Issue 50

K. Meftah et alii, Frattura ed Integrità Strutturale, 50 (2019) 276-285; DOI: 10.3221/IGF-ESIS.50.23 278     T f x y xy      ;     T s xz yz     (2) The linear relationships between the displacements and strains can be obtained by using the definitions of strains from the theory of elasticity: ; y x x y u v z z x x y y                   (3) 2 y x xy xy u v z y x y x                         (4) 2 xz xz x w x         ; 2 yz yz y w y         (5) Assuming normal stress zz  to be negligibly small compared to other normal stresses, the stress-strain relationship in the matrix takes the form:   D    (6) where    = { xx  yy  xy  yz  zx  } T and the matrix   D for isotropic materials is defined:   0 0 f s D D D        (7) with   1 0 . . 0 1 s D G k h        ; 3 2 1 0 . 1 0 12(1 ) 1 0 0 2 f E h D                         (8) where h is the thickness of the plate, k is a shear correction coefficient, E is the Young's modulus and  is the Poisson's ratio. The generalized forces per unit of length of the plate side can be obtained using the stress field; these forces are the bending moments ( M ) and the shear forces ( V ):   2 2 h xx yy h xy M z dz                  ;   2 2 h yz xz h V dz            (9) C ONSTITUTIVE EQUATION FOR RATE INDEPENDENT ELASTOPLASTICITY fter initial yielding the material behavior will be partly elastic and partly plastic. During any increment of stress, the changes of strain are assumed to be divisible into elastic and plastic components, so that: A