Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM

In this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent patch recovery (SPR). Boundary equilibrium is enforced using a nearest point approach that modifies the MLS functional. Lagrange multipliers are used to impose a nearly exact satisfaction of the internal equilibrium equation. The numerical results show the high accuracy of the proposed error estimator

eXtended Variational Quasicontinuum Methodology for Lattice Networks with Damage and Crack Propagation

Lattice networks with dissipative interactions are often employed to analyze materials with discrete micro- or meso-structures, or for a description of heterogeneous materials which can be modelled discretely. They are, however, computationally prohibitive for engineering-scale applications. The (variational) QuasiContinuum (QC) method is a concurrent multiscale approach that reduces their computational cost by fully resolving the (dissipative) lattice network in small regions of interest while coarsening elsewhere. When applied to damageable lattices, moving crack tips can be captured by adaptive mesh refinement schemes, whereas fully-resolved trails in crack wakes can be removed by mesh coarsening. In order to address crack propagation efficiently and accurately, we develop in this contribution the necessary generalizations of the variational QC methodology. First, a suitable definition of crack paths in discrete systems is introduced, which allows for their geometrical representation in terms of the signed distance function. Second, special function enrichments based on the partition of unity concept are adopted, in order to capture kinematics in the wakes of crack tips. Third, a summation rule that reflects the adopted enrichment functions with sufficient degree of accuracy is developed. Finally, as our standpoint is variational, we discuss implications of the mesh refinement and coarsening from an energy-consistency point of view. All theoretical considerations are demonstrated using two numerical examples for which the resulting reaction forces, energy evolutions, and crack paths are compared to those of the direct numerical simulations.Comment: 36 pages, 23 figures, 1 table, 2 algorithms; small changes after review, paper title change

Uniqueness of human running coordination: The integration of modern and ancient evolutionary innovations

Running is a pervasive activity across human cultures and a cornerstone of contemporary health, fitness and sporting activities. Yet for the overwhelming predominance of human existence running was an essential prerequisite for survival. A means to hunt, and a means to escape when hunted. In a very real sense humans have evolved to run. Yet curiously, perhaps due to running’s cultural ubiquity and the natural ease with which we learn to run, we rarely consider the uniqueness of human bipedal running within the animal kingdom. Our unique upright, single stance, bouncing running gait imposes a unique set of coordinative difficulties. Challenges demanding we precariously balance our fragile brains in the very position where they are most vulnerable to falling injury while simultaneously retaining stability, steering direction of travel, and powering the upcoming stride: all within the abbreviated time-frames afforded by short, violent ground contacts separated by long flight times. These running coordination challenges are solved through the tightly-integrated blending of primitive evolutionary legacies, conserved from reptilian and vertebrate lineages, and comparatively modern, more exclusively human, innovations. The integrated unification of these top-down and bottom-up control processes bestows humans with an agile control system, enabling us to readily modulate speeds, change direction, negotiate varied terrains and to instantaneously adapt to changing surface conditions. The seamless integration of these evolutionary processes is facilitated by pervasive, neural and biological, activity-dependent adaptive plasticity. Over time, and with progressive exposure, this adaptive plasticity shapes neural and biological structures to best cope with regularly imposed movement challenges. This pervasive plasticity enables the gradual construction of a robust system of distributed coordinated control, comprised of processes that are so deeply collectively entwined that describing their functionality in isolation obscures their true irrevocably entangled nature. Although other species rely on a similar set of coordinated processes to run, the bouncing bipedal nature of human running presents a specific set of coordination challenges, solved using a customized blend of evolved solutions. A deeper appreciation of the foundations of the running coordination phenomenon promotes conceptual clarity, potentially informing future advances in running training and running-injury rehabilitation interventions

Towards recovery of complex shapes in meshes using digital images for reverse engineering applications

When an object owns complex shapes, or when its outer surfaces are simply inaccessible, some of its parts may not be captured during its reverse engineering. These deficiencies in the point cloud result in a set of holes in the reconstructed mesh. This paper deals with the use of information extracted from digital images to recover missing areas of a physical object. The proposed algorithm fills in these holes by solving an optimization problem that combines two kinds of information: (1) the geometric information available on the surrounding of the holes, (2) the information contained in an image of the real object. The constraints come from the image irradiance equation, a first-order non-linear partial differential equation that links the position of the mesh vertices to the light intensity of the image pixels. The blending conditions are satisfied by using an objective function based on a mechanical model of bar network that simulates the curvature evolution over the mesh. The inherent shortcomings both to the current holefilling algorithms and the resolution of the image irradiance equations are overcom