Convergence in non‐associated plasticity and fracture propagation for standard, rate‐dependent, and Cosserat continua

The use of pressure‐dependent plasticity models with a non‐associated flow rule causes a loss of the well‐posedness for sufficiently low hardening rates. Apart from a mesh dependence, this can result in poor convergence, or even divergence of the iterative procedure employed to find an equilibrium configuration. This can be aggravated when other nonlinear, dissipative mechanisms are introduced, for instance the propagation of cracks. This is demonstrated rigorously, as well as the regularizing effect of adding viscosity or employing a Cosserat continuum. In both cases the regularization is independent of the value of the internal length scale for a fairly wide range of parameters. The spatial discretization has been done using T‐splines, and the fracture is modeled using interface elements and propagated using mesh line insertions. The time integration has been done by an implicit Newmark scheme. The use of proper regularization techniques makes an implicit scheme feasible, resulting in a reduction in the number of time steps by an order of magnitude

Non-associated Cosserat plasticity

Frictional plasticity models with a non-associated flow rule, ubiquitous for describing failure in geomaterials, can lead to a local loss of ellipticity for low hardening rates, i.e. before entering a strain-softening regime. This leads to an excessive dependence on the spatial discretisation and to an inability of Newton–Raphson methods to converge. Higher-order continuum models can remedy this. The Cosserat continuum is particularly suitable for granular media because the rotational degrees of freedom of this model can represent the rotation of (assemblies of) grains or blocks which form the microstructure of such materials. We illustrate this analytically by the example of an infinitely long shear layer and through a three-dimensional bifurcation analysis. Numerical simulations show the consequences, i.e. the anomalies of standard continuum models and the correct behaviour of non-associated plasticity models embedded in a Cosserat continuum. The motivation for using a Cosserat continuum for granular and blocky materials is further strengthened through shear band simulations of biaxial tests, where the inclination angle shows the same dependence on the internal length scale as that on the grain size in tests. This result is the first proper explanation for this dependence

Crystal structure of dichlorido(4,11-dimethyl-1,4,8,11-tetraazabicyclo[6.6.2]hexadecane)iron(III) hexafluoridophosphate

The title compound, [FeCl₂(C₁₄H₃₀N₄)]PF₆, contains Fe³⁺ coordinated by the four nitro­gen atoms of an ethyl­ene cross-bridged cyclam macrocycle and two cis chloride ligands in a distorted octa­hedral environment. In contrast to other similar compounds this is a monomer. Inter­molecular C-H...Cl inter­actions exist in the structure between the complex ions. Comparison with the mononuclear Fe²⁺ complex of the same ligand shows that the smaller Fe³⁺ ion is more fully engulfed by the cavity of the bicyclic ligand. Comparison with the μ-oxido dinuclear complex of an unsubstituted ligand of the same size demonstrates that the methyl groups of 4,11-dimethyl-1,4,8,11-tetra­aza­bicyclo­[6.6.2]hexa­decane prevent dimerization upon oxidation

Population, Land Use and Deforestation in the Pan Amazon Basin: a Comparison of Brazil, Bolivia, Colombia, Ecuador, Perú and Venezuela

This paper discusses the linkages between population change, land use, and deforestation in the Amazon regions of Brazil, Bolivia, Colombia, Ecuador, Perú, and Venezuela. We begin with a brief discussion of theories of population–environment linkages, and then focus on the case of deforestation in the PanAmazon. The core of the paper reviews available data on deforestation, population growth, migration and land use in order to see how well land cover change reflects demographic and agricultural change. The data indicate that population dynamics and net migration exhibit to deforestation in some states of the basin but not others. We then discuss other explanatory factors for deforestation, and find a close correspondence between land use and deforestation, which suggests that land use is loosely tied to demographic dynamics and mediates the influence of population on deforestation. We also consider national political economic contexts of Amazon change in the six countries, and find contrasting contexts, which also helps to explain the limited demographic-deforestation correspondence. The paper closes by noting general conclusions based on the data, topics in need of further research and recent policy proposals.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42720/1/10668_2003_Article_6977.pd

Incorporation of Pb, Ti, and Zr into MOCVD grown PbZrxTi1-xO3 thin films

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MOCVD growth and characterization of PbTiO3 thin films on Pt/Ti/SiO2/Si substrates

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