# Discrete Element Method Modelling of the Diametral Compression of Starch Agglomerates

^{*}

## Abstract

**:**

## 1. Introduction

_{y}is compressive, while the stress component σ

_{x}(in the direction perpendicular to the load) is tensile in locations close to the disc centre and compressive at the upper most locations close to the loading plates. For x = 0 and y = 0, the stresses σ

_{x}and σ

_{y}are the principal stresses σ

_{1}and σ

_{2}, respectively [22]. The tensile strength σ

_{f}of the agglomerates is identified by the maximum tensile stress σ

_{1,max}in the direction perpendicular to the load in the centre of the disc (x = 0, y = 0) [23]:

^{b}to the elastic modulus of particle E can be distinguished: E

^{b}= E [25,26,27], E

^{b}> E [28], and E

^{b}< E [3,29]. For E

^{b}≥ E, the DEM models provide typical brittle behaviour, characterised by a rapid decrease of the force–displacement response [27]. As the E

^{b}/E ratio decreases, the breakage mode evolves from brittle to semi-brittle, with a round force–displacement response [30,31,32].

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Methods

^{−1}up to compaction pressures of σ

_{z}= 38, 76, 114, and 153 MPa (Figure 1a). The height of the tablet after unloading and relaxation, determined by a caliper with an accuracy of 0.01 mm, was 4.8 ± 0.1 mm. The tensile strength was determined via a diametral compression test with a displacement rate of 0.033 mm s

^{−1}. The compression tests were performed immediately after the compaction process to avoid the effect of storage time on the strength. The reference material was PS with a moisture content of 17%, without additives. All variants of the experiments were repeated 10 times.

## 3. Discrete Element Method Setup

_{n}is the contact force, k

_{1}is the loading (plastic) stiffness, k

_{2}is the unloading (elastic) stiffness, k

_{c}is the adhesive stiffness, and δ

_{n}is the overlap in the normal direction (Figure 2a). During unloading, the force f

_{n}decreased to zero at the overlap δ

_{n,}

_{0}. The plastic stiffness k

_{1}was related to the yield strength p

_{y}of a particle as follows [36,37]:

_{n,y}is the yielding overlap, ${r}^{*}={r}_{i}{r}_{j}/({r}_{i}+{r}_{j})$ is the equivalent radius of the contacting particles, and p

_{y,i}and p

_{y,j}are the yield strengths of particles i and j, respectively. The energy dissipation in the normal direction was due to the difference between the loading and unloading stiffness and the elastic stiffness k

_{2}. For unloading and reloading, k

_{2}was related to k

_{1}through the restitution coefficient e [37], as follows:

_{t}was updated incrementally as follows:

_{t})

_{0}is the tangential force at the end of the previous timestep; k

_{t}and δ

_{t}are the stiffness and overlap in the tangential direction, respectively; and μ

_{p-p}is the particle–particle friction coefficient. The stiffness in the tangential direction k

_{t}was assumed to be equal to the stiffness in the normal direction. The velocity-dependent dissipative component ${f}_{t}^{d}$ of the tangential force f

_{t}is defined as follows [37,38]:

_{t}is the relative velocity in the tangential direction.

_{c}has a linear relationship with the adhesion energy density k and the equivalent radius of the contacting particles r

^{*}:

_{n}and v

_{t}are the relative velocities in the normal and tangential directions, respectively; ${k}_{n}^{b}$ and ${k}_{t}^{b}$ are the stiffnesses in the normal and tangential directions, respectively; $A=\pi {r}_{b}^{2}$ and $J=\frac{\pi {r}_{b}^{4}}{2}$ are the area and moment of inertia of the bond cross section, respectively; r

_{b}is the radius of the bond; and Δt is the time increment.

^{b}is:

_{i}and r

_{j}are radii of the contacting particles i and j, respectively.

