A Physics-Informed Assembly of Feed-Forward Neural Network Engines to Predict Inelasticity in Cross-Linked Polymers.

In solid mechanics, data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and accuracy. However, the implementation of machine-learned approaches in material modeling has been modest due to the high-dimensionality of the data space, the significant size of missing data, and limited convergence. This work proposes a framework to hire concepts from polymer science, statistical physics, and continuum mechanics to provide super-constrained machine-learning techniques of reduced-order to partly overcome the existing difficulties. Using a sequential order-reduction, we have simplified the 3D stress-strain tensor mapping problem into a limited number of super-constrained 1D mapping problems. Next, we introduce an assembly of multiple replicated neural network learning agents (L-agents) to systematically classify those mapping problems into a few categories, each of which were described by a distinct agent type. By capturing all loading modes through a simplified set of dispersed experimental data, the proposed hybrid assembly of L-agents provides a new generation of machine-learned approaches that simply outperform most constitutive laws in training speed, and accuracy even in complicated loading scenarios. Interestingly, the physics-based nature of the proposed model avoids the low interpretability of conventional machine-learned models.

Necking of double-network gels: Constitutive modeling with microstructural insight.

In this study, a constitutive model is proposed to describe the necking behavior of double network (DN) gels based on statistical micromechanics of interpenetrating polymer networks. Accordingly, the constitutive response of DN gels in large deformations has been divided into three zones, i.e., prenecking, necking, and postnecking. The behavior of the DN gel is dominated by the behavior of the first and the second networks in each stage. In a previous study, we described how the destruction of the first network can govern the inelastic effects during the prenecking stage. Here, we elucidate the role of the second network to govern the material behavior in the necking and postnecking stages. To incorporate the effect of necking, the material behavior at each zone is described through the competition of three mechanisms that control the rearrangement of the two networks. Here, we challenge a general simplifying assumption in the modeling of DN gels, which considers the second network to be fully elastic. The recent experimental observations show the reduction of energy dissipation in the first network after necking initiation due to the localization of the damage in an active zone. Thus, we assumed that the chains of the second network contribute to the energy dissipation of the matrix by keeping the connection between the fragments of the first network. The proposed model has been validated in all three stages against different sets of experimental data on the uniaxial cyclic tensile behavior of DN gels. Moreover, the initiation and propagation of necking instability have been comprehensively illustrated through a finite-element implementation of the proposed model.

Improved approximations of non-Gaussian probability, force, and energy of a single polymer chain.

The mechanical behavior of polymers such as their probability density function (PDF), strain energy, and entropic force, has long been described by the non-Gaussian statistical model. Non-Gaussian models are often approximated by the Kuhn-Grün (KG) distribution function, which is derived from the first-order approximation of the complex Rayleigh's exact Fourier integral distribution. The KG function is widely accepted in polymer physics, where the non-Gaussian theory is often used to describe energy of the chains with various flexibility ratios. However, the KG function is shown to be relevant only for long chains and becomes extremely inaccurate for chains with fewer than 40 segments. In comparison to the KG model, other approximations of the non-Gaussian statistical model are often less accurate, and those with higher accuracy are usually too complex to be implemented in large-scale simulations. Here a new accurate approximation of the non-Gaussian PDF, entropic force, and strain energy of a single chain subsequently is developed to describe the mechanics of a polymer chain. With a similar level of complexity, the presented approximations of non-Gaussian PDF, strain energy, and entropic force are at least 10 times more accurate than KG approximations and thus are an excellent alternative option to be used in micromechanical constitutive models.

PEGylation on mixed monolayer gold nanoparticles: Effect of grafting density, chain length, and surface curvature.

PEGylation on nanoparticles (NPs) is widely used to prevent aggregation and to mask NPs from the fast clearance system in the body. Understanding the molecular details of the PEG layer could facilitate rational design of PEGylated NPs that maximize their solubility and stealth ability without significantly compromising the targeting efficiency and cellular uptake. Here, we use molecular dynamics (MD) simulation to understand the structural and dynamic the PEG coating of mixed monolayer gold NPs. Specifically, we modeled gold NPs with PEG grafting densities ranging from 0-2.76chain/nm2, chain length with 0-10 PEG monomers, NP core diameter from 5nm to 500nm. It is found that the area accessed by individual PEG chains gradually transits from a "mushroom" to a "brush" conformation as NP surface curvature become flatter, whereas such a transition is not evident on small NPs when grafting density increases. It is shown that moderate grafting density (∼1.0chain/nm2) and short chain length are sufficient enough to prevent NPs from aggregating in an aqueous medium. The effect of grafting density on solubility is also validated by dynamic light scattering measurements of PEGylated 5nm gold NPs. With respect to the shielding ability, simulations predict that increase either grafting density, chain length, or NP diameter will reduce the accessibility of the protected content to a certain size molecule. Interestingly, reducing NP surface curvature is estimated to be most effective in promoting shielding ability. For shielding against small molecules, increasing PEG grafting density is more effective than increasing chain length. A simple model that includes these three investigated parameters is developed based on the simulations to roughly estimate the shielding ability of the PEG layer with respect to molecules of different sizes. The findings can help expand our current understanding of the PEG layer and guide rational design of PEGylated gold NPs for a particular application by tuning the PEG grafting density, chain length, and particle size.

