Modeling fracture in rate-dependent polymer networks: A quasicontinuum approach

2021 ◽  
pp. 1-22
Author(s):  
Ahmed Ghareeb ◽  
Ahmed Elbanna
Keyword(s):  
Adaptive Mesh Refinement ◽  
Polymer Networks ◽  
Viscoelastic Behavior ◽  
Adaptive Mesh ◽  
Soft Materials ◽  
Polymer Chains ◽  
Loading Rates ◽  
Viscous Forces ◽  
Rate Dependent ◽  
Bond Breakage

Abstract Soft materials, such as rubber and gels, exhibit rate-dependent response where the stiffness, strength and fracture patterns depend largely on loading rates. Thus, accurate modeling of the mechanical behavior requires accounting for different sources of rate-dependence such as the intrinsic viscoelastic behavior of the polymer chains and the dynamic bond breakage and formation mechanism. In this chapter, we extend the QC approach presented in Ghareeb and Elbanna [Journal of the Mechanics and Physics of Solids, 137, 103819 (2020)] to include ratedependent behavior of polymer networks. We propose a homogenization rule for the viscous forces in the polymer chains and update the adaptive mesh refinement algorithm to account for dynamic bond breakage. Then, we use nonlinear finite element framework with predictorcorrector scheme to solve for the nodal displacements and velocities. We demonstrate the accuracy of the method by verifying it against fully discrete simulations for different examples of network structures and loading conditions. We further use the method to investigate the effects of the loading rates on the fracture characteristics of networks with different ratedependent parameters. Finally, We discuss the implications of the extended method for multiscale analysis of fracture in rate-dependent polymer networks.

scholarly journals Mechanical Response of Two-Dimensional Polymer Networks: Role of Topology, Rate Dependence, and Damage Accumulation

2018 ◽  
Vol 85 (3) ◽  
Author(s):  
Konik Kothari ◽  
Yuhang Hu ◽  
Sahil Gupta ◽  
Ahmed Elbanna
Keyword(s):  
Mechanical Response ◽  
Polymer Networks ◽  
Soft Materials ◽  
Crosslinking Density ◽  
State Theory ◽  
Polymer Chains ◽  
Local Network ◽  
Network Characteristics ◽  
Rate Dependent

The skeleton of many natural and artificial soft materials can be abstracted as networks of fibers/polymers interacting in a nonlinear fashion. Here, we present a numerical model for networks of nonlinear, elastic polymer chains with rate-dependent crosslinkers similar to what is found in gels. The model combines the worm-like chain (WLC) at the polymer level with the transition state theory for crosslinker bond dynamics. We study the damage evolution and the force—displacement response of these networks under uniaxial stretching for different loading rates, network topology, and crosslinking density. Our results suggest a complex nonmonotonic response as the loading rate or the crosslinking density increases. We discuss this in terms of the microscopic deformation mechanisms and suggest a novel framework for increasing toughness and ductility of polymer networks using a bio-inspired sacrificial bonds and hidden length (SBHL) mechanism. This work highlights the role of local network characteristics on macroscopic mechanical observables and opens new pathways for designing tough polymer networks.

Using VOF Slip Velocity to Improve Productivity of Planing Hull CFD Simulations

2021 ◽  
Author(s):  
Miles P. Wheeler ◽  
Philip Ryan ◽  
Flavio Cimolin ◽  
Andrew Gunderson ◽  
John Scherer
Keyword(s):  
Adaptive Mesh Refinement ◽  
High Speed ◽  
Slip Velocity ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Computationally Efficient ◽  
Design Environment ◽  
Viscous Forces ◽  
Calm Water ◽  
Numerical Tools

Use of Computational fluid dynamics (CFD) tools is becoming common practice in the analysis of high speed craft. These numerical tools are of great value, since they can provide high-fidelity insight into performance of various designs by modelling non-linear effects due to viscous forces and turbulence. However, CFD tools are often seen as computationally expensive and prohibitive in a design environment. One of the main issues that impacts the use of CFD tools is numerical ventilation, when air is artificially entrained beneath the hull while using the Volume of Fluid (VOF) scheme to model the free surface. To overcome this issue, traditionally, very fine grids are requested near the surface of the hull to resolve the flow. In this paper, it will be illustrated how the use of an algebraic VOF slip velocity, in conjunction with a tight overset model and adaptive mesh refinement prevent the issue of numerical ventilation while simultaneously using a more computationally efficient mesh that produces accurate results in calm water resistance calculations. A verification and validation process comparing the VOF slip velocity method against experimental data for a known hull was conducted. Computational cost and accuracy associated with VOF slip velocity is discussed. The methodology is then applied to a stepped hull and comparisons between towing tank experiments and simulation results are looked at.