^{c}or the maximum tangent stress ${\tau}_{\mathrm{max}}^{b}$ exceeds the shear strength τ

^{c}:

^{−3}m s

^{−1}to the assumed value of the agglomeration pressure ${\sigma}_{z}^{c}$ (Figure 3b). After the desired agglomeration pressure was reached, the sample was unloaded with the same velocity (Figure 3c). After complete unloading, the mould was removed, and relaxation of the agglomerate was performed (Figure 3d). Simulations of the diametral compression were performed, with the displacement velocity in the range from 10

^{−5}to 10

^{−3}m s

^{−1}.

_{1}of 3 × 10

^{4}N m

^{−1}was adjusted to provide an in-die agglomerate porosity of ε < 0.1 under the compaction pressure of 153 MPa. For the assumed Young’s modulus of the PS (2.5 × 10

^{3}MPa) [41], the corresponding value of the yielding overlap δ

_{y}(Equation (3)) was 0.0354r. The adopted value of the restitution coefficient (e = 0.5), which is typical for biological materials [42], provided an elastic stiffness coefficient of k

_{2}= 1.2 × 10

^{5}N m

^{−1}.

_{c}was set as 300 N m

^{−1}[43] to match the experimental tensile strength of the agglomerate. For the diametral compression test, the adhesion model was replaced with the parallel BPM to prevent simulations from appearing on secondary adhesive contacts, which might affect the resultant tensile strength of the agglomerates.

_{p-w}of 0.1 was taken as half of the coefficient of the sliding friction of PS against stainless steel [44], in order to account for lubrication with magnesium stearate [45]. The coefficient of particle–particle friction μ

_{p-p}was set to 0.5 to reproduce the typical values of 30°−35° for the angle of internal friction of PS [46]. The coefficient of rolling friction m

_{r}was set as 0.01, in accordance with the best-fit values from similar studies on spherical particles [47].

^{6}. To keep the gravitational force unchanged, the gravitational acceleration was reduced by a factor of 10

^{6}. As shown in [43], scaling the density by a factor of 10

^{6}did not change the shape of the σ

_{1}(ΔL/D) characteristics, and reduced the tensile strength σ

_{f}by 1.2% of the strength of the sample without density scaling. Time integration was performed with steps of 3 × 10

^{−6}s, i.e., 14% of the Rayleigh timestep [48]. The EDEM software package [37] was used for the numerical simulations.

_{ij}in the system of particles averaged over all the contacts in volume V were determined as the dyadic product of the contact force ${f}_{j}^{c}$ vector at contact c and the branch vector ${l}_{i}^{c}$ connecting two contacting particles a and b, according to the concept presented by Christoffersen et al. [49]:

## 4. Results

#### 4.1. Tensile Strength of Agglomerates

_{1}and the diametral deformation ΔL/D, the tensile strength of the agglomerates σ

_{f}during diametral compression, and the breakage mode were performed. These simulations and analyses included the shear strength of the bond τ

^{c}, the tensile strength of the bond σ

^{c}, the Young’s modulus of the bond E

^{b}, and the residual overlap at the instant of bond initiation δ

_{n}

_{,0}.

#### 4.1.1. Impact of Deformation Velocity

^{c}= 10 MPa and E

^{b}= 200 MPa, as well as the deformation velocity in the range from 10

^{−5}to 10

^{−3}m s

^{−1}. The increase of the velocity from 10

^{−5}to 10

^{−4}m s

^{−1}did not change considerably the shape of the σ

_{1}(ΔL/D) characteristic or the tensile strength σ

_{f}. An increase of the velocity to 10

^{−3}m s

^{−1}increased the σ

_{f}by an amount of 4%, as compared with the lowest velocity case (Figure 4). Taking into account the computing time for the simulations, this level of error was considered as acceptable for the purpose of this study.

