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where [sigma] is the macroscopic stress of the cemented sand microelement, [[sigma].sup.*] is the microscopic stress of the undamaged part, and D is the damage factor.
The forces and movements at all contact planes are used to obtain the macroscopic stress and strain tensors (Figure 7).
It was assumed that incipient microcracks appear in the planes with orientation close to the basic area corresponding to the principal macroscopic stress [[sigma].sub.1] while local criterion of fracture is [[xi].sub.11] [greater than or equal to] [[xi].sub.c].
Here, we use [[SIGMA].sub.m] = tr([SIGMA])/3 and [[SIGMA].sub.v] = [square root of ([[SIGMA].sub.d] : [[SIGMA].sub.d])] to denote the macroscopic stress invariant.
(32), substantial cavitation in polymer leads to a weakening effect characterized by a lower macroscopic stress supported by the tensile specimen.
The macroscopic stress and the lattice constant can be calculated from lattice plane distances d (17) by using equations (2) and (3).
The difference in the principle of macroscopic stress and deformation is entirely due to the additional stress increment, which is a typical stress-induced anisotropy.
The macroscopic stress versus displacement curve of the concrete specimen without void ([A.sub.F] = 40%) under uniaxial tension is shown in Figure 7, and the elements with nonzero equivalent tensile plastic strain at different loading levels are illustrated in Figure 8, in which the elements with equivalent tensile plastic strain bigger than 100 microstrains are highlighted in red color.
43 into 42, the relationship between the average reduced stress and the macroscopic stress can be expressed as
In technical engineering praxis under the term residual stress only the first type (macroscopic stress).
The description of the viscoplastic behavior is based on the splitting of the macroscopic stress (28) into thermal and athermal back stresses (associated with incompatibilities of deformation caused by the behavior of crystalline and amorphous phases), and thermal and athermal effective stresses (associated with shortrange interactions).
The macroscopic stress was spilt into an effective stress and a back stress so that the interactions between crystalline lamellae and amorphous phases could be taken into account.