By Various, Karl kerschl
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This needs to be taken into account when GLIIHUHQWLDWLQJ WKH VHFRQG WHUP LQ 7KH UHVXOWLQJ UDWH equation thus reads ˙ : ε − (λ + 2μ)ε˙cnn = E c ε˙cnn λ1 : ε˙ + 2μN : ε˙ + 2μN ˙ can be exwhere E c = df c /dεcnn is the softening modulus. The rates n˙ and N pressed in terms of the current strain and the strain rate, but the derivation is some˙ = N : ε˙ where N is a certain what tedious. , n = p1 is the normalized eigenvector of ε DVVRFLDWHG ZLWK WKH ODUJHVW HLJHQYDOXH ,I WKH PD[LPXP SULQcipal strain ε1 is strictly greater than the other two principal strains, ε2 and ε3 , the expression for the rate of p1 can be derived by manipulating the rate form of the relations ε · pI = εI pI and pI · pJ = δIJ , I, J = 1, 2, 3.
The images in the second row correspond to a state shortly before the peak load and those in the third row to a state shortly after the peaN ORDG 'DPDJH LV irreversible and it cannot decrease, but in the post-peak range it remains constant in the predamaged region around the bottom face of the beam, except for a narrow band around the axis of symmetry that propagates to the top. The damage band keeps a certain minimum thickness while the band of increasing strains becomes 46 M. Jirasek progressively thinner.
For a given strain level ε, the value of D = g(ε) can be obtained by solving ,W LV WDFLWO\ DVVXPHG WKDW ORFDOL]DWLRQ VWDUWV DW WKH RQVHW RI QRQOLQHDULW\ ,Q D JHQHUDO FDVH LW LV QHF essary to use the decomposition into strain in the unloading material and additional strain in the softening material, rather than the decomposition into elastic and inelastic strain. Damage and Smeared Crack Models 39 QXPHULFDOO\ XVLQJ HJ WKH 1HZWRQ PHWKRG )RU UHDVRQDEle functions f w the iterative process usually converges very fast.