Fractional-orderuniaxial visco-elasto-plastic models for structural analysis

Three fractional-order models for uniaxial large strains and rate-dependent plastic behavior of materials instructural analysis are proposed. Our approach is a menable to modeling nonlinear and more sophisticated effects namely visco-elasto-plastic response of materials. This approach seamlessly interpolates between the standard elasto-plastic and visco-plastic models in plasticity, taking in to account the history-dependency of the accumulated plastic strain to specify the state of stress. To this end, we propose three models namely i) viscoelasto-plastic with linear hardening plastic model, ii )elasto-viscoplastic model, and iii) visco-elasto-plastic model, which combines the first the second models. We employ afractional-order constitutive law that relates the Kirchhoff stress to its Caputo time-fractional derivative of order α ∈ (0,1]. When α → 0 the standard elasto-plastic (rate-independent) model and when α = 1, the corresponding visco-plastic model is recovered. Since the material behavior is path-dependent the evolution of the plastic strainis achieved by fractional-order time integration of the plastic strain rate with respect to time. The strain rate is then obtained by means of the corresponding plastic multiplier and deriving proper consistency conditions. Finally, we develop a so called fractional return-mapping algorithm for solving the nonlinear system of the equilibrium equations developing in each model

Mesh update techniques for free-surface flow solvers using spectral element method

This paper presents a novel mesh-update technique for unsteady free-surface Newtonian flows using spectral element method and relying on the arbitrary Lagrangian--Eulerian kinematic description for moving the grid. Selected results showing compatibility of this mesh-update technique with spectral element method are given

Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows

We present a review of the semi-Lagrangian method for advection-diusion and incompressible Navier-Stokes equations discretized with high-order methods. In particular, we compare the strong form where the departure points are computed directly via backwards integration with the auxiliary form where an auxiliary advection equation is solved instead; the latter is also referred to as Operator Integration Factor Splitting (OIFS) scheme. For intermediate size of time steps the auxiliary form is preferrable but for large time steps only the strong form is stable

Multi-fidelity Modelling via Recursive Co-kriging and Gasussian-Markov Random Fields

The article of record as published may be found at http://dx.doi.org/10.1098/rspa.2015.0018We propose a new framework for design under uncertainty based on stochastic computer simulations and multi-level recursive co-kriging. The proposed methodology simultaneously takes into account multi-fidelity in models, such as direct numerical simulations versus empirical formulae, as well as multi-fidelity in the probability space (e.g. sparse grids versus tensor product multi-element probabilistic collocation). We are able to construct response surfaces of complex dynamical systems by blending multiple information sources via auto-regressive stochastic modelling. A computationally efficient machine learning framework is developed based on multi-level recursive co-kriging with sparse precision matrices of Gaussian–Markov random fields. The effectiveness of the new algorithms is demonstrated in numerical examples involving a prototype problem in risk-averse design, regression of random functions, as well as uncertainty quantification in fluid mechanics involving the evolution of a Burgers equation from a random initial state, and random laminar wakes behind circular cylinders.DARPA grant HR0011-14-1-0060AFOSR grant FA9550-12-1-0463Argonne Leadership Computing Facility (ALCF)DARPA grant HR001-14-1-225DARPA grant HR0011-14-1-0060AFOSR grant FA9550-12-1-0463DARPA grant HR001-14-1-22

Time-dependent and outflow boundary conditions for Dissipative Particle Dynamics

We propose a simple method to impose both no-slip boundary conditions at fluid-wall interfaces and at outflow boundaries in fully developed regions for Dissipative Particle Dynamics (DPD) fluid systems. The procedure to enforce the no-slip condition is based on a velocity-dependent shear force, which is a generalized force to represent the presence of the solid-wall particles and to maintain locally thermodynamic consistency. We show that this method can be implemented in both steady and time-dependent fluid systems and compare the DPD results with the continuum limit (Navier-Stokes) results. We also develop a force-adaptive method to impose the outflow boundary conditions for fully developed flow with unspecified outflow velocity profile or pressure value. We study flows over the backward-facing step and in idealized arterial bifurcations using a combination of the two new boundary methods with different flow rates. Finally, we explore the applicability of the outflow method in time-dependent flow systems. The outflow boundary method works well for systems with Womersley number of O(1), i.e., when the pressure and flowrate at the outflow are approximately in-phase

Wall Shear Stress-Based Model for Adhesive Dynamics of Red Blood Cells in Malaria

Red blood cells (RBCs) infected by the Plasmodium falciparum (Pf-RBCs) parasite lose their membrane deformability and they also exhibit enhanced cytoadherence to vascular endothelium and other healthy and infected RBCs. The combined effect may lead to severe disruptions of normal blood circulation due to capillary occlusions. Here we extend the adhesion model to investigate the adhesive dynamics of Pf-RBCs as a function of wall shear stress (WSS) and other parameters using a three-dimensional, multiscale RBC model. Several types of adhesive behavior are identified, including firm adhesion, flipping dynamics, and slow slipping along the wall. In particular, the flipping dynamics of Pf-RBCs observed in experiments appears to be due to the increased stiffness of infected cells and the presence of the solid parasite inside the RBC, which may cause an irregular adhesion behavior. Specifically, a transition from crawling dynamics to flipping behavior occurs at a Young's modulus approximately three times larger than that of healthy RBCs. The simulated dynamics of Pf-RBCs is in excellent quantitative agreement with available microfluidic experiments if the force exerted on the receptors and ligands by an existing bond is modeled as a nonlinear function of WSS

Predicting dynamics and rheology of blood flow: A comparative study of multiscale and low-dimensional models of red blood cells

We compare the predictive capability of two mathematical models for red blood cells (RBCs) focusing on blood flow in capillaries and arterioles. Both RBC models as well as their corresponding blood flows are based on the dissipative particle dynamics (DPD) method, a coarse-grained molecular dynamics approach. The first model employs a multiscale description of the RBC (MS-RBC), with its membrane represented by hundreds or even thousands of DPD-particles connected by springs into a triangular network in combination with out-of-plane elastic bending resistance. Extra dissipation within the network accounts for membrane viscosity, while the characteristic biconcave RBC shape is achieved by imposition of constraints for constant membrane area and constant cell volume. The second model is based on a low-dimensional description (LD-RBC) constructed as a closed torus-like ring of only 10 large DPD colloidal particles. They are connected into a ring by worm-like chain (WLC) springs combined with bending resistance. The LD-RBC model can be fitted to represent the entire range of nonlinear elastic deformations as measured by optical-tweezers for healthy and for infected RBCs in malaria. MS-RBCs suspensions model the dynamics and rheology of blood flow accurately for any vessel size but this approach is computationally expensive for vessel diameters above 100μm. Surprisingly, the much more economical suspensions of LD-RBCs also capture the blood flow dynamics and rheology accurately except for small-size vessels comparable to RBC diameter. In particular, the LD-RBC suspensions are shown to properly capture the experimental data for the apparent viscosity of blood and its cell-free layer (CFL) in tube flow. Taken together, these findings suggest a hierarchical approach in modeling blood flow in the arterial tree, whereby the MS-RBC model should be employed for capillaries and arterioles below 100μm, the LD-RBC model for arterioles, and the continuum description for arteries