skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Validating bond-based peridynamic model using displacement potential approach
Although peridynamics is widely used to investigate mechanical responses in materials, the ability of peridynamics to capture the main features of realistic stress states remains unknown. Here, we present a procedure that combines analytic investigation and numerical simulation to capture the elastic field in the mixed boundary condition. By using the displacement potential function, the mixed boundary condition elasticity problem is reduced to a single partial differential equation which can be analytically solved through Fourier analysis. To validate the peridynamic model, we conduct a numerical uniaxial tensile test using peridynamics, which is further compared with the analytic solution through a convergence study. We find that, when the parameters are carefully calibrated, the numerical predicted stress distribution agrees very well with the one obtained from the theoretical calculation.  more » « less
Award ID(s):
1826420
PAR ID:
10387279
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Proceedings of the Institution of Mechanical Engineers Part C Journal of mechanical engineering science
ISSN:
0954-4062
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; (, Physics of Fluids)
    In fluid dynamics applications that involve flow adjacent to a porous medium, there exists some ambiguity in how to model the interface. Despite different developments, there is no agreed upon boundary condition that should be applied at the interface. We present a new analytical solution for laminar boundary layers over permeable beds driven by oscillatory free stream motion where flow in the permeable region follows Darcy's law. We study the fluid boundary layer for two different boundary conditions at the interface between the fluid and a permeable bed that was first introduced in the context of steady flows: a mixed boundary condition proposed by Beavers and Joseph [“Boundary conditions at a naturally permeable bed,” J. Fluid Mech. 30, 197–207 (1967)] and the velocity continuity condition proposed by Le Bars and Worster [“Interfacial conditions between a pure fluid and a porous medium: Implications for binary alloy solidification,” J. Fluid Mech. 550, 149–173 (2006)]. Our analytical solution based on the velocity continuity condition agrees very well with numerical results using the mixed boundary condition, suggesting that the simpler velocity boundary condition is able to accurately capture the flow physics near the interface. Furthermore, we compare our solution against experimental data in an oscillatory boundary layer generated by water waves propagating over a permeable bed and find good agreement. Our results show the existence of a transition zone below the interface, where the boundary layer flow still dominates. The depth of this transition zone scales with the grain diameter of the porous medium and is proportional to an empirical parameter that we fit to the available data. 
    more » « less
  2. ; ; ; ; ; ; (, Journal of the American Ceramic Society)
    Abstract Nanoindentation is a widely used method to probe the mechanical properties of glasses. However, interpreting glasses’ response to nanoindentation can be challenging due to the complex nature of the stress field under the indenter tip and the lack ofin situcharacterization techniques. Here, we present a numerical model describing the nanoindentation of an archetypical soda‐lime silicate window glass by means of peridynamic simulations. We show that, although it does not capture shear flow and permanent densification, peridynamics exhibits a good agreement with experimental nanoindentation data and offers a direct access to the stress field forming under the indenter tip. 
    more » « less
  3. ; (, Solid Earth)
    Abstract. Modelling the pressure in the Earth's interior is a common problem in Earth sciences. In this study we propose a method based on the conservation of the momentum of a fluid by using a hydrostatic scenario or a uniformly moving fluid to approximate the pressure. This results in a partial differential equation (PDE) that can be solved using classical numerical methods. In hydrostatic cases, the computed pressure is the lithostatic pressure. In non-hydrostatic cases, we show that this PDE-based approach better approximates the total pressure than the classical 1D depth-integrated approach. To illustrate the performance of this PDE-based formulation we present several hydrostatic and non-hydrostatic 2D models in which we compute the lithostatic pressure or an approximation of the total pressure, respectively. Moreover, we also present a 3D rift model that uses that approximated pressure as a time-dependent boundary condition to simulate far-field normal stresses. This model shows a high degree of non-cylindrical deformation, resulting from the stress boundary condition, that is accommodated by strike-slip shear zones. We compare the result of this numerical model with a traditional rift model employing free-slip boundary conditions to demonstrate the first-order implications of considering “open” boundary conditions in 3D thermo-mechanical rift models. 
    more » « less
  4. ; (, The ANZIAM Journal)
    The immersed boundary method is a widely used mixed Eulerian/Lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids. In this work, we consider a poroelastic immersed boundary method in which a fluid permeates a porous, elastic structure of negligible volume fraction, and extend this method to include stress relaxation of the material. The porous viscoelastic method presented here is validated for a prescribed oscillatory shear and for an expansion driven by the motion at the boundary of a circular material by comparing numerical solutions to an analytical solution of the Maxwell model for viscoelasticity. Finally, an application of the modelling framework to cell biology is provided: passage of a cell through a microfluidic channel. We demonstrate that the rheology of the cell cytoplasm is important for capturing the transit time through a narrow channel in the presence of a pressure drop in the extracellular fluid. 
    more » « less
  5. ; ; ; (, Kinetic and Related Models)
    We prove the inviscid limit for the incompressible Navier-Stokes equations for data that are analytic only near the boundary in a general two-dimensional bounded domain. Our proof is direct, using the vorticity formulation with a nonlocal boundary condition, the explicit semigroup of the linear Stokes problem near the flatten boundary, and the standard wellposedness theory of Navier-Stokes equations in Sobolev spaces away from the boundary. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email