The emergence of renewable, degradable polymers in everyday applications necessitates the prediction of their mechanical behavior during service. In a recent contribution, Alkhoury et al. (2024) characterized changes in microstructural and mechanical behavior resulting from stress-enhanced photo-degradation of cellulose acetate, a renewable and degradable glassy amorphous polymer used in various consumer products. In this work, we complement the existing set of experiments and develop a thermodynamically consistent constitutive model informed by both micro- and macro-scale information. The outcome of this work enables the prediction of the mechanical behavior of photo-degrading glassy amorphous polymers while subjected to stresses. This can help engineers design sustainable devices while ensuring product integrity.

The force-extension response of a polymer chain provides a direct link between molecular conformations and mechanical behavior. Motivated by directional control conditions commonly encountered in single-molecule stretching, we investigate the elasticity of a polymer chain with deformable bond lengths and bond angles in fixed-extension (FE) and constant-force (CF) ensembles, where the extension is defined as the chain's end-to-end distance projected along the pulling direction. We formulate both ensembles in terms of this projected extension and express their partition functions in transfer-matrix form. Exploiting the resulting structural similarity, we develop a unified computational framework that enables a direct comparison of their finite-chain responses. We show that the FE-CF difference is a finite-chain effect that decreases with increasing force and chain length. We further establish quantitative criteria for the onset of practical ensemble equivalence over finite force ranges and examine their dependence on bond stretching and bond-angle coupling. Applied to realistic carbon-backbone chains, we show that FE-like and CF-like responses become practically equivalent at experimentally relevant chain lengths in the higher-force regime probed by atomic force microscopy, whereas finite-chain ensemble differences remain appreciable in the lower-force regimes accessed by optical and magnetic tweezers. In the long-chain regime of practical equivalence, the semianalytical deformable freely rotating chain (dFRC) model proposed in our previous work [J. Zhu and L. Brassart, Phys. Rev. Lett. 134, 218101 (2025)] provides an accurate reduced description of the full statistical-mechanical response. These results clarify how ensemble choice, finite-chain effects, and local bond deformations jointly shape single-chain elasticity and provide a framework for interpreting and modeling single-chain stretching experiments.

Hydrolysis is the primary degradation mechanism of poly(lactic acid) (PLA) in aqueous media. It involves the scission of polymer chains, leading to a gradual reduction in mechanical properties and mass loss. Although the hydrolysis of PLA under various conditions of temperature and pH has been widely studied, the impact of mechanical loads on the degradation rate has comparatively received limited attention. In this study, we investigated the degradation behaviour of initially-amorphous PLA subjected to mechanical loads. We first examined the hydrolysis degradation behaviour at three different temperatures (45 degrees C, 50 degrees C and 60 degrees C) without applied loads to establish its baseline hydrolytic degradation behaviour. The reduction in molecular weight, water uptake and mass loss were measured as a function of degradation time, along with changes in the glass transition temperature and degree of crystallinity. We next characterised the effect of static tensile and compressive loads on the degradation rate at 45 degrees C. We found that the hydrolysis rate increases with the magnitude of the compressive load when the molecular weight falls below a threshold of approximately 10 kg mol-1. Furthermore, both hydrolytic degradation and mechanical loads significantly contribute to the reduction in yield stress. This PLA also experienced very significant creep during degradation under small loads, suggesting that this polymer is susceptible to creep failure before significant degradation can take place. These results have implications for the prediction of long-term mechanical performance of degradable polymers in load-bearing applications.

The macroscopic failure response of rubbery networks such as elastomers and hydrogels involves the scission of individual polymer chains, mediated by the network topology. However, the precise mechanisms by which individual chain scission events result in macroscopic failure remain poorly understood. In this work, we use Discrete Network (DN) simulations to investigate failure mechanisms in model random networks in uniaxial tension. Our DN simulation results suggest that macroscopic failure, characterised by a sharp drop in the macroscopic stress-stretch response, only requires the scission of a small fraction of chains in a localised region of the network, even in perfect monodisperse networks. Localised failure is triggered by pre-existing heterogeneities in the chain stretch and is further modulated by network parameters such as the chain length or chain strength. Simple micromechanical models of rubber elasticity, such as the three-chain and eight-chain models, fail to capture the onset of damage because they do not capture the chain stretch heterogeneity. More sophisticated microsphere theories in their affine and non-affine versions only partially address this shortcoming. Overall, our results provide new insights into failure mechanisms of rubbery networks, while providing reference results useful for the validation of improved constitutive theories.

