The effect of the through-thickness moisture content gradient on the moisture accelerated creep of paperboard: Hygro-viscoelastic modeling approach

2018 ◽  
Vol 33 (1) ◽  
pp. 122-132 ◽  
Author(s):  
Joonas Sorvari ◽  
Teemu Leppänen ◽  
Jukka Silvennoinen
Keyword(s):  
Finite Element Method ◽  
Moisture Content ◽  
Constitutive Law ◽  
Time Dependent ◽  
The Finite Element Method ◽  
Dependent Behavior ◽  
Accelerated Creep ◽  
Moisture Accelerated Creep ◽  
Viscoelastic Modeling ◽  
Moisture Content Gradient

Abstract Paper-based materials are viscous materials, the time-dependent behavior of which depends strongly on moisture content. Particularly the creep of paperboard containers under compressive forces is greatly affected by changes in the relative humidity. In the present paper, we examine the creep behavior of paperboard under cyclic humidity conditions using the finite element method. Especially the shape and rate of the through-thickness moisture content gradient on moisture accelerated creep are studied. An isotropic hygro-viscoelastic constitutive law is used for paperboard. The results of the simulations are compared with experiments. It is concluded that the through-thickness moisture gradients have a great impact on the moisture accelerated creep of paperboard. Furthermore, the results show that depending on the direction of external load the through-thickness moisture content gradient may increase or decrease creep rate.

A parallel partition of unity method for the unsteady Stokes equations

2017 ◽  
Vol 27 (9) ◽  
pp. 2105-2114
Author(s):  
Xiaoying Zhao ◽  
Yanren Hou ◽  
Guangzhi Du
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Partition Of Unity ◽  
Time Dependent ◽  
The Finite Element Method ◽  
Partition Of Unity Method ◽  
Content Type ◽  
Standard Galerkin Method ◽  
Unsteady Stokes Equations

Purpose The purpose of this paper is to propose a parallel partition of unity method to solve the time-dependent Stokes problems. Design/methodology/approach This paper solved the time-dependent Stokes equations using the finite element method and the partition of unity method. Findings The proposed method in this paper obtained the same accuracy as the standard Galerkin method, but it, in general, saves time. Originality/value Based on a combination of the partition of unity method and the finite element method, the authors, in this paper, propose a new parallel partition of unity method to solve the unsteady Stokes equations. The idea is that, at each time step, one need to only solve a series of independent local sub-problems in parallel instead of one global problem. Numerical tests show that the proposed method not only reaches the same convergence orders as the fully discrete standard Galerkin method but also saves ample computing time.

The Research of Nano-Mechanical Properties of Mono-Crystalline Silicon

2013 ◽  
Vol 834-836 ◽  
pp. 18-22
Author(s):  
Xiao Jing Yang ◽  
Wei Xing Zhang
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Penetration Depth ◽  
Crystalline Silicon ◽  
Constitutive Law ◽  
The Finite Element Method ◽  
Approximate Relationship ◽  
Actual Load ◽  
Plastic Phase ◽  
Depth Curve

The research of the nano-mechanical properties on mono-crystalline silicon by nanoindention technology is reported in this paper . Using the calculation method given by Oliver and Pharr, the hardness and the elastic modulus of mono-crystalline silicon are gained from the load-penetration depth curve. The simulation on mono-crystalline silicon in the plastic phase is carried out by ABAQUS. Based on the bilinear constitutive law and approximate relationship between the hardness and the yield strength, the obtained load-penetration depth curve through the finite element method is compared with the materials actual load-penetration depth curve and good correlation is achieved.

scholarly journals A Map-plane Finite-element Model: Three Modeling Experiments

1989 ◽  
Vol 35 (119) ◽  
pp. 48-52 ◽  
Author(s):  
James L. Fastook ◽  
Judith E.. Chapman
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Ice Sheet ◽  
Time Dependent ◽  
Element Formulation ◽  
Initial Surface ◽  
The Finite Element Method ◽  
Sheet Flow ◽  
Flow Law ◽  
Element Method

AbstractPreliminary results are presented on a solution of the two-dimensional time-dependent continuity equation for mass conservation governing ice-sheet dynamics. The equation is solved using a column-averaged velocity to define the horizontal flux in a finite-element formulation. This yields a map-plane model where flow directions, velocities, and surface elevations are defined by bedrock topography, the accumulation/ablation pattern, and in the time-dependent case by the initial surface configuration. This alleviates the flow-band model limitation that the direction of flow be defined and fixed over the course of the modeling experiment. The ability of the finite-element method to accept elements of different dimensions allows detail to be finely modeled in regions of steep gradients, such as ice streams, while relatively uniform areas, such as areas of sheet flow, can be economically accommodated with much larger elements. Other advantages of the finite-element method include the ability to modify the sliding and/or flow-law relationships without materially affecting the method of solution.Modeling experiments described include a steady-state reconstruction showing flow around a three-dimensional obstacle, as well as a time-dependent simulation demonstrating the response of an ice sheet to a localized decoupling of the bed. The latter experiment simulates the initiation and development of an ice stream in a region originally dominated by sheet flow. Finally, a simulation of the effects of a changing mass-balance pattern, such as might be anticipated from the expected carbon dioxide warming, is described. Potential applications for such a model are also discussed.SYMBOLS USEDa(x,y) Accumulation/ablation rate.A Flow-law parameter.B Sliding-law parameter.CijC Global capacitance matrix.f Fraction of the bed melted.Fij,F Global load vector.g Acceleration of gravity.hj,h Ice-surface elevation.H Ice thickness.k(x,y) Constitutive equation constant of proportionality.kij Global stiffness matrix.m Sliding-law exponent.n Flow-law exponent.ρ Density of ice.σ(x,y) Ice flux.t Time.U Column-average ice velocity.UF Column-average deformation (flow) velocity.US Sliding velocity.v Variational trial function.x,y Map-plane coordinates.

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