A computational framework for polyconvex large strain elasticity

This paper presents a novel computational formulation for large strain polyconvex elasticity. The formulation, based on the original ideas introduced by Schröder etal. (2011), introduces the deformation gradient (the fibre map), its adjoint (the area map) and its determinant (the volume map) as independent kinematic variables of a convex strain energy function. Compatibility relationships between these variables and the deformed geometry are enforced by means of a multi-field variational principle with additional constraints. This process allows the use of different approximation spaces for each variable. The paper extends the ideas presented in Schröder etal. (2011) by introducing conjugate stresses to these kinematic variables which can be used to define a generalised convex complementary energy function and a corresponding complementary energy principle of the Hellinger-Reissner type, where the new conjugate stresses are primary variables together with the deformed geometry. Both compressible and incompressible or nearly incompressible elastic models are considered. A key element to the developments presented in the paper is the new use of a tensor cross product, presented for the first time by de Boer (1982), page 76, which facilitates the algebra associated with the adjoint of the deformation gradient. For the numerical examples, quadratic interpolation of the displacements, piecewise linear interpolation of strain and stress fields and piecewise constant interpolation of the Jacobian and its stress conjugate are considered for compressible cases. In the case of incompressible materials two formulations are presented. First, continuous quadratic interpolation for the displacement together with piecewise constant interpolation for the pressure and second, linear continuous interpolation for both displacement and pressure stabilised via a Petrov-Galerkin technique

hp-Finite element solution of coupled stationary magnetohydrodynamics problems including magnetostrictive effects

We extend our existing hp-finite element framework for non-conducting magnetic fluids (Jin et al., 2014) to the treatment of conducting magnetic fluids including magnetostriction effects in both two- and three-dimensions. In particular, we present, to the best of our knowledge, the first computational treatment of magnetostrictive effects in conducting fluids. We propose a consistent linearisation of the coupled system of non-linear equations and solve the resulting discretised equations by means of the Newton–Raphson algorithm. Our treatment allows the simulation of complex flow problems, with non-homogeneous permeability and conductivity, and, apart from benchmarking against established analytical solutions for problems with homogeneous material parameters, we present a series of simulations of multiphase flows in two- and three-dimensions to show the predicative capability of the approach as well as the importance of including these effects

An energy-momentum consistent time integration scheme based on a mixed framework for non-linear electro-elastodynamics

The objective of the present work is the introduction of new mixed variational principles for EM time integrators in electromechanics, hence bridging the gap between the previous work presented by the authors in References [11] and [1], opening up the possibility to a variety of new Finite Element implementations

A comparative evaluation of interest point detectors and local descriptors for visual SLAM

Abstract In this paper we compare the behavior of different interest points detectors and descriptors under the conditions needed to be used as landmarks in vision-based simultaneous localization and mapping (SLAM). We evaluate the repeatability of the detectors, as well as the invariance and distinctiveness of the descriptors, under different perceptual conditions using sequences of images representing planar objects as well as 3D scenes. We believe that this information will be useful when selecting an appropriat

A new method for nocturnal aerosol measurements with a lunar photometer prototype

This paper presents the preliminary results of nocturnal Aerosol Optical Depth (τa) and Angström Exponent (α) obtained from a new lunar photometer prototype, trade name Cimel CE-318U. Due to the variation of the moon's illumination inherent to the lunar cycle, the typical Langley-plot Method used in solar photometry to calibrate these instruments cannot be applied. In this paper, we propose three different methods to carry out the lunar-photometer calibration. In order to validate the results, we have selected three events which encompass seven nights and ten days under different atmospheric conditions, including several saharan dust intrusions episodes. Method#1 is introduced in this work as a modification of the usual Langley Method. This technique, called Lunar-Langley Method, requires the extraterrestrial irradiances from a lunar irradiance model, providing similar accuracies on τa to those of AERONET (±0.01-0.02). It makes comparable daytime and nighttime measurements. Method#2 consists of transferring the current calibration from a master used by sunphotometers. Its results are again within the limit of accuracy expected for the instrument. Method#3 uses an integrating sphere and the methodology proposed by Li et al. (2008) to determine sky calibration coefficients (Cj) and the instrument's solid angle field-of-view (Ω), respectively. We observe significant τa differences between Method#1 and #3 (up to 0.07), which might be attributed to the errors propagation in Method#3. The good results obtained from the comparison against a second CE-318U prototype, and against daytime data from a Precision Filter Radiometer (PFR), constitute a valuable assessment of CE-318U performance. Results of α and its spectral variation (δα) show good agreement between daytime and nighttime, being able to identify the aerosol properties associated with each event. © Author(s) 2013