Hydrolysis is the primary degradation mechanism in biodegradable polymers in aqueous environments, involving water diffusion and polymer chain scission. These two processes dynamically alter the composition of the polymer, significantly influencing its thermomechanical properties and deformation behaviour. In this work, we develop a constitutive modelling approach that couples water diffusion, hydrolytic chain scission and viscoplastic deformation in glassy polymers. The effect of water concentration and hydrolytic degradation on the mechanical properties is captured through an effective temperature, reflecting the reduction in glass transition temperature brought about by water uptake and the reduction in average molecular weight. The model is calibrated using experimental data for polylactic acid (PLA), including thermo-mechanical characterisation in the wet degraded state and dry undegraded state at different temperatures. Our model accurately captures the evolution of molecular weight and water concentration distributions measured experimentally, and successfully predicts the deformation behaviour at different degradation stages. The potential of the model for weakly coupled simulations is also illustrated in representative case studies. Overall, this study supports the use of the effective temperature as a practical yet physically-motivated method for capturing the effect of degradation on mechanical properties, while providing a robust tool for the design and analysis of degradable polymer devices.

Chain scission is a key molecular process underlying damage and fracture in polymer networks. In this Letter, we develop a statistical-mechanical framework for predicting chain-scission kinetics while accounting for three-dimensional (3D) conformational fluctuations. Within transition-state theory, scission is formulated as a multichannel first-rupture problem, with bond-specific rates governed primarily by self-consistent potentials of mean force. In the freely jointed limit, the additional 3D configurational freedom enhances rupture relative to the collinear 1D reference. Finite bending stiffness introduces orientational correlations that can reverse this enhancement and, at high stiffness, reduce rupture rates by orders of magnitude. These correlations also make rupture bond-position dependent, with higher rates near the chain ends and a common interior rate. For sufficiently long chains, the interior contribution dominates, yielding linear scaling of the chain-scission rate with chain length. These molecularly resolved rates provide physically grounded inputs for future network-scale models of polymer damage and fracture.

The stretching response of polymer chains fundamentally determines the mechanical properties of polymer networks. In this Letter, we develop a statistical mechanics model that incorporates both bond stretching and bond angle deformation, enabling accurate predictions of chain behavior up to large forces. We further propose a semianalytical deformable freely rotating chain (dFRC) model, which represents the chain as a freely rotating chain with effective bond stretch and bond angle that depend on the chain stretch. Using physical parameters without fitting, both the statistical and dFRC models achieve excellent agreement with experimental data for carbon chains across all force regimes. Additionally, the dFRC model provides a direct estimate of the bond force, which is important to predict chain scission. By capturing key bond deformations while remaining computationally efficient, our work lays the foundation for future modeling of polymer network elasticity and failure.

Electrospun polymeric fibres are promising materials for biomedical applications, owing to their biocompatibility, biodegradability, and ability to be assembled into a non-woven fibrous mesh. In particular, continuous filaments can be produced and subsequently assembled into multi-filament braided structures for ligament and tendon tissue repair. In these applications, characterising the evolution of the mechanical properties of the filament as it degrades is of primary importance. The role of applied mechanical loads during the degradation process also needs to be understood. In this study, we characterised the hydrolytic degradation behaviour of pre-stretched electrospun filaments made of poly(ɛ- caprolactone) (PCL) in buffer saline solution at 45 °C for up to 5 weeks, considering both non-loaded and loaded conditions. We show that PCL filaments degrade significantly over this relatively short time period, with non-loaded specimens showing a 21 % reduction in molecular weight after 5 weeks of exposure. Tensile loads applied during degradation further accelerate the degradation rate, with filaments subjected to a 25 g load showing a 33 % reduction in molecular weight over the same time period. Applied loads also impact the mechanical properties of the degraded specimens, causing an increase in elastic modulus and strength but a sharp decrease in elongation at break with exposure time. Our findings have implications for the design of PCL electrospun constructs in load bearing biomedical applications.