Dynamic structural analysis of connecting rod through adaptive mesh refinement for different materials

2018 ◽  
Vol 50 (04) ◽  
pp. 561-570
Author(s):  
I. A. QAZI ◽  
A. F. ABBASI ◽  
M. S. JAMALI ◽  
INTIZAR INTIZAR ◽  
A. TUNIO ◽  
...  
Keyword(s):  
Structural Analysis ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Connecting Rod ◽  
Dynamic Structural Analysis

scholarly journals Insights into the physics when modelling cold gas clouds in a hot plasma

2019 ◽  
Vol 490 (1) ◽  
pp. L52-L56
Author(s):  
Bastian Sander ◽  
Gerhard Hensler
Keyword(s):  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Careful Consideration ◽  
Necessary Condition ◽  
Interstellar Clouds ◽  
Hot Plasma ◽  
Magnetic Dipole Field ◽  
Set Up ◽  
Self Gravity ◽  
Cold Gas

ABSTRACT This paper aims at studying the reliability of a few frequently raised, but not proven, arguments for the modelling of cold gas clouds embedded in or moving through a hot plasma and at sensitizing modellers to a more careful consideration of unavoidable acting physical processes and their relevance. At first, by numerical simulations we demonstrate the growing effect of self-gravity on interstellar clouds and, by this, moreover argue against their initial set-up as homogeneous. We apply the adaptive-mesh refinement code flash with extensions to metal-dependent radiative cooling and external heating of the gas, self-gravity, mass diffusion, and semi-analytic dissociation of molecules, and ionization of atoms. We show that the criterion of Jeans mass or Bonnor–Ebert mass, respectively, provides only a sufficient but not a necessary condition for self-gravity to be effective, because even low-mass clouds are affected on reasonable dynamical time-scales. The second part of this paper is dedicated to analytically study the reduction of heat conduction by a magnetic dipole field. We demonstrate that in this configuration, the effective heat flow, i.e. integrated over the cloud surface, is suppressed by only 32 per cent by magnetic fields in energy equipartition and still insignificantly for even higher field strengths.

scholarly journals Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver

2021 ◽  
Author(s):  
Alexander Haberl ◽  
Dirk Praetorius ◽  
Stefan Schimanko ◽  
Martin Vohralík
Keyword(s):  
Adaptive Algorithm ◽  
Adaptive Mesh Refinement ◽  
Elliptic Boundary ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Picard Iteration ◽  
Optimal Rate ◽  
Stopping Criteria ◽  
Element Discretization ◽  
Fully Adaptive

AbstractWe consider a second-order elliptic boundary value problem with strongly monotone and Lipschitz-continuous nonlinearity. We design and study its adaptive numerical approximation interconnecting a finite element discretization, the Banach–Picard linearization, and a contractive linear algebraic solver. In particular, we identify stopping criteria for the algebraic solver that on the one hand do not request an overly tight tolerance but on the other hand are sufficient for the inexact (perturbed) Banach–Picard linearization to remain contractive. Similarly, we identify suitable stopping criteria for the Banach–Picard iteration that leave an amount of linearization error that is not harmful for the residual a posteriori error estimate to steer reliably the adaptive mesh-refinement. For the resulting algorithm, we prove a contraction of the (doubly) inexact iterates after some amount of steps of mesh-refinement/linearization/algebraic solver, leading to its linear convergence. Moreover, for usual mesh-refinement rules, we also prove that the overall error decays at the optimal rate with respect to the number of elements (degrees of freedom) added with respect to the initial mesh. Finally, we prove that our fully adaptive algorithm drives the overall error down with the same optimal rate also with respect to the overall algorithmic cost expressed as the cumulated sum of the number of mesh elements over all mesh-refinement, linearization, and algebraic solver steps. Numerical experiments support these theoretical findings and illustrate the optimal overall algorithmic cost of the fully adaptive algorithm on several test cases.

scholarly journals AMReX: Block-structured adaptive mesh refinement for multiphysics applications

2021 ◽  
pp. 109434202110228
Author(s):  
Weiqun Zhang ◽  
Andrew Myers ◽  
Kevin Gott ◽  
Ann Almgren ◽  
John Bell
Keyword(s):  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Uniform Mesh ◽  
Physical Processes ◽  
Structured Adaptive Mesh Refinement ◽  
Core Elements ◽  
Accelerator Design ◽  
Block Structured

Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of Exascale Computing Project applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion, cosmology, multiphase flow, and wind plant modeling. AMReX is a software framework that provides a unified infrastructure with the functionality needed for these and other AMR applications to be able to effectively and efficiently utilize machines from laptops to exascale architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multiphysics algorithms. AMReX supports algorithms that solve systems of partial differential equations in simple or complex geometries and those that use particles and/or particle–mesh operations to represent component physical processes. In this article, we will discuss the core elements of the AMReX framework such as data containers and iterators as well as several specialized operations to meet the needs of the application projects. In addition, we will highlight the strategy that the AMReX team is pursuing to achieve highly performant code across a range of accelerator-based architectures for a variety of different applications.

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