Locking-Proof Tetrahedra

The simulation of incompressible materials suffers from locking when using the standard finite element method (FEM) and coarse linear tetrahedral meshes. Locking increases as the Poisson ratio gets close to 0.5 and often lower Poisson ratio values are used to reduce locking, affecting volume preservation. We propose a novel mixed FEM approach to simulating incompressible solids that alleviates the locking problem for tetrahedra. Our method uses linear shape functions for both displacements and pressure, and adds one scalar per node. It can accommodate nonlinear isotropic materials described by a Young’s modulus and any Poisson ratio value by enforcing a volumetric constitutive law. The most realistic such material is Neo-Hookean, and we focus on adapting it to our method. For , we can obtain full volume preservation up to any desired numerical accuracy. We show that standard Neo-Hookean simulations using tetrahedra are often locking, which, in turn, affects accuracy. We show that our method gives better results and that our Newton solver is more robust. As an alternative, we propose a dual ascent solver that is simple and has a good convergence rate. We validate these results using numerical experiments and quantitative analysis.

Geometric linearization of theories for incompressible elastic materials and applications

We derive geometrically linearized theories for incompressible materials from nonlinear elasticity theory in the small displacement regime. Our nonlinear stored energy densities may vary on the same (small) length scale as the typical displacements. This allows for applications to multiwell energies as, e.g. encountered in martensitic phases of shape memory alloys and models for nematic elastomers. Under natural assumptions on the asymptotic behavior of such densities we prove Gamma-convergence of the properly rescaled nonlinear energy functionals to the relaxation of an effective model. The resulting limiting theory is geometrically linearized in the sense that it acts on infinitesimal displacements rather than finite deformations, but will in general still have a limiting stored energy density that depends in a nonlinear way on the infinitesimal strains. Our results, in particular, establish a rigorous link of existing finite and infinitesimal theories for incompressible nematic elastomers.

Use of the hyperelastic model for plastic materials by example of the three-bar truss

Particular features and traits of a model of large deformations applied for static analysis and design of metal structures with plasticity are considered. Foundations of the deformation theory of plasticity relevant for incompressible materials are formally generalized for the model of hyperelastic body described by equation of state in the Finger form. The behavior of the model is analyzed for the case of uniaxial tension. The collected results are used to explore a symmetrical three-bar truss made of two materials. Relations describing behavior of the truss under conditions of the geometric and physical nonlinearities are obtained. Specifics arising in the analysis and design of the truss using standard structural alloys are analyzed.

Motion-Induced Imbalance of Contact Impedance in ECG Capture: Comparison of Electrode Materials in Capacitive Coupling

Differences in contact impedance of the ECG measurement electrodes lead to asymmetries of the signal paths and thus result in reduced common-mode rejection and artifacts. Here, the imbalance of contact impedance is investigated for<br>different types of electrodes with capacitive coupling in terms of static imbalance as well as dynamic variation during body movement. Flexible and incompressible materials like conductive foam and fabric showed the best overall performance. The negative effect of rigidity can partly be compensated by adding conducting foam, while soft materials can profit from an increase of electrode area. <br>

Motion-Induced Imbalance of Contact Impedance in ECG Capture: Comparison of Electrode Materials in Capacitive Coupling

Differences in contact impedance of the ECG measurement electrodes lead to asymmetries of the signal paths and thus result in reduced common-mode rejection and artifacts. Here, the imbalance of contact impedance is investigated for<br>different types of electrodes with capacitive coupling in terms of static imbalance as well as dynamic variation during body movement. Flexible and incompressible materials like conductive foam and fabric showed the best overall performance. The negative effect of rigidity can partly be compensated by adding conducting foam, while soft materials can profit from an increase of electrode area. <br>

Motion-Induced Imbalance of Contact Impedance in ECG Capture: Comparison of Electrode Materials in Capacitive Coupling

Differences in contact impedance of the ECG measurement electrodes lead to asymmetries of the signal paths and thus result in reduced common-mode rejection and artifacts. Here, the imbalance of contact impedance is investigated for<br>different types of electrodes with capacitive coupling in terms of static imbalance as well as dynamic variation during body movement. Flexible and incompressible materials like conductive foam and fabric showed the best overall performance. The negative effect of rigidity can partly be compensated by adding conducting foam, while soft materials can profit from an increase of electrode area. <br>