#### 4.1.2. Impact of the Ratio of Shear to Tensile Strength of the Bond

_{1}and the diametral deformation ΔL/D was not significantly influenced by the change in the τ

^{c}/σ

^{c}ratio (Figure 5a), while the tensile strength of the agglomerates σ

_{f}increased to a saturation value, stabilising for a τ

^{c}/σ

^{c}ratio slightly higher than 1 (Figure 5b). Analysis of the distribution of the bond normal and tangent forces performed for the τ

^{c}/σ

^{c}ratio of 1 indicated that the mean bond tangent force ${\overline{f}}_{t}^{b}$ at ${\sigma}_{1,\mathrm{max}}^{}$ ranged from 0.35 to 0.47 of the mean bond normal tension force ${\overline{f}}_{n}^{b}$ for the ductile and brittle breakage modes, respectively. This is consistent with the experimental findings of Jonsén et al. [23], that tension is the primary failure mode in the diametral compression test and is opposite to the shear primary failure mode in the uniaxial compression test, as reported by He et al. [4].

#### 4.1.3. Impact of Strength and Young’s Modulus of Bond

_{f}increased nonlinearly to a limiting value, indicating a qualitative change in the behaviour of the agglomerates with an increase in the tensile (and shear σ

^{c}= τ

^{c}) strength of the bond (Figure 6a). In the entire range of change of the σ

_{1}and σ

_{f}with the σ

^{c}change, the following two regions were distinguished: (1) an almost linear increase of the σ

_{f}, with an accompanying round and a slowly flattening σ

_{1}(ΔL/D) relationship with a clear maximum (typical for semi-brittle breakage); and (2) the saturation of σ

_{f}with a further increase in σ

^{c}

_{,}with an accompanying growing range of the deformation ΔL/D with a constant value of σ

_{1}(typical for ductile breakage).

^{b}= 100 MPa. With a further increase in Young’s modulus, the σ

_{1}(ΔL/L) characteristics (typical for the semi-brittle breakage mode) evolved towards the brittle mode, i.e., exhibited a sudden drop of σ

_{1}after approaching the peak stress. There was no clear threshold for the transition from semi-brittle to brittle behaviour.

#### 4.1.4. Impact of Ratio of Bond Strength to Young’s Modulus

_{1}(ΔL/L), the transition from ductile to semi-brittle breakage can be attributed to the σ

^{c}/E

^{b}ratio (Figure 7a). For σ

_{z}= 153 MPa, a ratio of σ

^{c}/E

^{b}< 0.1 provided semi-brittle breakage, whereas a ratio of σ

^{c}/E

^{b}> 0.15 provided ductile breakage (Figure 7b).

#### 4.1.5. Impact of Bond Cross-Sectional Area

_{1}(ΔL/L) characteristics for selected values of the ratio of the mean overlap at the instant of bond initiation to the mean particle radius ${\overline{\delta}}_{n,0}/\overline{r}$. The mean overlap at the instant of bond initiation (${\overline{\delta}}_{n,0}$) did not increase linearly with the increase of the compaction pressure σ

_{z}; rather, the increase was slower. Thus, the bond cross-sectional area also exhibited a slower-than-linear increase with the increasing compaction pressure. The consequence of this is discussed in Section 4.2.1. The threshold value of the σ

^{c}/E

^{b}ratio for the semi-brittle and ductile transitions increased with the ${\overline{\delta}}_{n,0}/\overline{r}$ ratio (Figure 8b).

#### 4.1.6. Breakage Modes

_{z}and the σ

^{c}/E

^{b}ratio (Figure 10b). With the increase of the agglomeration pressure and the decrease of the σ

^{c}/E

^{b}ratio, the X-shaped conjugate cracks changed to Y-shaped cracks for moderately compacted agglomerates (σ

_{z}= 76 MPa). A single crack aligned with the direction of the loading occurred for the highest level of the agglomeration pressure and the lowest value of the σ

^{c}/E

^{b}ratio. The gradual change of shape of the crack pattern with the changes of the compaction pressure and the σ

^{c}/E

^{b}ratio obtained in the DEM simulations are consistent with the results of the experimental study of the breakage of three-dimensional (3D)-printed agglomerates performed by Ge et al. [51]. Their study indicates that brittle breakage is typical for dense structures with a high bond stiffness, and that ductile breakage is typical for loose structures with a low bond stiffness.

