Linear Cohesion V2 Model

The Linear Cohesion V2 contact model is an enhancement of the Linear Cohesion model and was made accessible for the first time in EDEM version 2017.2) owing to its improved performance for non-uniform particle size distributions.

Similar to the Linear Cohesion model, this modifies the Base contact model by adding a normal cohesion force. This force is described as follows:

F = k A MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiabg2 da9iaadUgacaWGbbaaaa@397C@

Where A is calculated as:

A=π*RadiusofOverlapSquared MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiabg2 da9iabec8aWjaacQcacaWGsbGaamyyaiaadsgacaWGPbGaamyDaiaa dohacaWGVbGaamOzaiaad+eacaWG2bGaamyzaiaadkhacaWGSbGaam yyaiaadchacaWGtbGaamyCaiaadwhacaWGHbGaamOCaiaadwgacaWG Kbaaaa@4E85@

However, in this model, the radius of overlap squared is calculated as:

RadiusofOverlapSquared= R 1 * R 2 R 1 + R 2 *normalOverlap MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuaiaadg gacaWGKbGaamyAaiaadwhacaWGZbGaam4BaiaadAgacaWGpbGaamOD aiaadwgacaWGYbGaamiBaiaadggacaWGWbGaam4uaiaadghacaWG1b GaamyyaiaadkhacaWGLbGaamizaiabg2da9maalaaabaGaamOuamaa BaaaleaacaaIXaaabeaakiaacQcacaWGsbWaaSbaaSqaaiaaikdaae qaaaGcbaGaamOuamaaBaaaleaacaaIXaaabeaakiabgUcaRiaadkfa daWgaaWcbaGaaGOmaaqabaaaaOGaaiOkaiaad6gacaWGVbGaamOCai aad2gacaWGHbGaamiBaiaad+eacaWG2bGaamyzaiaadkhacaWGSbGa amyyaiaadchaaaa@60E7@
 

Where R1 and R2 are the radii of the particles in contact in cases where the element 2 is a Geometry. 

R 2 >> R 1 ,andtherefore,RadiusofOverlapSquared R 1 *normalOverlap MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuamaaBa aaleaacaaIYaaabeaakiabg6da+iabg6da+iaadkfadaWgaaWcbaGa aGymaaqabaGccaGGSaGaamyyaiaad6gacaWGKbGaaGPaVlaadshaca WGObGaamyzaiaadkhacaWGLbGaamOzaiaad+gacaWGYbGaamyzaiaa cYcacaaMc8UaamOuaiaadggacaWGKbGaamyAaiaadwhacaWGZbGaam 4BaiaadAgacaWGpbGaamODaiaadwgacaWGYbGaamiBaiaadggacaWG WbGaam4uaiaadghacaWG1bGaamyyaiaadkhacaWGLbGaamizaiabgI Ki7kaadkfadaWgaaWcbaGaaGymaaqabaGccaGGQaGaamOBaiaad+ga caWGYbGaamyBaiaadggacaWGSbGaam4taiaadAhacaWGLbGaamOCai aadYgacaWGHbGaamiCaaaa@6FE2@

k is a cohesion energy density with units Jm-3.

This means that, for the same input parameters, the ratio between the forces calculated with Linear cohesion V2 (FV2) and Linear Cohesion (F) models will be as follows:

F V2 F = 1 2 R 2 R 1 + R 2 MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGgbWaaSbaaSqaaiaadAfacaaIYaaabeaaaOqaaiaadAeaaaGaeyyp a0ZaaSaaaeaacaaIXaaabaGaaGOmaaaadaWcaaqaaiaadkfadaWgaa WcbaGaaGOmaaqabaaakeaacaWGsbWaaSbaaSqaaiaaigdaaeqaaOGa ey4kaSIaamOuamaaBaaaleaacaaIYaaabeaaaaaaaa@4237@

In the case of uniform particle size distribution: 

F V 2 F = 0.25 MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGgbWaaSbaaSqaaiaadAfacaaIYaaabeaaaOqaaiaadAeaaaGaeyyp a0JaaGimaiaac6cacaaIYaGaaGynaaaa@3D55@

In this case, the cohesive force calculated in the Linear Cohesive V2 model is therefore four times smaller than the one calculated in the Linear Cohesive model (for a uniform particle size distribution).

In cases where element 2 is a Geometry, the force is two times smaller as follows:

F V 2 F = 1 2 MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGgbWaaSbaaSqaaiaadAfacaaIYaaabeaaaOqaaiaadAeaaaGaeyyp a0ZaaSaaaeaacaaIXaaabaGaaGOmaaaaaaa@3BF5@

Interaction Configurable Parameters Position
Particle to Particle, Particle to Geometry Click the + icon to add cohesion to particle-particle or particle-geometry interactions. Set the energy density for each interaction. Energy density is the scaling function for the cohesiveness of the material. The SI units of energy density are J/m3. Any