Finite Element Modelling of Adaptive Composite
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ABSTRACT The deformation of adaptive composite with active polydomain components has been calculated by finite element modelling (FEM). The average deformation, the distribution of stresses and the elastic energy of the composite as a function of different extent of twinning of the composite active component are calculated. Comparing the results of the FEM with the results of the analytical theory demonstrates the effect of the microstresses on the mechanics of the adaptive composite. INTRODUCTION The concept of adaptative composite with polydomain active component has been formulated and the theory of this composite has been developed in papers [1-31. The theory predicts some unusual physical and mechanical properties of the composite, particularly, considerable decrease of the effective elastic modulus of the composite, non linear stress strain relations, critical behaviour at changing relative thickness of an active layer. Due to importancy of the results obtained theoritically for applications of the composite it is very desirable to verify the theoritical conclusions by numerical modelling. The modelling can avoid some assumption of the theoritical analysis. The 2D finite element model developed in [4, 5] is an ideal tool for numerical analysis of the layer adaptive composite considered theoritically. This paper contains the results of the modelling of adaptive composite and the comparison with the results of the analytical theory. LAYER ADAPTIVE COMPOSITE: ANALYTICAL RESULTS The analytical theory of adaptive composite [1] is briefly reviewed. The simplest structure of a layer of adaptive composite is presented in Fig.la. An "elementary unit" of multilayer composite is shown. It consists of an active layer between two passive ones. Under mechanical stress, the active layer changes its structure by twinning. The change of the structure results in a self strain co. An average self strain of the active layer is then proportional to the change of twin fraction (a). We assume that the active layer with equal fractions of both twin component (x = 1/2) fits to the passive layers, so there is no internal stress at a = 1/2 (Fig. lb). Under deformation, the fraction of the black domains grows, leading to misfit between layers and resulting in internal stresses. According to the theory, the mechanical behaviour of the composite under external stress is determined by its internal stress state. When the black domains become thicker, the elongation of the active layer corresponds to the self strain (Fig. lc) so(x) = oO(a-1/2) (1) An average strain of the composite is:
e= 0 eo (a)
(2)
where 03is the relative thickness of the active layer 13= h/H.
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Mat. Res. Soc. Symp. Proc. Vol. 459 0 1997 Materials Research Society
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H a b c d Figure 1 : Schematic changes of the structure and corresponding deformation in the layers. The density of the elastic energy of internal stress is: e = 3(1-P)i E (tEa)2= • Et2
(3)
where E is the Young's modulus. 2D model with an uniaxial misfit is considered for simp
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