By B. Daya Reddy
This paintings contains papers in response to the various talks awarded on the IUTAM Symposium of a similar identify, held in Cape city, January 14-18, 2008. This volume treats state-of-the-art concerns in modelling, the behaviour of assorted sessions of inelastic media, and linked algorithms for conducting computational simulations. A key function of the contributions are works directed at modelling behaviour on the meso and micro-scales, and at bridging the micro-macro scales.
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Extra info for IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media: Proceedings of the IUTAM Symposium Held at Cape Town, South Africa, January 14-18, 2008
Conti S, Theil F (2005) Arch Rat Mech Anal 178:125–148. 3. Mielke A (2004) Comp Meth Appl Meth Eng 193:5095–5127. 4. Lambrecht M, Miehe C, Dettmar J (2003) Int J Solids Struct 40:1369–1391. 5. Ortiz M, Repetto EA (1999) J Mech Phys Solids 47:397–462. 6. Mielke A, Ortiz M (2007) ESAIM Control Optim Calc Var, online since December 21. Relaxed Potentials and Evolution Equations for Inelastic Microstructures 7. 8. 9. 10. 11. 12. 13. 14. 39 Conti S, Ortiz M (2008) J Mech Phys Solids 56:1885–1904. Hackl K, Schmidt-Baldassari M, Zhang W (2003) Mat Sci Eng A 378:503–506.
Again, due to the loss of rank-one convexity, the homogeneous deformation state is not stable and decomposes into micro-deformations. Figure 4 shows the microstructure evolution, displaying the path of energy, volume fractions, and stress components upon straining. In both examples, the body behaves elastically first, until a second phase with finite, non-zero slip γ2 originates from the uniform ground state, until finally phase 1 becomes plastic, too. Once, the laminate has formed with a distinct orientation vector b, we do not observe laminate rotations due to the large amount of dissipation necessary for a rotation.
Then, we assume an energy density for an incompressible neo-Hookean material in the form (F e , p) = 12 µtrF Te F e + κp4 , det F = 1. (21) Multiplicative split of the deformation gradient into an elastic part F e and an irreversible, plastic part F p yields the decomposition F = F e F p . The single active slip-system is characterised by unit vectors s and m (|s| = |m| = 1, s · m = 0). Consider the following flow rule with slip-rate γ˙ , F˙ p F −1 p , p˙ = (γ˙ s ⊗ m, |γ˙ |) (22) with initial conditions γ (0) = 0 and p(0) = 0.
IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media: Proceedings of the IUTAM Symposium Held at Cape Town, South Africa, January 14-18, 2008 by B. Daya Reddy