Bulletin of the American Physical Society
APS March Meeting 2024
Monday–Friday, March 4–8, 2024; Minneapolis & Virtual
Session Z31: Statistical Physics in Constitutive ModelingFocus
|
Hide Abstracts |
Sponsoring Units: GSNP DPOLY Chair: Michael Buche, Sandia National Laboratories Room: 102C |
Friday, March 8, 2024 11:30AM - 11:42AM |
Z31.00001: A perspective on statistical physics in constitutive modeling Michael R Buche Constitutive models are required to complete the governing equations describing a material. While continuum mechanics and thermodynamics provide some guidelines for deriving these models, they provide no guidance on actually deriving a model from the molecules that constitute the material. In contrast, statistical physics allows thermodynamic quantities to be derived from molecular structure. Consequently, constitutive models have been successfully developed using features of statistical physics, and these models have many desirable thermodynamic characteristics as a direct result. However, since the molecular physics of a given material are extremely complicated, drastic simplifications must be made in order to actually obtain constitutive models. The task is therefore to prescribe the mechanics of molecules constituting the material with (1) sufficient complexity to capture the desired physics, and (2) sufficient simplicity such that the resulting constitutive model is still analytically tractable. This presentation will highlight this overall perspective on statistical physics in constitutive modeling while providing some examples from the literature. |
Friday, March 8, 2024 11:42AM - 11:54AM |
Z31.00002: A Statistical Mechanics Framework for Polymer Chain Scission, Based on the Concepts of Distorted Bond Potential and Asymptotic Matching, with Implications to the Lake-Thomas Theory of Polymer Fracture Jason P Mulderrig, Samuel C Lamont, Franck J Vernerey, Brandon L Talamini, Nikolaos Bouklas To design tough and resilient elastomers, the tools of statistical mechanics ought to be used to connect molecular constituents to macroscopic fracture toughness. Since polymer chain rupture is an enthalpically driven process, bond extensibility ought to be intrinsically incorporated in statistical mechanics-based extensible freely-jointed chain (FJC) models. This objective was rigorously satisfied only recently via the arbitrarily-extensible FJC (uFJC) model, formalized by Buche and colleagues. Despite this notable achievement, the uFJC model is unable to be fully cast in a numerically tractable fashion, limiting its applicability in an upscaled continuum setting. To rectify this, we develop the "composite" uFJC (cuFJC) model. Notably, the principles of asymptotic matching are utilized to derive a simple, quasipolynomial "composite" bond potential. This potential is then supplemented to a slightly-extended version of the uFJC model. The result is the cuFJC model, which is cast in an analytical closed form. Using the cuFJC model, a stochastic thermal fluctuation-driven chain rupture framework is developed based upon a tilted bond potential that accounts for distortional bond energy. Dissipated chain scission energy is then derived in a probabilistic sense, which is incorporated into the Lake-Thomas theory of polymer fracture. The sensitivity of the resulting richly-statistical Lake-Thomas fracture toughness with respect to loading rate and chain composition is presented. |
Friday, March 8, 2024 11:54AM - 12:30PM |
Z31.00003: Molecular-Level Constitutive Modeling of Nonlinear Deformations, Damage, and Fracture in Polymers Invited Speaker: Nikolaos Bouklas Constitutive modeling for elastomer networks is crucial for modeling the macroscopic response from a continuum mechanics perspective. But the underlying multiscale nature of elastomers, from polymerization statistics, to statistical meachanics considerations at the single chain level, to network architecture, make that task of obtaining accurate constitutive models to connect to the chain-level and network-level characteristic of the elastomer exceedingly complex. This has been an area of intense study for many decades. But the recent rise of use of elastomers in a load-bearing capacity, from soft robotics, to flexible electronics and bioengineering application, has required going yet another step further, towards understanding the multiscale cascade of elastomer damage and fracture. Advances in experiments and synthesis have recently provided a new level of insight towards uncovering some of the hidden processes that occur during cavitation, fracture and damage. This presentation will focus on an array of theoretical and computational advancements, from statiscical mechanics of rupture at the single chain level, to different load-sharing modalities at the network level, to phase field fracture and gradient enhanced damage formulations to connect the dots between experimental observations in multiple scales and their theoretical underpinning towards obtaining deeper mechanistic insight for this complex process. |
Friday, March 8, 2024 12:30PM - 12:42PM |
Z31.00004: Micromechanics of dynamically cross-linked nematics Samuel Lamont, Franck J Vernerey In soft nematic networks, flexible polymer chains coexist with stiff, rod-like constituents to yield a material with one hybrid soft-and-stiff phase. The resulting mechanical behavior is drastically different from that of either phase alone and may be different from that of a more typical composite material as well. This is because coupled interactions between the two phases are inherent to the microstructure and cannot be ignored. To account for this, we use a physical description of the material that accounts for each constituent and their naturally arising interactions at its foundation. We approximate a soft nematic network as a collection of 'hairy rods,' which consist of a stiff rod-like molecule connected by soft flexible polymer chains. We develop a statistical description of the network by considering the conformation of chains linking each unit. An assumption of affine motion at the level of the chain-rod unit is employed, but the motion of the rod itself is assigned its own degrees-of-freedom, akin to a Cosserat or higher-order continuum theory. Using this description, the motion of the rod is dictated by the forces and torques that are transmitted to it by the polymer network, which are defined using a statistically formulated free energy and resulting constitutive laws. Using this framework, we illustrate the unique mechanical properties of nematic networks, including soft elasticity and anisotropy, as well as additional time-dependency that arises when dynamic crosslinks are introduced. |
Friday, March 8, 2024 12:42PM - 12:54PM |
