Research on a New Constitutive Model for Cohesive Powder Simulation

Research on a New Constitutive Model for Cohesive Powder Simulation Carmen Jiawen SuSupervisors: Prof. BradleyProf. PericleousDr. Patel

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceContentsIntroductionEmpirical Numerical Further Work

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceIntroduction

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceProblem Description Seminar 08/06/20114

Cohesive a cohesive material has the ability to retain strength when external applied stress is removedArching a solid bridge that is formed usually at the outlet of the silo.

Cohesive Arching a bridge of cohesive material formed at the outlet.

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceThe problem we try to solve here is to break the cohesive arching occur when it is formed. Two key words cohesive and arching:Cohesive a cohesive material has the ability to retain strength when external applied stress is removed. (example)Arching a solid bridge that is formed usually at the outlet of the silo. A cohesive arching a bridge of cohesive material formed at the outlet. 4

Free-body DiagramArching -Fundamental PrinciplesSeminar 08/06/20115

mg

mg

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceMg generates the resultant forces acting on the element.Vertically: Horizontally: the stress acting on the element exceeds the strength in the element, slip plane will occur(incipient flow) Each arch can be treated individually, as they arch under their own weight. Two ways to increase the forces, a) increase mg; b) decrease Alpha, increase width. 5

1st Stage - ConsolidationVertical applied stress -

2nd Stage Failure Vertical stress detected at where the specimen fail catastrophically -Seminar 08/06/20116Uniaxial Compression Test

Stress -

Solid Strength -

Yield Locus

Becomesunconfined

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceThe element shown in last slide can be represented by this test. 6

Yield Locus and Flow FunctionSeminar 08/06/20117

Solid Strength -

Yield LociStress -

Flow Function

C

is the angle of internal friction C is cohesion

More sticky materialMore free-flowing material

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical SciencePowder gains strength though consolidation, in order to shear(fail) such a powder, the angle of internal friction (Phi) needs to be overcome. [Tau>Sigma*tan(Phi)+C] this is the Yield Locos (YL), its meaning is the area above YL, the powder will shear. Family of loci is produced. And Flow Function (measure to characterise powder) is produced from corresponding pairs of Sigma_c and Sigma_1. aread above FF, the powder will shear. 7

Empirical

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceUniaxial compression test (confined) Establishing Stress Density Material Strength relationship The wall of the cylinder cells is greased and affixed with a rubber surfaceTwo cylinder cells are wrapped together with rubber bandsPrepare the material in the cylinder cells Apply vertical load on top

10kg

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceUniaxial compression test (confined) cont.

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceNumerical

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceReview on Mathematical Models

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical Science

12

Model in PHYSICA Two stages of simulation, filling stage and incipient flow stage. Changing material properties according to the stress exerted on the material during filling stage. Examine material with Failure Criteria at incipient flow stage.

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceFilling stage

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceIncipient Flow failure criterion

Yield Loci

Failure

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceComparison Resultant stress

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceComparison arching/failure condition

Failure

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceIncipient flow Failure Criterion Implementation

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceFurther Work

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical ScienceFurther workThesis write-up

The Wolfson Centre forBulk Solids Handling TechnologyComputing and Mathematical Science