EEPA Parameter Estimator Model

The EEPA model includes an Estimated Parameters section to help understand the behavior of the bulk material being defined.

Based on the model parameters inputted and the particle properties a Bond Number is calculated. The Bond Number (Bo) positively correlates with the cohesiveness of the material interaction, where:
B o < 0.1 C o h e s i o n l e s s I n t e r a c t i o n B o > 10 V e r y C o h e s i v e I n t e r a c t i o n MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGcb WaaSbaaSqaaiaad+gaaeqaaOGaaGPaVlabgYda8iaaicdacaGGUaGa aGymaiaaykW7caaMc8UaaGPaVlaaykW7cqGHshI3caaMc8UaaGPaVl aaykW7caWGdbGaam4BaiaadIgacaWGLbGaam4CaiaadMgacaWGVbGa amOBaiaadYgacaWGLbGaam4CaiaadohacaaMc8Uaamysaiaad6gaca WG0bGaamyzaiaadkhacaWGHbGaam4yaiaadshacaWGPbGaam4Baiaa d6gaaeaacaWGcbWaaSbaaSqaaiaad+gaaeqaaOGaaGPaVlabg6da+i aaykW7caaIXaGaaGimaiaaykW7caaMc8UaaGPaVlaaykW7caaMc8Ua eyO0H4TaaGPaVlaaykW7caaMc8UaaGPaVlaadAfacaWGLbGaamOCai aadMhacaaMc8Uaam4qaiaad+gacaWGObGaamyzaiaadohacaWGPbGa amODaiaadwgacaaMc8Uaamysaiaad6gacaWG0bGaamyzaiaadkhaca WGHbGaam4yaiaadshacaWGPbGaam4Baiaad6gaaaaa@90E3@

The cohesiveness is stated alongside the Bond Number value.

The Bond Number (Capece, 2015) is derived from the ratio of the cohesive forces, Fcohesion to the weight of the particles, Wg:

B o = F c o h e s i o n W g MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaWGVbaabeaakiabg2da9maalaaabaGaamOramaaBaaaleaa caWGJbGaam4BaiaadIgacaWGLbGaam4CaiaadMgacaWGVbGaamOBaa qabaaakeaacaWGxbWaaSbaaSqaaiaadEgaaeqaaaaaaaa@4371@

The cohesive force is defined as:

F c o h e s i o n = 2 3 γ r 2 π Δ + f 0 MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaWGJbGaam4BaiaadIgacaWGLbGaam4CaiaadMgacaWGVbGa amOBaaqabaGccqGH9aqpdaWcaaqaaiaaikdaaeaacaaIZaaaamaaka aabaWaaSaaaeaacqaHZoWzcaWGYbaabaGaaGOmaaaaaSqabaGccqaH apaCcqGHuoarcqGHRaWkdaabdaqaaiaadAgadaWgaaWcbaGaaGimaa qabaaakiaawEa7caGLiWoaaaa@4D97@

Where γ is the mean normal overlap, r is the mean particle radius, Δ is the surface energy and fo is the constant pull-off force. The Bond Number will be calculated live as model parameters are populated:


 
In addition to the Bond Number, critical Time Step information is displayed in the Estimated Properties, where:
  1. Current Interaction Timestep

    Shows the maximum allowable Time Step for the current interaction parameters.

  2. Recommended Simulation Timestep

    Shows the maximum allowable Time Step for all interactions. This is found by finding the smallest Current Critical Time step for each of the interactions.

  3. Critical Timestep Interaction

    States which interaction has the smallest Time Step, and is therefore the critical interaction.

Tip: Use the Minimum Critical Time Step in the Solver when running the simulation.

Each interaction’s Time Step is found using the following equation (O'Sullivan, 2004):

Δ t = 0.17 m / k 2 MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyiLdqKaam iDaiabg2da9iaaykW7caaIWaGaaiOlaiaaigdacaaI3aWaaOaaaeaa caWGTbGaai4laiaadUgadaWgaaWcbaGaaGOmaaqabaaabeaaaaa@415B@

Where Δt is the Time Step, m is the mean particle mass and k2 is the unloading/reloading stiffness. k2 is defined as:

k 2 = 1 1 λ p k 1 MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4AamaaBa aaleaacaaIYaaabeaakiabg2da9iaaykW7daWcaaqaaiaaigdaaeaa caaIXaGaeyOeI0Iaeq4UdW2aaSbaaSqaaiaadchaaeqaaaaakiaadU gadaWgaaWcbaGaaGymaaqabaaaaa@4191@