_{1}during loading was related almost linearly to the mean value of the magnitude of the contact normal force $\left|{\overline{f}}_{n}\right|$ (Figure 11a), as the result of the same value of the contact stiffness k

_{1}and k

_{2}applied for all simulations. Figure 11b presents profiles of the normalized average stress component σ

_{x}/σ

_{x}

_{,max}along the y direction. Negative values correspond to the compressive stress, and positive values correspond to the tension stress. Stress profiles in the y direction were very similar for all three breakage modes: the stress was tensile in the central part of the disc and compressive in locations close to the loading platens. The shape of this stress profile was consistent with the findings of experimental [23], theoretical [22], finite element [52], and DEM [43] studies. These studies have indicated the domination of the tension stress in locations close to centre of the disc, which results in cracking, and domination of the compressive stress in locations close to the loading platens, which results in crushing.

_{1}(ΔL/D) relationships between the ductile, semi-brittle, and brittle breakage modes can be attributed to the difference in the dynamics of bond breakage when approaching the peak of σ

_{1}. Figure 11c illustrates the normalized rate of the breakage of bonds for three breakage modes. For the ductile breakage mode, the rate was almost constant during the entire process of deformation. For the brittle and semi-brittle breakage modes, the maximum of the rate was observed. The brittle and semi-brittle breakage modes were initiated at the instance of the highest increase in the rate of bond breakage. This indicates a very rapid change in the rate of bond breakage in the case of the brittle and semi-brittle breakage modes, and an almost constant rate in the case of the ductile breakage mode. Therefore, it seems that the course of change of the rate of breakage of bonds during deformation can be used to distinguish ductile and semi-brittle behaviour. The difference in the dynamic of breakage of bonds resulted in a difference in the rate of change of the kinetic energy of particles during deformation (Figure 11d). Kinetic energy started to increase rapidly at the instance of the σ

_{1}peak, in the case of the brittle and semi-brittle breakage modes, and increased much more slowly but slightly faster than linearly during the entire process of deformation in the case of the ductile breakage mode.

^{b}/E). In the bond-to-contact elasticity-ratio range of 0.12 to 0.2, the brittle and semi-brittle modes were observed alternately, owing to the effects of other materials and process parameters, such as the compaction pressure, additives, and steaming, which modified the elasticity, strength, and compaction of the tablets (Figure 10). For E

^{b}≥ E, i.e., when the dominating interaction was the elastic deformation of the bonds limited by their relatively low strength (σ

^{c}< 0.01E

^{b}), the breakage appeared as clearly brittle (the case of σ

^{c}/E

^{b}= 0.004 in Figure 10b). Therefore, brittle behaviour appears for high bond stiffness and low strength.

#### 4.2. Effect of Compaction Pressure

^{b}and the bond coordination number BCN on the compaction pressure σ

_{z}were considered as the relationships explaining the effect of the compaction pressure on the tensile strength.

#### 4.2.1. Bond Cross-Sectional Area and Bond Coordination Number

^{b}) was assumed to be equal to the average contact area of the particles, and was approximated as

^{b}(Figure 12a), and the coordination number of the bond, BCN (Figure 12b), exhibited a slower-than-linear increase with the increase of the compaction pressure. The dependences were approximated by the power functions:

#### 4.2.2. Impact of the Effective Bond Cross-Sectional Area

_{1}(ΔL/D) well for the diametral compression of PS agglomerates in the agglomeration-pressure (σ

_{z}) range of 76–153 MPa, for constant values of the bond parameters: E

^{b}= 220 MPa and σ

^{c}= 12 MPa (Figure 13a). In the case of σ

_{z}= 36 MPa, the tensile strength of the bond had to be reduced to 3.6 MPa to fit the experimental data well. A less than three-fold change in the tensile strength of the bond indicates a qualitative change in the binding mechanisms in low and intermediate regions of the strength–pressure relationship, as described by Alderborn [53].

