Get Analysis and Computation of Microstructure in Finite PDF

By Sergio Conti, Klaus Hackl

ISBN-10: 3319182412

ISBN-13: 9783319182414

ISBN-10: 3319182420

ISBN-13: 9783319182421

This ebook addresses the necessity for a primary figuring out of the actual foundation, the mathematical habit and the numerical remedy of types which come with microstructure. best scientists current their efforts concerning mathematical research, numerical research, computational mechanics, fabric modelling and scan. The mathematical analyses are in accordance with equipment from the calculus of adaptations, whereas within the numerical implementation international optimization algorithms play a relevant function. The modeling covers all size scales, from the atomic constitution as much as macroscopic samples. the improvement of the versions ware guided through experiments on unmarried and polycrystals and effects should be checked opposed to experimental data.

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63–88. : A model for the evolution of laminates in finite-strain elastoplasticity. : Discontinuous Galerkin and the Crouzeix-Raviart element: application to elasticity. M2AN Math. Model. Numer. Anal. : Variational phase field modeling of laminate deformation microstructure in finite gradient crystal plasticity. Proc. Appl. Math. Mech. : The evolution of laminates in finite crystal plasticity: a variational approach. : The relaxation of a double-well energy. Contin. Mech. Thermodyn. 3(3), 193–236 (1991) 30 [KP91] C.

Optimal design and relaxation of variational problems. III. Comm. Pure Appl. Math. : On a certain variational problem of phase equilibrium. In: Material instabilities in Continuum Mechanics (Edinburgh, 1985–1986), pp. 257–268. Oxford Univ. : On the computation of crystalline microstructure. : Variational approaches and methods for dissipative material models with multiple scales. , Conti, S. ) Analysis and Computation of Microstructure in Finite Plasticity. LNACM, vol. 78, pp. 125–156. : Convergence of adaptive finite element methods.

Again, if the domain subdivision is fine enough, the macroscopic deformation is approximately a compression in the horizontal direction and a stretching in the vertical one. A related discussion, focused on the phenomenon of geometrical softening in plasticity, is given in [OR99]. In order to understand qualitatively the difference between the two laminates, it is important to notice that the effect used here is purely nonlinear and would not be present in a geometrically linear theory. Indeed, the elongation is in both cases second-order in the slip γ , as the Taylor series 1 1 + γ 2 = 1 + γ 2 + O(γ 4 ) 2 shows.

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Analysis and Computation of Microstructure in Finite Plasticity by Sergio Conti, Klaus Hackl

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