71,836 research outputs found
Cardiac Electromechanics: The effect of contraction model on the mathematical problem and accuracy of the numerical scheme
Models of cardiac electromechanics usually contain a contraction model determining the active tension induced at the cellular level, and the equations of nonlinear elasticity to determine tissue deformation in response to this active tension. All contraction models are dependent on cardiac electro-physiology, but can also be dependent on\ud
the stretch and stretch-rate in the fibre direction. This fundamentally affects the mathematical problem being solved, through classification of the governing PDEs, which affects numerical schemes that can be used to solve the governing equations. We categorise contraction models into three types, and for each consider questions such as classification and the most appropriate choice from two numerical methods (the explicit and implicit schemes). In terms of mathematical classification, we consider the question of strong ellipticity of the total strain energy (important for precluding ‘unnatural’ material behaviour) for stretch-rate-independent contraction models; whereas for stretch-rate-dependent contraction models we introduce a corresponding third-order problem and explain how certain choices of boundary condition could lead to constraints on allowable initial condition. In terms of suitable numerical methods, we show that an explicit approach (where the contraction model is integrated in the timestep prior to the bulk deformation being computed) is: (i) appropriate for stretch-independent contraction models; (ii) only conditionally-stable, with the stability criterion independent of timestep, for contractions models which just depend on stretch (but not stretch-rate), and (iii) inappropriate for stretch-rate-dependent models
Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening
This study presents the ordinary state-based peridynamic constitutive relations for plastic deformation based on von Mises yield criteria with isotropic hardening. The peridynamic force density-stretch relations concerning elastic deformation are augmented with increments of force density and stretch for plastic deformation. The expressions for the yield function and the rule of incremental plastic stretch are derived in terms of the horizon, force density, shear modulus, and hardening parameter of the material. The yield surface is constructed based on the relationship between the effective stress and equivalent plastic stretch. The validity of peridynamic predictions is established by considering benchmark solutions concerning a plate under tension, a plate with a hole and a crack also under tension
Study on instability and forming limit of sheet metal under stretch-bending
Under stretch-bending conditions, a significant tensile stress gradient through sheet thickness is induced, especially for a small punch radius. The traditional instability theories were developed assuming a uniform tensile stress / strain distribution through thickness; hence, may lead to unreliable prediction of stretch-bending formability. In this study, the instability behavior of sheet metal under stretch-bending is analyzed via FE-simulation of an Angular Stretch-Bend Test (ASBT). In order to reflect the influence of bending, contact normal stress etc., solid elements are used in the simulation. Three deformation stages are identified: (a). stable deformation; (b). strain localization through sheet thickness; (c). localized necking. Based on the instability characteristics, a localized necking criterion is proposed for predicting forming limits of sheet metal under stretch-bending. By combining the proposed criterion and solid element simulation, good agreement between numerical and experimental results is indicated. This work provides a new approach for predicting stretch-bend formability with sufficient accuracy and convenience.</jats:p
Finite elastic deformations of transversely isotropic circular cylindrical tubes
We consider the finite radially symmetric deformation of a circular cylindrical tube of a homogeneous transversely isotropic elastic material subject to axial stretch, radial deformation and torsion, supported by axial load, internal pressure and end moment. Two different directions of transverse isotropy are considered: the radial direction and an arbitrary direction in planes normal locally to the radial direction, the only directions for which the considered deformation is admissible in general. In the absence of body forces, formulas are obtained for the internal pressure, and the resultant axial load and torsional moment on the ends of the tube in respect of a general strain-energy function. For a specific material model of transversely isotropic elasticity, and material and geometrical parameters, numerical results are used to illustrate the dependence of the pressure, (reduced) axial load and moment on the radial stretch and a measure of the torsional deformation for a fixed value of the axial stretch
Non-aqueous retention measurements: ultrafiltration behaviour of polystyrene solutions and colloidal silver particles
The retention behaviour of polyimide ultrafiltration membranes was investigated using dilute solutions of polystyrene in ethyl acetate as test solutions. It is shown that flow-induced deformation of the polystyrene chains highly affects the membrane retention. This coil-stretch transition is not instantaneous, but gradual. The concept of a deformation resistance has been ontroduced to explain this behaviour. This concept can be applied to describe the flux behaviour of the membranes during the tests as well. Solute deformation allows comparison of the pore size distributions of the membranes qualitatively. Retention measurements were also performed with silver sol particles that were prepared in mixtures of ethanol and water; these sols remain stable as long as the ethanol concentration does not exceed 57 vol%. The sols were completely retained by the membranes, which is probably caused by the fact that the effective diameter of the particles is much larger than that observed by transmission electron microscopy
Polymer stretching in laminar and random flows: entropic characterization
Polymers in non-uniform flows undergo strong deformation, which in the
presence of persistent stretching can result in the coil-stretch transition.
The statistics of polymer deformation depends strongly on the nature and the
properties of the flow. Sultanov et al. [Phys. Rev. E 103, 033107 (2021)] have
characterized the coil-stretch transition in an elastic turbulence of von
K\'arm\'an flow by measuring the entropy of polymer extension as a function of
the Weissenberg number. The entropic characterization of the coil-stretch
transition is here extended to a set of laminar and random velocity fields that
are benchmarks for the study of polymer stretching in flow. In the case of
random velocity fields, a suitable description of the transition is obtained by
considering the entropy of the logarithm of the extension instead of the
entropy of the extension itself. Entropy emerges as an effective tool for
capturing the coil-stretch transition and comparing its features in different
flows.Comment: 6 pages, 2 figure
On the Multiplicative Logarithmic Strain Space Formulation
A new constitutive approach to finite-deformation formulations of elasto-plasticity (with isotropic thermal expansion) is presented, which is well-suited to a broad range of metals used for industrial applications. The constitutive equations are formulated within the logarithmic strain space. The coupling of elasticity, plasticity and thermal expansion is based on a multiplicative approach of commutative-symmetric stretch tensor products with symmetrizing rotation tensors in the middle of two symmetric stretch tensors. It is essential for finite-deformation formulations to refer to an appropriate reference configuration K0 in order to model material orthotropy correctly (and not to mix up material / physical anisotropy with deformation-induced / geometrical anisotropy). Furthermore, it is essential to define proper stretch and strain tensors which are geometrical interpretable, i.e. which only depend on a current K and a reference K0 configuration (and not on the geometrical deformation path between these configurations). Therefore, all stretch and strain tensors are defined with respect to the same reference configuration K0, the total stretches and strains as well as the partial ones: the elastic, plastic and thermal stretches and strains. And these reference configurations should be the appropriate ones, where—in the case of fiber-reinforced (metal) bodies—the fibers are placed orthogonal to each other or where Walter Noll’s symmetry group considerations characterize the physical nature of materials with their most specificity as: orthotropic, transversal isotropic or fully isotropic
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