Generalized loading-unloading contact laws for elasto-plastic spheres with bonding strength

Abstract

We present generalized loading-unloading contact laws for elasto-plastic spheres with bonding strength. The proposed mechanistic contact laws are continuous at the onset of unloading by means of a regularization term, in the spirit of a cohesive zone model, that introduces a small and controllable error in the conditions for interparticle breakage. This continuity property is in sharp contrast with the behavior of standard mechanistic loading and unloading contact theories, which exhibit a discontinuity at the onset of unloading when particles form solid bridges during plastic deformation. The formulation depends on five material properties, namely two elastic properties (Young's modulus and Poisson's ratio), two plastic properties (a plastic stiffness and a power-law hardening exponent) and one fracture mechanics property (fracture toughness), and its predictions are in agreement with detailed finite-element simulations. The numerical robustness and efficiency of the proposed formulation are borne out by performing three-dimensional particle mechanics static calculations of microstructure evolution during the three most important steps of powder die-compaction, namely during compaction, unloading, and ejection. These simulations reveal the evolution, up to relative densities close to one, of microstructural features, process variables and compact mechanical attributes which are quantitatively similar to those experimentally observed and in remarkable agreement with the (semi-)empirical formulae reported in the literature.

Quantification of lubrication and particle size distribution effects on tensile strength and stiffness of tablets

“…Furthermore, the elusidation of the mechanistic basis of these relationships and how lubrication conditions affect particle properties and solid brigde formation during compaction are desirable for fundamentaly understanding the achievable design space map. Thus, particle mechanics simulations capable of describing strength formation and evolution during the compaction process are desirable Gonzalez andCuitiño (2012, 2016); Yohannes et al (2016Yohannes et al ( , 2017; Gonzalez (2017), if beyond the scope of this paper. Figure 12: Comparsion of the validation experiments to the model predictions for (a) elastic modulus and (b) tensile strength of spray-dried lactose tablets as a function of relative density (cases 24 (in black) and 33 (in blue) in Table 1).…”

Loading-unloading contact law for micro-crystalline cellulose particles under large deformations

“…We close by pointing out that the proposed semi-empirical mechanistic contact law is relevant to three-dimensional particle mechanics calculations (Gonzalez & Cuitiño, 2012;Yohannes et al, 2016Yohannes et al, , 2017Gonzalez et al, 2018;Gonzalez, 2019). Therefore, the work presented in this paper, in combination with these detailed calculations, can contribute to develop microstructure-mediated process-structure-property-performance interrelationships and, thus, to establish the relationship between particle-level material properties and tablet performance.…”

“…This formulation assumes elastic behavior, approximated by Hooke's law, and Irwin's fracture mechanics to describe elastic recovery of the deformed spheres and the breakage of solid bridges. Gonzalez (2019) developed generalized loading-unloading contact laws for elasto-plastic spheres with bonding strength, which are continuous at the onset of unloading by means of a regularization term, in the spirit of a cohesive zone model. These contact laws are updated incrementally to account for strain path dependency and have been shown to be numerically robust, efficient, and mechanistically sound in three-dimensional particle mechanics static calculations.…”

“…Here we endow the master contact law for micro-crystalline cellulose particles, proposed in Section 5, with elastic relaxation during unloading. Specifically, we follow Gonzalez (2019) and modify Eqn. (16) accordingly, i.e.…”

Statistical characterization of microstructure evolution during compaction of granular systems composed of spheres with hardening plastic behavior

“…Therefore, the elucidation of the relationship between particle properties, granular morphology, loading conditions, and microstructural features developed during compaction is desirable for fundamentally understanding the achievable design space map, which in turn allows for optimizing performance. Mechanistic continuum models, such as such as the granular micromechanics approach [3][4][5][6][7], and discrete models, such as the particle mechanics approach [8][9][10][11][12], capable of describing strength formation and microstructure evolution during the compaction process are of great interest. In this communication, we restrict attention to die compaction of monodisperse plastic spheres that exhibit power-law plastic hardening behavior.…”