Z31.00005: Statistical Physics of (Quasi)-Brittle Fracture: Theory and Applications to Construction Materials Ariel Attias, Franz-Josef Ulm In this presentation, we introduce a novel fracture model for quasi-brittle materials that is grounded in statistical principles. This approach redefines the treatment of the underlying discretization, by conceptualizing it as interacting atoms within a semi-grand ensemble, drawing parallels to binary mixtures in experimental physics. This unique perspective allows us to characterize fracture as a phase transition and assess its evolution statistically, employing the concept of heat of adsorption. The model's validity is demonstrated through comprehensive benchmark examples, with a particular emphasis on 2D bending tests and shear tests on (un)notched beams. We discuss the predicted fracture patterns, peak loads, and the incorporation of size-effect. We also present a phase-diagram of beam fracture. Finally, a first approach of softening is discussed on a 1D example. |
Friday, March 8, 2024 12:54PM - 1:30PM |
Z31.00006: Bridging polymer network scales: crosslinks as fundamental structural units, and emergent multiphysics phenomena Invited Speaker: Matthew J Grasinger There are deep, yet elusive, connections between the structure of a polymer network and its bulk properties. The structure is both hierarchical and statistical in nature, with local order among monomers depending on entropy, pairwise interactions, and external stimuli (e.g. electromagnetic fields); and the connectivity and polydispersity of polymer chains within the network depending on the stochastic process of polymerization. Here we use statistical mechanics to bridge between the monomer and polymer chain scales, then explore different ways of bridging between the chain and network scales, i.e. we explore different polymer network models. Specifically, polymer network models are used to connect network structure to different emergent multiscale phenomena such as flexoelectricity (i.e. coupling between electrical polarization and strain gradients), conventional electromechanical actuation modes, and asymmetric actuation of elastomers. Remarkably, different network models yield notably distinct predictions, both quantitatively and qualitatively. This underscores the need for a new approach to relate macroscopic deformations to chain-level deformations. A new approach is introduced which unifies previously disparate polymer network models and provides more intuitive insights into emergent phenomena in specific scenarios. We contend that it prompts a shift from regarding a single polymer chain as the fundamental unit to considering crosslinks as potentially more suitable fundamental units within the broader network. To conclude, we discuss how this new approach provides a potential path forward for efficient and rational modeling of networks with statistical variations in chain molecular weights, crosslink functionalities, and crosslink geometries. |
Friday, March 8, 2024 1:30PM - 1:42PM |
Z31.00007: Negative Energetic Elasticity in Gels: Insights from a Lattice Polymer Chain Nobu C Shirai, Naoyuki Sakumichi The recent observation of negative energetic elasticity in polymer gels challenges the traditional notion that the elastic moduli of rubberlike materials primarily arise from entropic elasticity. To understand the microscopic origin of this phenomenon, we examined the n-step interacting self-avoiding walk (ISAW) on a cubic lattice [Phys. Rev. Lett. 130, 148101 (2023)]. This model represents a single polymer chain—a subchain in a polymer gel network. Our theoretical investigations, based on exact enumerations up to n=20, reveal the emergence of negative energetic elasticity. The underpinning of this behavior is the attractive interaction between polymer and solvent. This model reproduces the temperature-dependent behavior of negative energetic elasticity observed in polymer gel experiments, suggesting that single-chain analysis can elucidate the properties intrinsic to polymer gel's negative energetic elasticity. Through these insights, our work offers a comprehensive understanding of polymer gel mechanics. |
Friday, March 8, 2024 1:42PM - 1:54PM |
Z31.00008: Coarse grained simulation of Molecular-motor Gels. Jude Ann Vishnu, Xuyang Yao, Andreas Walther, Friederike Schmid In recent years, significant progress has been made in the field of light-driven molecular motors. These motors can convert light energy into uni-directional rotational motion and have promising applications in nanotechnology and drug delivery. To study their cooperative motion, researchers have attached these motors to polymer chains, creating polymer gels known as motor gels. By irradiating these gels with light, the motors undergo directional isomerization, causing the gel to contract or expand. In this study, we present a coarse-grained model to simulate and analyze the volume contraction of these gels. We vary the strand-lengths of the gel and investigate the impact of excluded volume on the contraction ratio. Additionally, we examine the work done by the motors in the gel and observe similar limitations. Finally, we analyze the local entanglements in the system using the Gaussian Linking number and explore the influence of strand-length on the degree of entanglement. |
Friday, March 8, 2024 1:54PM - 2:06PM |
Z31.00009: When is the Poisson Ratio of Polymer Networks and Gels Larger than 0.5? Yuan Tian, Zilu Wang, Andrey V Dobrynin The mechanical properties of elastic materials are characterized by Young's modulus and Poisson ratio (ν) defining a sample shape transformation under applied external stress. A Poisson ratio falls within the range -1≤ν≤0.5 with a specific value determined by Young's modulus and bulk modulus characterizing materials’ compressibility. We use coarse-grained molecular dynamics simulations of networks and gels made of linear and brush-like strands to obtain deformation-dependent Youngs’ modulus and Poisson ratio in both linear and nonlinear deformation regimes. Simulations show that the Poisson ratio of polymer networks and brush gels exceeds 0.5 value in the nonlinear deformation regime. This unusual behavior is due to the ability of the network and gel strands to sustain large reversible deformations, which are impossible to achieve in hard materials. In combination with the finite strand extensibility, this results in strand alignment and monomer density increase with increasing strand’s elongation. We developed a nonlinear network deformation model which defines conditions for the Poisson ratio to exceed 0.5 value. Model predictions are in agreement with the results of coarse-grained simulations of networks and gels. |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700