_{z}= 153 MPa (E

^{b}∈ 200–300 MPa, σ

^{c}∈ 10–12 MPa), resulting from the variability of their mechanical characteristics, the applied model provided a decent approximation. To analyse the nonlinear dependence of the tensile strength of the agglomerates on the compaction pressure σ

_{f}(σ

_{z}), according to a uniform formula, σ

^{c}was assumed to be 12 MPa for the entire range of σ

_{z}(Figure 13b). The tensile strength σ

_{f}exhibited a faster-than-linear increase with the increase of the compaction pressure σ

_{z}. The rate of this increase followed the faster-than-linear increase of the effective cross-sectional area of the elastic bonds (ΔA

_{e}) with the increase of the compaction pressure:

^{b}and BCN to the mechanical strength over the entire range of applied values of the compaction pressure, DEM simulations were performed for a series of values of r

_{b}and BCN related to σ

_{z}or ${\sigma}_{z,\mathrm{max}}^{}$, according to the following scheme (Figure 14):

^{2}= 0.998) for all three cases over the entire range of σ

_{z}(Figure 15). The product obtained from cases 2 and 3, which is denoted in Figure 15 as case 4, is as follows:

^{b}and BCN to the mechanical strength of the bulk materials simulated by the BPM. The faster-than-linear increase of the tensile strength σ

_{f}with the increase of the compaction pressure σ

_{z}reflects the increase of the inter-particle contact area to a critical point, as described by Alderborn [53].

## 5. Discussion

^{b}= E separates semi-brittle and brittle breakage. The rate of breakage of the bonds during deformation can be used to distinguish ductile and semi-brittle behaviour. The similar shapes of the experimental and modelled force–displacement relationships, as well as the outlined mechanisms of breakage at the microscale, confirm the applicability of the BPM for simulating the behaviour of agglomerates under compression in a wide range of breakage modes, ranging from brittle to ductile.

_{f}(σ

_{z}) low-, intermediate-, and high-pressure regions. In the low-pressure region, the pressure is too low for the particles to cohere into a compact. In the intermediate-pressure region, the inter-particle contact area increases up to a critical point. In the high-pressure region, the maximal tablet tensile strength is reached. The results of our study correspond to the low- and intermediate-pressure regions. The experimental results indicated that at the compaction-pressure (σ

_{z}) range of 38–153 MPa, the tensile strength increased linearly with the increase of σ

_{z}. Below this σ

_{z}range, obtainment of a stable agglomerate with adequate strength was impossible. The DEM simulations indicated a faster-than-linear increase of σ

_{f}with the increase of σ

_{z}in both the low- and intermediate-pressure regions, owing to the dependence of two micro-variables—the bond cross-section and bond coordination number—on σ

_{z}.

## 6. Conclusions

- Potato starch agglomerates may exhibit a brittle, semi-brittle, or ductile breakage mode, depending on the applied binder. Starch agglomerates with a moisture content of 17% behaved as semi-brittle materials. The addition of sugar increased the tensile strength of the agglomerates and resulted in the brittle breakage mode. The addition of gluten significantly reduced the tensile strength and resulted in the ductile breakage mode.
- The BPM, applied together with the linear elastic–plastic contact model, described the brittle, semi-brittle, or ductile breakage mode, depending on the ratio of the strength to the Young’s modulus of the bond σ
^{c}/E^{b}and the bond-to-contact elasticity ratio E^{b}/E. A low Young’s modulus and high strength of the bond resulted in the ductile breakage mode. A high Young’s modulus of the bond and high compaction resulted in the brittle breakage mode. Intermediate conditions resulted in the semi-brittle breakage mode. - The tensile strength of agglomerates determined experimentally increased linearly with the increase of the compaction pressure. The tensile strength determined via DEM modelling exhibited a faster-than-linear increase with the increase of the compaction pressure, which resulted from the faster-than-linear increase of the product of two micro-variables—the bond cross-sectional area A
^{b}and the bond coordination number BCN—with the increase of the compaction pressure. - The bonded-particle model is promising for DEM simulations of the diametral compression tests of agglomerates.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Constitutive linear elastic–plastic contact models: (