The mechanical behaviour of composites of liquid crystal inclusions embedded in soft matrices involves a complex interplay between the elasticity of the matrix, the surface elasticity of the interfaces, and the reorientation of the liquid crystal molecules. Directors of the (nematic) liquid crystal tend to be aligned in the bulk, but may "anchor" along the interface. In addition, the interface deforms according to the bulk deformation, while trying to minimise the surface area. In this paper, we present a continuum theory for an incompressible hyperelastic matrix containing nematic liquid crystal inclusions. The elastic energy of the inclusions, attributed to the distortion of the director field, is described using Landau-de Gennes theory. The matrix is described as an incompressible neo-Hookean solid. Anchoring effects at the inclusion- matrix interface are described through anisotropic surface tension. The model is implemented numerically using the FEniCSx finite element code. Through parametric study, we investigate the impact of energy competitions on the macroscopic and inclusion responses. Similar to the case of liquid inclusions, composites containing liquid crystal inclusions can be stiffer or softer than the matrix, depending on the value of the elasto-capillary number. The softening or stiffening effect is further affected by the distortional energy of the inclusion and the anchoring strength of the interface. Conversely, applied mechanical loads can reorient the director field. In particular, we show that stress-induced reorientation is significant when the dimensionless volume of the inclusion is large, involving alignment of the directors under tension, and disorientation under compression. The proposed theory and new physical insights could be useful for the design of smart stimuli-responsive materials.

This study investigates the effect of force-assisted chemical reaction leading to chain scission on the mechanical and swelling behaviour of rubbery networks. A Discrete Network (DN) modelling approach is adopted, in which polymer chains are represented as entropic springs connected at crosslink points. Force-accelerated chain scission is simulated using a Kinetic Monte Carlo algorithm. The model further accounts for degradation-induced swelling due to solvent uptake and mass loss due to the release of chain clusters detached from the main network. Discrete Network simulations highlight the role of force heterogeneities on the degradation of mechanical properties. Chains bearing the largest forces are cut preferentially, which accelerates the reduction in modulus and loss of percolation. When degradation occurs under constraint, force-biased degradation leads to anisotropic residual elastic properties. These effects cannot be captured by a state-of-the-art micromechanics-based continuum model, which does not account for the redistribution of forces through the network. Overall, the discrete network framework provides a promising platform to study a broader range of mechano-chemical phenomena in elastomers and gels.

Renewable and degradable polymers have emerged in everyday applications ranging from mundane eating utensils to high-tech medical devices. However, the current literature lacks a thorough experimental characterization of the mechanical behavior change due to degradation. In this work, we characterize the microscopic chemical changes due to photo-degradation and resulting stress effects on the mechanical behavior of cellulose acetate, a renewable and degradable polymer that is used in various consumer products. Specifically, we photo-degrade this polymer under (i) traction-free conditions and (ii) under applied stress. A key finding of this work is that upon photo-degradation, this material undergoes chain scission, which affects its mechanical properties and may be further affected by the applied stress.

The Mullins effect is a highly anisotropic damage phenomenon exhibited by filled rubbers among other soft materials. When filled rubbers are subjected to uniaxial tension, their apparent stiffness drops in the direction of stretching but is essentially unaltered in the transverse directions. However, micromechanical full-network models where Mullins softening is described at the level of individual chains often predict that uniaxial deformations induce transverse softening in addition to softening in the stretching direction. Moreover, these approaches typically require the storage of damage state variables for each chain, which is computationally expensive. Taking an alternative approach, we present a full-network model for the Mullins effect where the damage state is described by a single macroscopic damage tensor from which the damage state in each direction can be calculated. The evolution of damage is specified through damage surfaces and damage flow rules, which depend on the directions of principal stretches. The model is shown to reproduce experimental data for filled rubbers sequentially subjected to uniaxial tension in different directions. The model is also implemented in the finite element software ABAQUS as a user subroutine UMAT to illustrate the suitability of the model to simulate non-homogeneous deformation states.