A new energy–momentum time integration scheme for non-linear thermo-mechanics

The aim of this paper is the design a new one-step implicit and thermodynamically consistent Energy–Momentum (EM)preserving time integration scheme for the simulation of thermo-elastic processes undergoing large deformations and temperature fields. Following Bonet et al. (2020), we consider well-posed constitutive models for the entire range of deformations and temperature. In that regard, the consideration of polyconvexity inspired constitutive models and a new tensor cross product algebra are shown to be crucial in order to derive the so-called discrete derivatives, fundamental for the construction of the algorithmic derived variables, namely the second Piola–Kirchoff stress tensor and the entropy (or the absolute temperature).The proposed scheme inherits the advantages of the EM scheme recently published by Franke et al. (2018), whilst resulting in a simpler scheme from the implementation standpoint. A series of numerical examples will be presented in order to demonstrate the robustness and applicability of the new EM scheme. Although the examples presented will make use of a temperature-based version of the EM scheme (using the Helmholtz free energy as the thermodynamical potential and the temperature as thethermodynamical state variable), we also include in an Appendix an entropy-based analogue EM scheme (using the internal energy as the thermodynamical potential and the entropy as the thermodynamical state variable)

ZnO-mesoporous glass scaffolds loaded with osteostatin and mesenchymal cells improve bone healing in a rabbit bone defect

The use of 3D scaffolds based on mesoporous bioactive glasses (MBG) enhanced with therapeutic ions, biomolecules and cells is emerging as a strategy to improve bone healing. In this paper, the osteogenic capability of ZnO-enriched MBG scaffolds loaded or not with osteostatin (OST) and human mesenchymal stem cells (MSC) was evaluated after implantation in New Zealand rabbits. Cylindrical meso-macroporous scaffolds with composition (mol %) 82.2SiO2–10.3CaO–3.3P2O5–4.2ZnO (4ZN) were obtained by rapid prototyping and then, coated with gelatin for easy handling and potentiating the release of inorganic ions and OST. Bone defects (7.5 mm diameter, 12 mm depth) were drilled in the distal femoral epiphysis and filled with 4ZN, 4ZN + MSC, 4ZN + OST or 4ZN + MSC + OST materials to evaluate and compare their osteogenic features. Rabbits were sacrificed at 3 months extracting the distal third of bone specimens for necropsy, histological, and microtomography (µCT) evaluations. Systems investigated exhibited bone regeneration capability. Thus, trabecular bone volume density (BV/TV) values obtained from µCT showed that the good bone healing capability of 4ZN was significantly improved by the scaffolds coated with OST and MSC. Our findings in vivo suggest the interest of these MBG complete systems to improve bone repair in the clinical practice

A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics

The paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first-order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first-order conservation laws. Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. For spatial discretisation, a vertex-based Finite Volume method is employed and suitably adapted. To guarantee stability from both the continuum and the semi-discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstrated via the use of the time variation of the Hamiltonian of the system, seeking to ensure the positive production of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. Examples will be restricted to the case of isothermal reversible elasticity to demonstrate the potential of the new formulation

Intramuscular EMG-Driven Musculoskeletal Modelling: Towards Implanted Muscle Interfacing in Spinal Cord Injury Patients

Objective: Surface EMG-driven modelling has been proposed as a means to control assistive devices by estimating joint torques. Implanted EMG sensors have several advantages over wearable sensors but provide a more localized information on muscle activity, which may impact torque estimates. Here, we tested and compared the use of surface and intramuscular EMG measurements for the estimation of required assistive joint torques using EMG driven modelling. Methods: Four healthy subjects and three incomplete spinal cord injury (SCI) patients performed walking trials at varying speeds. Motion capture marker trajectories, surface and intramuscular EMG, and ground reaction forces were measured concurrently. Subject-specific musculoskeletal models were developed for all subjects, and inverse dynamics analysis was performed for all individual trials. EMG-driven modelling based joint torque estimates were obtained from surface and intramuscular EMG. Results: The correlation between the experimental and predicted joint torques was similar when using intramuscular or surface EMG as input to the EMG-driven modelling estimator in both healthy individuals and patients. Conclusion: We have provided the first comparison of non-invasive and implanted EMG sensors as input signals for torque estimates in healthy individuals and SCI patients. Significance: Implanted EMG sensors have the potential to be used as a reliable input for assistive exoskeleton joint torque actuation.The authors would like to thank Enrique Pérez Rizo, Natalia Comino Suárez and María Isabel Sinovas Alonso for their assistance on the experimental and data acquisition procedure