Lipid Flip-Flop and Pore Nucleation on Zwitterionic Bilayers are Asymmetric under Ionic Imbalance.

Lipid flip-flop and its associated transient pore formation are key thermodynamic properties of living cell membranes. However, there is a lack of understanding of whether ionic imbalance that exists ubiquitously across cell membranes affects lipid flip-flop and its associated functions. Potential of mean force calculations show that the free-energy barrier of lipid flip-flop on the extracellular leaflet reduces with the presence of ionic imbalance, whereas the barrier on the intracellular leaflet is generally not affected. The linear decrease of the activation energy of lipid flip-flop on the extracellular leaflet is consistent with the experimentally measured conductance-voltage relationship of zwitterionic lipid bilayers. This suggests: 1) lipid flip-flop has a directionality under physiological conditions and phospholipids accumulate at a rate on the order of 105 µm-2 h-1 on the cytoplasmic side of cell membranes; 2) ion permeation across a lipid membrane is moderated by lipid flip-flop; 3) the energy barrier of pore formation is aligned with the weaker leaflet that has a lower energy of lipid flip-flop. The asymmetry of lipid flip-flop and pore nucleation may have substantial implications for protein translocation, signaling, enzymatic activities, vesicle fusion, and transportation of biomolecules on cell membranes.

Micromechanical model for isolated polymer-colloid clusters under tension.

Binary polymer-colloid (PC) composites form the majority of biological load-bearing materials. Due to the abundance of the polymer and particles, and their simple aggregation process, PC clusters are used broadly by nature to create biomaterials with a variety of functions. However, our understanding of the mechanical features of the clusters and their load transfer mechanism is limited. Our main focus in this paper is the elastic behavior of close-packed PC clusters formed in the presence of polymer linkers. Therefore, a micromechanical model is proposed to predict the constitutive behavior of isolated polymer-colloid clusters under tension. The mechanical response of a cluster is considered to be governed by a backbone chain, which is the stress path that transfers most of the applied load. The developed model can reproduce the mean behavior of the clusters and is not dependent on their local geometry. The model utilizes four geometrical parameters for defining six shape descriptor functions which can affect the geometrical change of the clusters in the course of deformation. The predictions of the model are benchmarked against an extensive set of simulations by coarse-grained-Brownian dynamics, where clusters with different shapes and sizes were considered. The model exhibits good agreement with these simulations, which, besides its relative simplicity, makes the model an excellent add-on module for implementation into multiscale models of nanocomposites.

Constitutive modeling of strain-induced crystallization in filled rubbers.

Strain-induced crystallization is a unique crystallization process taking place solely in polymers subjected to large deformations. It plays a major role for reinforcement and improvement of mechanical properties of polymers with a high regularity of the molecular structure. In this paper, we develop a micromechanical model for the strain-induced crystallization in filled rubbers. Accordingly, the strain-induced crystallization is considered as a process triggered by fully stretched and continued by semistretched polymer chains. The model extends the previously proposed network evolution model [Dargazany and Itskov, Int. J. Solids Struct. 46, 2967 (2009)] and can thus, in addition to the stress upturn and evolution of crystallinity, take into account several inelastic features of filled rubbers, such as the Mullins effect, permanent set, and induced anisotropy. Finally, the accuracy of the model is verified against different set of experimental data both with respect to the stress-strain and crystallization-strain relations. The model exhibits good agreement with the experimental results, which, besides its relative simplicity, makes it a good option for finite-element implementations.

Constitutive modeling of the Mullins effect and cyclic stress softening in filled elastomers.

The large strain behavior of filled rubbers is characterized by the strong Mullins effect, permanent set, and induced anisotropy. Strain controlled cyclic tests also exhibit a pronounced hysteresis as a strain rate independent phenomenon. Prediction of these inelastic features in elastomers is an important challenge with immense industrial and technological relevance. In the present paper, a micromechanical model is proposed to describe the inelastic features in the behavior of filled elastomers. To this end, the previously developed network decomposition concept [Dargazany and Itskov, Int. J. Solids Struct. 46, 2967 (2009)] is extended and an additional network (CP network) is added to the classical elastic rubber (CC) and polymer-filler (PP) networks. The new network is considered to account for the damage of filler aggregates in the cyclic deformation as the source of hysteresis energy loss. The accuracy of the resulting model is evaluated in comparison to a new set of experimental data.

Yield behavior of colloidal aggregates due to combined tensile-bending loads.

In this contribution, the yield behavior of a strongly flocculated colloidal structure subjected to a tensile-bending load is micromechanically modeled. The yielding of a cluster is assumed to be triggered by the failure of one bond (critical bond) and accompanied by massive breakage of further bonds. Thus, identifying the position of the critical bond and evaluating its yield force are the main goals of this study. Interparticle bonds are considered as flexible nanoscale bridges which fail when the force applied on them reaches a critical value. The yield of the critical bonds can result from both tensile and bending stresses. By means of the yield stresses in the critical bonds, the yield force of the whole cluster can be calculated.