**a**) linear adhesion model following concept of Luding [35], (

**b**) parallel BPM.

**Figure 3.**Stages of the simulation: (

**a**) filling, (

**b**) compaction, (

**c**) unloading, (

**d**) relaxation, and (

**e**) diametral compression modelled with use of EDEM software.

**Figure 4.**Effect of the displacement velocity V on the σ

_{1}(ΔL/D) characteristic of agglomerates for σ

^{c}= 10 MPa and E

^{b}= 200 MPa.

**Figure 5.**Effect of the τ

^{c}/σ

^{c}ratio on the tensile strength of agglomerates for σ

^{c}= 10 MPa and E

^{b}= 200 MPa: (

**a**) tension stress vs. diametral deformation relationships σ

_{1}(ΔL/D), and (

**b**) tensile strength vs. bond shear strength-to-tensile strength relationship σ

_{f}(τ

^{c}/σ

^{c}).

**Figure 6.**Tension stress vs. diametral deformation relationships σ

_{1}(ΔL/D): (

**a**) effect of the bond strength σ

^{c}= τ

^{c}for E

^{b}= 200 MPa; (

**b**) effect of the bond’s Young’s modulus for σ

^{c}= τ

^{c}= 10 MPa.

**Figure 7.**Effect of the σ

^{c}/E

^{b}ratio on the breakage behaviour of the agglomerates for σ

_{z}= 153 MPa: (

**a**) comparison of the tension stress vs. diametral deformation σ

_{1}(ΔL/D) for ductile and semi-brittle breakage of the agglomerates; (

**b**) (E

^{b}, σ

^{c}) map of the ductile and semi-brittle behaviour of the agglomerates.

**Figure 8.**Effect of the σ

^{c}/E

^{b}ratio on the breakage behaviour of the agglomerates during diametral compression: (

**a**) comparison of the tension stress vs. diametral deformation σ

_{1}(ΔL/D) for the ductile and semi-brittle breakage modes at E

^{b}= 200 MPa; (

**b**) (σ

^{c}/E

^{b}, ${\overline{\delta}}_{n,0}/\overline{r}$) map of the ductile and semi-brittle behaviour of the agglomerates.

**Figure 9.**Effects of additives and pretreatment on the σ

_{1}(ΔL/L) relationships during the diametral compression of the PS agglomerates: (

**a**) without steaming and (

**b**) with steaming. The bars indicate the standard deviation.

**Figure 10.**Profiles of the ductile, semi-brittle, and brittle breakage modes: (

**a**) experimental and (

**b**) simulated for σ

^{c}= 10 MPa.

**Figure 11.**Relationships between micro- and macro-variables for brittle (σ

^{c}= 18 MPa, E

^{b}= 400 MPa), semi-brittle (σ

^{c}= 7.5 MPa, E

^{b}= 200 MPa), and ductile (σ

^{c}= 10 MPa, E

^{b}= 25 MPa) breakage modes: (

**a**) dependence of σ

_{1}on the mean value of the magnitude of the contact normal force $\left|{\overline{f}}_{n}\right|$; (

**b**) profiles of the normalized averaged stress component σ

_{x}/σ

_{x,}

_{max}along the y direction; (

**c**) the normalized rate of bond breakages $\mathsf{\Delta}N/\mathsf{\Delta}{L}_{0}\cdot D/{N}_{0}$ vs. diametral deformation, where ΔN is the number of bonds broken during the diametral deformation increment ΔL

_{0}/D of 3.92 × 10

^{−5}, and N

_{0}is the initial number of bonds; (

**d**) normalized kinetic energy of particles E

_{k}/E

_{k,}

_{0}vs. diametral deformation.

