Comment on Hyperbolicity of Wave Problem for Valanis’ Global Damage Theory
In a very interesting and stimulating recent paper, Valanis (199l) proposed a new type of nonlocal damage theory, called the global damage theory. Some conclusions of this paper, however, require further analysis, which is the purpose of this technical note. Offering as motivation some questionable and unfounded critical comments on the nonlocal damage theory originally proposed by Pijaudier-Cabot and Baiant (1987) and Baiant and Pijaudier-Cabot ( 1988), Valanis formulated a different theory and cltrimed it to be superior because, as he stated, it exhibits unconditional hyperbolicity of the wave problem. On closer scrutiny, though, Valanis' claim is found to be invalid, and for further development of nonlocal damage models it is important to understand why.
Nonlocal damage theory
In the usual local finite element analysis, strain softening causes spurious mesh sensitivity and incorrect convergence when the element is refined to vanishing size. In a previous continuum formulation, these incorrect features were overcome by the imbricate nonlocal continuum, which, however, introduced some unnecessary computational complications due to the fact that all response was treated as nonlocal. The key idea of the present nonlocal damage theory is to subject to nonlocal treatment only those variables that control strain softening, and to treat the elastic part of the strain as local. The continuum damage mechanics formulation, convenient for separating the nonlocal treatment of damage from the local treatment of elastic behavior, is adopted in the present work. The only required modification is to replace the usual local damage energy release rate with its spatial average over the representative volume of the material whose size is a characteristic of the material. Avoidance of spurious mesh ...
Unity Identity Text Self
Abstract Understanding the receptivity of literature, how one work admits many readers, begins with an analogy: unity is to text as identity is to self. Unity here means the way all a text’s features can be related through one central theme. Identity describes a person’s sameness within different behaviors as variations on one identity theme (Lichtenstein). To find unity or identity, however, the interpreter himself plays a behavioral variation on his identity theme. In interpreting, his identity re-creates itself as he shapes the text to match his characteristic defenses, fantasies, and coherences. Thus, what a poet says about fictional, political, or scientific texts expresses the same identity theme as the poems he writes. To understand reading, criticism, and any knowing or making in symbols, then, we need to let go the Cartesian craving for objectivity and accept the themes in ourselves with which we construe the world—including literary works.