Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations

A new semi-implicit stress integration algorithm for finite strain plasticity (compatible with hyperelas- ticity) is introduced. Its most distinctive feature is the use of different parameterizations of equilibrium and reference configurations. Rotation terms (nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the reference configuration. In contrast, relative Green–Lagrange strains (which are quadratic in terms of displacements) represent the equilibrium configuration implicitly. In addition, the adequacy of several objective stress rates in the semi-implicit context is studied. We para- metrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use coinciding configurations. A single constitutive framework provides quantities needed by common discretization schemes. This is computationally convenient and robust, as all elements only need to provide pre-established quantities irrespectively of the constitutive model. In this work, mixed strain/stress control is used, as well as our smoothing algorithm for the complemen- tarity condition. Exceptional time-step robustness is achieved in elasto-plastic problems: often fewer than one-tenth of the typical number of time increments can be used with a quantifiable effect in accuracy. The proposed algorithm is general: all hyperelastic models and all classical elasto-plastic models can be employed. Plane-stress, Shell and 3D examples are used to illustrate the new algorithm. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.

Least-squares finite strain hexahedral element/constitutive coupling based on parametrized configurations and the Löwdin frame

Two novelties are introduced: (i) a finite-strain semi-implicit integration algorithm compatible with current element technologies and (ii) the application to assumed-strain hexahedra. The Löwdin algo- rithm is adopted to obtain evolving frames applicable to finite strain anisotropy and a weighted least- squares algorithm is used to determine the mixed strain. Löwdin frames are very convenient to model anisotropic materials. Weighted least-squares circumvent the use of internal degrees-of-freedom. Het- erogeneity of element technologies introduce apparently incompatible constitutive requirements. Assumed-strain and enhanced strain elements can be either formulated in terms of the deformation gradient or the Green–Lagrange strain, many of the high-performance shell formulations are corotational and constitutive constraints (such as incompressibility, plane stress and zero normal stress in shells) also depend on specific element formulations. We propose a unified integration algorithm compatible with possibly all element technologies. To assess its validity, a least-squares based hexahedral element is implemented and tested in depth. Basic linear problems as well as 5 finite-strain examples are inspected for correctness and competitive accuracy.

Detection of Glass pattern configurations by the primary visual cortex

The neurons in the primary visual cortex that respond to the orientation of visual stimuli were discovered in the late 1950s (Hubel, D.H. & Wiesel, T.N. 1959. J. Physiol. 148:574-591) but how they achieve this response is poorly understood. Recently, experiments have demonstrated that the visual cortex may use the image processing techniques of cross or auto-correlation to detect the streaks in random dot patterns (Barlow, H. & Berry, D.L. 2010. Proc. R. Soc. B. 278: 2069-2075). These experiments made use of sinusoidally modulated random dot patterns and of the so-called Glass patterns - where randomly positioned dot pairs are oriented in a parallel configuration (Glass, L. 1969. Nature. 223: 578-580). The image processing used by the visual cortex could be inferred from how the threshold of detection of these patterns in the presence of random noise varied as a function of the dot density in the patterns. In the present study, the detection thresholds have been measured for other types of patterns including circular, hyperbolic, spiral and radial Glass patterns and an indication of the type of image processing (cross or auto-correlation) by the visual cortex is presented. As a result, it is hoped that this study will contribute to an understanding of what David Marr called the ‘computational goal’ of the primary visual cortex (Marr, D. 1982. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. New York: Freeman.)