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 ...
Parboiled rice effluent: A wastewater niche for microalgae and cyanobacteria with growth coupled to comprehensive remediation and phosphorus biofertilization
Abstract The potential of microalgae and cyanobacteria for bioremediation of wastewater by nutrient uptake combined with simultaneous biomass production is a well recognized perception of today's world. The present study illustrates the treatment of a highly polluted wastewater generated during parboiling of paddy in rice mill industries, widely operational in developing countries where rice is the staple food crop, with the help of microalgal and cyanobacterial isolates capable of growing at high rates in parboiled rice mill effluent (RME). This endeavor leads to comprehensive bioremediation of the said effluent and subsequent use of the harvested biomass as slow release phosphorus biofertilizers and the treated effluent for crop irrigation. The RME-acclimatized algal consortium demonstrated highest growth in terms of fresh weight and greatest remediation efficiency at the end of 36 days' treatment of RME, with 93.9% phosphorus and 100% ammonia-nitrogen removal, 98.7%, 91.6% and 93.5% reduction in biological oxygen demand, chemical oxygen demand and total dissolved solid, respectively, and an increment of 186 ± 0.3 mg L − 1 dissolved oxygen, bringing down the pollutants level well below the discharge limits suggested by Central Pollution Control Board, India. Additionally, microalgae in the consortium aggregated in clumps spontaneously in presence of the filaments of Phormidium sp. facilitating easy harvest. The RME-acclimatized algal consortium demonstrated highest accumulation of polyphosphate (poly-P) (0.76 ± 0.01% of dry weight) as well as highest release of phosphorus in non-sterile soil emphasizing the essential role of soil phosphorus solubilizing organisms to leach soluble phosphorus from the insoluble poly-P present in the biomass. The rice seedlings watered with treated RME also showed improved growth effect on shoot height and leaf width. The study results establish the suitability of RME as an excellent growth media for microalgae and cyanobacteria.