Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms

This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators

Formulation and performance of variational integrators for rotating bodies

Variational integrators are obtained for two mechanical systems whose configuration spaces are, respectively, the rotation group and the unit sphere. In the first case, an integration algorithm is presented for Euler’s equations of the free rigid body, following the ideas of Marsden et al. (Nonlinearity 12:1647–1662, 1999). In the second example, a variational time integrator is formulated for the rigid dumbbell. Both methods are formulated directly on their nonlinear configuration spaces, without using Lagrange multipliers. They are one-step, second order methods which show exact conservation of a discrete angular momentum which is identified in each case. Numerical examples illustrate their properties and compare them with existing integrators of the literature

A model for the compressible, viscoelastic behavior of human amnion addressing tissue variability through a single parameter

A viscoelastic, compressible model is proposed to rationalize the recently reported response of human amnion in multiaxial relaxation and creep experiments. The theory includes two viscoelastic contributions responsible for the short- and long-term time- dependent response of the material. These two contributions can be related to physical processes: water flow through the tissue and dissipative characteristics of the collagen fibers, respectively. An accurate agreement of the model with the mean tension and kinematic response of amnion in uniaxial relaxation tests was achieved. By variation of a single linear factor that accounts for the variability among tissue samples, the model provides very sound predictions not only of the uniaxial relaxation but also of the uniaxial creep and strip-biaxial relaxation behavior of individual samples. This suggests that a wide range of viscoelastic behaviors due to patient-specific variations in tissue composition

Thermomechanical couplings in shape memory alloy materials

In this work we address several theoretical and computational issues which are related to the thermomechanical modeling of shape memory alloy materials. More specifically, in this paper we revisit a non-isothermal version of the theory of large deformation generalized plasticity which is suitable for describing the multiple and complex mechanisms occurring in these materials during phase transformations. We also discuss the computational implementation of a generalized plasticity based constitutive model and we demonstrate the ability of the theory in simulating the basic patterns of the experimentally observed behavior by a set of representative numerical examples

Phenomenological modelling of damage in polymer blends

To describe the constitutive behaviour of a certain class of polymer blends an elastoperfectly-viscoplastic and creep damageable material characterization is proposed. For a composite of 80 % Polystyrene and 20 % Ethylene Propylene Diene Monomer rubber (PSIEPDM) the specific parameters are determined from tensile tests in a particular range of strain velocities. To investigate the applicability of the model, the results of a finite element analysis for a laterally loaded thin plate (plane stress) with a circular hole are compared to measurements. Numerically calculated values are in reasonable agreement with reality; discrepancies can be ascribed to noise in experimental data. The finite element approach is evaluated with respect to the occurrence of mesh-dependence. Mesh-refinement shows convergence of solutions, attributable to the stabilizing influence of the viscous contribution in the constitutive equations

Do salivary bypass tubes lower the incidence of pharyngocutaneous fistula following total laryngectomy? A retrospective analysis of predictive factors using multivariate analysis

Salivary bypass tubes (SBT) are increasingly used to prevent pharyngocutaneous fistula (PCF) following laryngectomy and pharyngolaryngectomy. There is minimal evidence as to their efficacy and literature is limited. The aim of the study was to determine if SBT prevent PCF. The study was a multicentre retrospective case control series (level of evidence 3b). Patients who underwent laryngectomy or pharyngolaryngectomy for cancer or following cancer treatment between 2011 and 2014 were included in the study. The primary outcome was development of a PCF. Other variables recorded were age, sex, prior radiotherapy or chemoradiotherapy, prior tracheostomy, type of procedure, concurrent neck dissection, use of flap reconstruction, use of prophylactic antibiotics, the suture material used for the anastomosis, tumour T stage, histological margins, day one post-operative haemoglobin and whether a salivary bypass tube was used. Univariate and multivariate analysis were performed. A total of 199 patients were included and 24 received salivary bypass tubes. Fistula rates were 8.3% in the SBT group (2/24) and 24.6% in the control group (43/175). This was not statistically significant on univariate (p value 0.115) or multivariate analysis (p value 0.076). In addition, no other co-variables were found to be significant. No group has proven a benefit of salivary bypass tubes on multivariate analysis. The study was limited by a small case group, variations in tube duration and subjects given a tube may have been identified as high risk of fistula. Further prospective studies are warranted prior to recommendation of salivary bypass tubes following laryngectomy

A finite strain fibre-reinforced viscoelasto-viscoplastic model of plant cell wall growth

A finite strain fibre-reinforced viscoelasto-viscoplastic model implemented in a finite element (FE) analysis is presented to study the expansive growth of plant cell walls. Three components of the deformation of growing cell wall, i.e. elasticity, viscoelasticity and viscoplasticity-like growth, are modelled within a consistent framework aiming to present an integrative growth model. The two aspects of growth—turgor-driven creep and new material deposition—and the interplay between them are considered by presenting a yield function, flow rule and hardening law. A fibre-reinforcement formulation is used to account for the role of cellulose microfibrils in the anisotropic growth. Mechanisms in in vivo growth are taken into account to represent the corresponding biologycontrolled behaviour of a cell wall. A viscoelastic formulation is proposed to capture the viscoelastic response in the cell wall. The proposed constitutive model provides a unique framework for modelling both the in vivo growth of cell wall dominated by viscoplasticity-like behaviour and in vitro deformation dominated by elastic or viscoelastic responses. A numerical scheme is devised, and FE case studies are reported and compared with experimental data