More Like this

1. A multiscale phase field fracture approach based on the non-affine microsphere model for rubber-like materials

   https://doi.org/10.1016/j.cma.2023.115982  

   Arunachala, Prajwal Kammardi; Abrari Vajari, Sina; Neuner, Matthias; Linder, Christian (May 2023, Computer Methods in Applied Mechanics and Engineering)

   - (Ed.)

   Rubber-like materials have a broad scope of applications due to their unique properties like high stretchability and increased toughness. Hence, computational models for simulating their fracture behavior are paramount for designing them against failures. In this study, the phase field fracture approach is integrated with a multiscale polymer model for predicting the fracture behavior in elastomers. At the microscale, damaged polymer chains are modeled to be made up of a number of elastic chain segments pinned together. Using the phase field approach, the damage in the chains is represented using a continuous variable. Both the bond stretch internal energy and the entropic free energy of the chain are assumed to drive the damage, and the advantages of this assumption are expounded. A framework for utilizing the non-affine microsphere model for damaged systems is proposed by considering the minimization of a hypothetical undamaged free energy, ultimately connecting the chain stretch to the macroscale deformation gradient. At the macroscale, a thermodynamically consistent formulation is derived in which the total dissipation is assumed to be mainly due to the rupture of molecular bonds. Using a monolithic scheme, the proposed model is numerically implemented and the resulting three-dimensional simulation predictions are compared with existing experimental data. The capability of the model to qualitatively predict the propagation of complex crack paths and quantitatively estimate the overall fracture behavior is verified. Additionally, the effect of the length scale parameter on the predicted fracture behavior is studied for an inhomogeneous system. 

   more » « less
2. A kinetic theory for the mechanics and remodeling of transient anisotropic networks

   https://doi.org/10.1016/j.jmps.2024.105713  

   Vernerey, Franck J; Rezaei, Behnam; Lamont, Samuel C (September 2024, Journal of the Mechanics and Physics of Solids)

   We present a statistically-based theoretical framework to describe the mechanical response of dynamically crosslinked semi-flexible polymer networks undergoing finite deformation. The theory starts from a statistical description, via a distribution function, of the chain conformation and orientation. Assuming a so-called tangent affine deformation of the chains, this distribution is then allowed to evolve in time due to a combination of elastic network distortion and a permanent chain reconfiguration enabled by dynamic crosslinks. After presenting the evolution law for the chain distribution function, we reduce the theory to the evolution of the network conformation tensor in both its natural and current state. With this model, we use classical thermodynamics to determine how the stored elastic energy, energy dissipation, and true stress evolve in terms of the network conformation. We show that the model degenerates to classical anisotropic hyperelastic models when crosslinks are permanent, while we recover the classical form of the transient network theory (that describes hyper-viscoelasticity) when chains are fully flexible. Theoretical predictions are then illustrated and compared to the literature for both basic model problems and biomechanically relevant situations 

   more » « less
3. Statistical mechanics of chromosomes: in vivo and in silico approaches reveal high-level organization and structure arise exclusively through mechanical feedback between loop extruders and chromatin substrate properties

   https://doi.org/10.1093/nar/gkaa871  

   He, Yunyan; Lawrimore, Josh; Cook, Diana; Van Gorder, Elizabeth Erin; De Larimat, Solenn Claire; Adalsteinsson, David; Forest, M Gregory; Bloom, Kerry (October 2020, Nucleic Acids Research)

   null (Ed.)

   Abstract The revolution in understanding higher order chromosome dynamics and organization derives from treating the chromosome as a chain polymer and adapting appropriate polymer-based physical principles. Using basic principles, such as entropic fluctuations and timescales of relaxation of Rouse polymer chains, one can recapitulate the dominant features of chromatin motion observed in vivo. An emerging challenge is to relate the mechanical properties of chromatin to more nuanced organizational principles such as ubiquitous DNA loops. Toward this goal, we introduce a real-time numerical simulation model of a long chain polymer in the presence of histones and condensin, encoding physical principles of chromosome dynamics with coupled histone and condensin sources of transient loop generation. An exact experimental correlate of the model was obtained through analysis of a model-matching fluorescently labeled circular chromosome in live yeast cells. We show that experimentally observed chromosome compaction and variance in compaction are reproduced only with tandem interactions between histone and condensin, not from either individually. The hierarchical loop structures that emerge upon incorporation of histone and condensin activities significantly impact the dynamic and structural properties of chromatin. Moreover, simulations reveal that tandem condensin–histone activity is responsible for higher order chromosomal structures, including recently observed Z-loops. 

   more » « less
4. Elastic particle model for coil-stretch transition of dilute polymers in an elongational flow

   https://doi.org/10.1017/jfm.2024.196  

   Gao, Tong (April 2024, Journal of Fluid Mechanics)

   The phenomenon of the ‘coil-stretch’ (C-S) transition, wherein a long-chain polymer initially in a coiled state undergoes a sudden configuration change to become fully stretched under steady elongational flows, has been widely recognized. This transition can display intricate hysteresis behaviours under specific critical conditions, giving rise to unique rheological characteristics in dilute polymer solutions. Historically, microscopic stochastic models and Brownian dynamics simulations have shed light on the underlying mechanisms of the transition by uncovering bistable configurations of polymer chains. Following the initial work by Cerf (J. Chem. Phys., vol. 20, 1952, pp. 395–402), we introduce a continuum model in this study to investigate the C-S transition in a constant uniaxial elongational flow. Our approach involves approximating the unfolding process of the polymer chain as an axisymmetric deformation of an elastic particle. We make the assumption that the particle possesses uniform material properties, which can be represented by a nonlinear, strain-hardening constitutive equation to replicate the finite extensibility of the polymer chain. Subsequently, we analytically solve for the steady-state deformation using a polarization method. By employing this reduced model, we effectively capture the C-S transition and establish its specific correlations with material and geometric properties. The hysteresis phenomena can be comprehended through a force-balance analysis, which involves comparing the externally applied viscous forces with the intrinsic elastic responsive forces. We demonstrate that our model, while simple, unveils rich elastohydrodynamics of the C-S transition. 

   more » « less
5. A general model for the ideal chain length distributions of polymers made with reversible deactivation

   https://doi.org/10.1039/D1PY01331A  

   Kearns, Madison M.; Morley, Colleen N.; Parkatzidis, Kostas; Whitfield, Richard; Sponza, Alvaro D.; Chakma, Progyateg; De Alwis Watuthanthrige, Nethmi; Chiu, Melanie; Anastasaki, Athina; Konkolewicz, Dominik (February 2022, Polymer Chemistry)

   Polymer molecular weight, or chain length distributions, are a core characteristic of a polymer system, with the distribution being intimately tied to the properties and performance of the polymer material. A model is developed for the ideal distribution of polymers made using reversible activation/deactivation of chain ends, with monomer added to the active form of the chain end. The ideal distribution focuses on living chains, with the system having minimal impact from irreversible termination or transfer. This model was applied to ATRP, RAFT, and cationic polymerizations, and was also used to describe complex systems such as blended polymers and block copolymers. The model can easily and accurately be fitted to molecular weight distributions, giving information on the ratio of propagation to deactivation, as well as the mean number of times a chain is activated/deactivated under the polymerization conditions. The mean number of activation cycles per chain is otherwise difficult to assess from conversion data or molecular weight distributions. Since this model can be applied to wide range of polymerizations, giving useful information on the underlying polymerization process, it can be used to give fundamental insights into macromolecular synthesis and reaction outcomes. 

   more » « less