We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions. Two categories of degradation functions are examined, and a process to derive a given degradation function based on a local stress-strain response in the cohesive zone is presented. The resulting model is characterized by a linear elastic regime prior to the onset of damage, and controlled strain-softening thereafter. The governing equations are derived according to macro-and microforce balance theories, naturally accounting for the irreversible nature of the fracture process by introducing suitable constraints for the kinetics of the underlying microstructural changes. The model is complemented by an efficient staggered solution scheme based on an augmented Lagrangian method. Numerical examples demonstrate that the proposed model is a robust and effective method for simulating cohesive crack propagation, with particular emphasis on dynamic fracture.

Excellent electrophoretic separations of a variety of biological molecules can be accomplished by using uncharged, triblock copolymers as the ''gel'' media. These copolymers form uncrosslinked, lyotropic liquid crystalline phases of large micelles between which molecules must travel. Unlike crosslinked hydrogels in common use, these alternative media have highly ordered internal structures. Pluronic F127, representative of the copolymer class, contains poly(ethylene oxide) (EO) and poly(propylene oxide) (PO) units with an approximate molecular formula (EO) 106 (PO) 70 (EO) 106 . Concentrated (18-30%) solutions of Pluronic F127 are freely f lowing liquids at low temperature (0-5°C) but form gel-like, cubic liquid crystals of large, spherical micelles when warmed. The utility of these media is illustrated by separations of linear, double-stranded DNA up to 3,000 bp long by conventional electrophoresis, and of single-stranded DNAs from 4 to 60 nt long by capillary electrophoresis. Extraordinary separations of supercoiled DNAs were also obtained by capillary electrophoresis. The versatility, availability, and ease of use of Pluronic polymers offer major advantages over conventional media for preparative and high performance analytical separations of nucleic acids and other biomolecules. Mechanisms of molecular transport and separation operating in polymer liquid crystals must differ in fundamental ways from those in crosslinked gels. Lyotropic polymer liquid crystals are unique systems for elucidating mechanisms of macromolecule migration in ordered, dense media, and provide opportunities in separations science.Electrophoresis is an essential separation method of biochemistry and molecular biology that distinguishes between proteins or nucleic acids differing only slightly in size, charge, conformation, or degree of association. Gene mapping, DNA sequencing, and transcription factor identification stand out among recent advances uniquely attributable to this method.Conventional electrophoresis is usually conducted on crosslinked hydrogels such as polyacrylamide ''chemical'' gels, formed by solution polymerization of simple monomers; or agarose ''physical'' gels formed by hydrogen bonding between pre-existing polymer chains. These completely interconnected polymer networks provide mechanical support and quench convection, and separate molecules by sieving according to size and shape. Structural details such as pore shape, size distribution, and connectivity strongly influence separations. The structures of both gel classes have been studied, and there is a basic understanding of how globular proteins (1-5) and semirigid polymers such as DNA (6-9) migrate through gel networks, but understanding of the influence of gel structure on separations is still incomplete.Capillary electrophoresis (CE) with high-voltage gradients offers much higher resolution than conventional electrophoresis or HPLC (10-13) and has been proposed to speed DNA sequencing for the Human Genome Project (14, 15). CE is often performed in con...

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Porous tantalum has been reported to be a promising material for use in bone tissue engineering. In the present study, the biocompatibility and osteogenic properties of porous tantalum were studied in vitro and in vivo. The morphology of porous tantalum was observed using scanning electron microscopy (SEM). Osteoblasts were cultured with porous tantalum, and cell morphology, adhesion and proliferation were investigated using optical microscopy and SEM. In addition, porous tantalum rods were implanted in rabbits, and osteogenesis was observed using laser scanning confocal microscopy and hard tissue slice examination. The osteoblasts were observed to proliferate over time and adhere to the tantalum surface and pore walls, exhibiting a variety of shapes and intercellular connections. The porous tantalum rod connected tightly with the host bone. At weeks 2 and 4 following implantation, new bone and small blood vessels were observed at the tantalum-host bone interface and pores. At week 10 after the porous tantalum implantation, new bone tissue was observed at the tantalum-host bone interface and pores. By week 12, the tantalum-host bone interface and pores were covered with new bone tissue and the bone trabeculae had matured and connected directly with the materials. Therefore, the results of the present study indicate that porous tantalum is non-toxic, biocompatible and a promising material for use in bone tissue engineering applications.