**Figure 12.**Effects of the compaction pressure on (

**a**) the bond cross-sectional area A

^{b}, as well as (

**b**) the coordination number CN and the bond coordination number BCN.

**Figure 13.**Experimental and DEM-simulated relationships: (

**a**) tension stress σ

_{1}vs. deformation ΔL/D; (

**b**) tensile strength σ

_{f}vs. compaction pressure. The bars indicate the standard deviation.

**Figure 15.**Change of normalized tensile strength $\mathsf{\Delta}{\sigma}_{f}^{}(\mathsf{\Delta}{A}_{e}^{})/\mathsf{\Delta}{\sigma}_{f}^{}(\mathsf{\Delta}{A}_{e,\mathrm{max}}^{})$ vs. change of the normalized effective bond cross-sectional area $\mathsf{\Delta}{A}_{e}^{}/\mathsf{\Delta}{A}_{e,\mathrm{max}}^{}$.

Parameter | Symbol | Value |
---|---|---|

Container | ||

Radius (mm) | R | 1.25 |

Height (mm) | H | 12 |

Solid density (kg m^{−3}) | ρ | 7800 |

Young’s modulus (MPa) | E | 1.561 × 10^{6} |

Poisson’s ratio | ν | 0.3 |

Particles | ||

Particles number | 120,000 | |

Mean particle radius (μm) | r | 20 |

Standard deviatio of particle radius (μm) | r_{sd} | 7.5 |

Particle radius range (μm) | 5–36 | |

Particle solid density (kg m^{−3}) | ρ | 1540 |

Young’s modulus (MPa) | E | 2.5 × 10^{3} |

Poisson’s ratio | ν | 0.25 |

Yield strength (MPa) | p_{y} | 3 × 10^{2} |

Mean loading (plastic) stiffness (N m^{−1}) | k_{1} | 3 × 10^{4} |

Mean unloading (elastic) stiffness (N m^{−1}) | k_{2} | 1.2 × 10^{5} |

Mean adhesion stiffness (N m^{−1}) | k_{c} | 300 |

Restitution coefficient | e | 0.5 |

Particle–particle friction coefficient | μ_{p-p} | 0.5 |

Particle–wall friction coefficient | μ_{p-w} | 0.1 |

Rolling friction coefficient | m_{r} | 0.01 |

Bond radius (μm) | r_{b} | 1–8.2 |

Bond tension strength (MPa) | σ^{c} | 2–70 |

Bond shear strength (MPa) | τ^{c} | 1–40 |

Bond Young’s modulus (MPa) | E^{b} | 20–2500 |

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## Share and Cite

**MDPI and ACS Style**

Horabik, J.; Wiącek, J.; Parafiniuk, P.; Stasiak, M.; Bańda, M.; Kobyłka, R.; Molenda, M.
Discrete Element Method Modelling of the Diametral Compression of Starch Agglomerates. *Materials* **2020**, *13*, 932.
https://doi.org/10.3390/ma13040932

**AMA Style**

Horabik J, Wiącek J, Parafiniuk P, Stasiak M, Bańda M, Kobyłka R, Molenda M.
Discrete Element Method Modelling of the Diametral Compression of Starch Agglomerates. *Materials*. 2020; 13(4):932.
https://doi.org/10.3390/ma13040932

**Chicago/Turabian Style**

Horabik, Józef, Joanna Wiącek, Piotr Parafiniuk, Mateusz Stasiak, Maciej Bańda, Rafał Kobyłka, and Marek Molenda.
2020. "Discrete Element Method Modelling of the Diametral Compression of Starch Agglomerates" *Materials* 13, no. 4: 932.
https://doi.org/10.3390/ma13040932