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By Jacek J. Skrzypek, Artur W. Ganczarski
The publication is targeted on constitutive description of mechanical behaviour of engineering fabrics: either traditional (polycrystalline homogeneous isotropic or anisotropic metal fabrics) and non-conventional (heterogeneous multicomponent anisotropic composite materials). potent fabric homes on the macro-level depend upon either the fabric microstructure (originally isotropic or anisotropic) in addition to dissipative phenomena happened on fabrication and consecutive loading part (hardening) leading to irreversible microstructure adjustments (acquired anisotropy). the cloth symmetry is a historical past and anisotropy is a center round which the e-book is shaped. during this manner a revision of classical principles of more desirable constitutive description of fabrics is required.
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Mursa [41] (Titanium alloy) but others contradict it cf. Hu and Marin [22] (Aluminum alloy), ´ Kowalewski and Sliwowski [26] (influence of first common invariant). 6 Strain Energy and Complementary Energy—The State Potentials for Isotropic or Anisotropic Materials Material is called elastic if its response (deformation) is independent of loading history (Fig. 121) or vice versa After the fully closed loading–unloading cycle (A-B-A), the initial material state A is recovered, independent of the loading–unloading path, Fig.
Chaboche [8], Krajcinovic [29] or Lubarda and Krajcinovic [35]. , by Gambarotta and Lagomarsino [15], Seweryn and Mróz [48] should also be mentioned. W. Ganczarski et al. were listed in following subject monographs by Krajcinovic [29, 30], Skrzypek and Ganczarski [51], Betten [3] or Murakami [40]. In the frame of continuum damage mechanics (CDM), three configurations are considered: initial configuration A that describes material in undamaged state D(A) = 0, physical configuration B referring to the damaged state D(B) = 0, and the equivalent, fictitious pseudo-undamaged configuration C in which real heterogeneous material is substituted by a homogeneous material, free of damage D(C) = 0, as schematically is shown in Fig.
49) or equivalently where [E] or [E−1 ] denote representation matrices of elastic stiffness or compliance tensors, whereas {ε} and {σ} denote the columnar vectors of strain and stress, respectively. W. Ganczarski et al. 51) where engineering notation for shear stress τ j = σ j ( j = 4, 5, 6) is used. It should be mentioned that symmetric stiffness [E i j ] = [E ji ] and symmetric com−1 pliance [E i−1 j ] = [E ji ] matrices, both having dimension 6 × 6, are representation matrices of fourth-rank elasticity tensors E i jkl or compliance E i−1 jkl .