Solid-state lithium-based batteries offer higher energy density than their Li-ion counterparts. Yet they are limited in terms of negative electrode discharge performance and require high stack pressure during operation. To circumvent these issues, we propose the use of lithium-rich magnesium alloys as suitable negative electrodes in combination with Li6PS5Cl solid-state electrolyte. We synthesise and characterise lithium-rich magnesium alloys, quantifying the changes in mechanical properties, transport, and surface chemistry that impact electrochemical performance. Increases in hardness, stiffness, adhesion, and resistance to creep are quantified by nanoindentation as a function of magnesium content. A decrease in diffusivity is quantified with 6Li pulsed field gradient nuclear magnetic resonance, and only a small increase in interfacial impedance due to the presence of magnesium is identified by electrochemical impedance spectroscopy which is correlated with x-ray photoelectron spectroscopy. The addition of magnesium aids contact retention on discharge, but this must be balanced against a decrease in lithium diffusivity. We demonstrate via electrochemical testing of symmetric cells at 2.5 MPa and 30∘C that 1% magnesium content in the alloy increases the stripping capacity compared to both pure lithium and higher magnesium content alloys by balancing these effects.

The inelastic behaviour of thermoplastic polymers below the glass transition temperature can involve shear plasticity or crazing, depending on the strain rate and temperature. Shear plasticity is driven by local shear stresses and is essentially volume preserving. In contrast, crazing is a failure phenomenon occurring under tension and causes significant volume change. In some cases, crazing can also result in large inelastic deformations at macroscopic scale, referred to as craze yielding. The aim of this study is to propose a thermodynamically-consistent constitutive framework that accounts for both shear plasticity and craze yielding in glassy polymers. The main assumption is that shear plasticity and craze yielding occur exclusively from each other, depending on the local stress state. Both are modelled as thermally-activated processes with different activation stresses and flow rules. The theory is validated against experimental data for polylactic acid (PLA). Our model is capable of reproducing the stress–strain response including yielding, softening, and drawing under both shear plasticity and craze yielding, and also accurately predicts the volumetric deformation under tension. In particular, our simulations well capture the interesting phenomenon that craze yielding stabilises localised deformations and prevents necking. Our model can also simulate complex scenarios where both mechanisms occur simultaneously at different locations of the specimen.

This study investigates the mechanical behaviour of poly(ɛ-caprolactone) (PCL) continuous filaments produced by a novel electrospinning (ES) method. These filaments can be processed into woven or braided structures, showing great promises as scaffolds for ligament and tendon repair. Mechanical characterisation of the filaments using DMA and uniaxial tensile tests shows that the filament response is viscoelastic-viscoplastic. Filaments tested using bollard grips present an initially linear elastic response, followed by plastic yielding with two-stage hardening. The filaments are highly stretchable, reaching more than 1000% strain. The different deformation stages are correlated to the evolution of the micro-fibre network observed using SEM, involving the untangling, alignment and stretching of the fibres. A large deformation viscoelastic-viscoplastic model is proposed, which successfully captures the mechanical response of the filaments under non-monotonic loading conditions. Our study also highlights the sensitivity of the measured mechanical response to the type of mechanical grips, namely bollard or screw-side grips.

Nacre-inspired brick-and-Mortar composite structures exhibit exceptional combinations of properties as well as a highly tuneable mechanical response, due to their large range of design parameters. Understanding the effect of these parameters on the response is essential to optimally design these structures and can be guided by modeling. Traditional models only consider 2D geometries and limited attempts at modeling 3D geometric designs exist. Herein, 3D brick-and-mortar structures using a finite element in conjunction with an experimentally calibrated cohesive zone model to represent the layers are proposed. The model is successfully validated against experimental results for a nonplanar brick assembly using so-called osteomorphic bricks. The capabilities of the model are further demonstrated through a parametric study, where the effect of brick shape, number of bricks, and soft layer material properties on the structure mechanical properties (elastic modulus, yield strength and toughness) are investigated. Numerical results show that toughness is significantly increased by transitioning from a "two-peak" failure mechanism to a "peak-plateau-peak," which is controlled by the brick shape. It is also shown that 3D structures may exhibit significant out-of-plane deformation involving the cooperative motion of many bricks, which may contribute to their improved toughness compared to 2D structures. A computational method to model bioinspired 3D (nonplanar) brick-and-mortar composite structures using a finite-element framework in conjunction with an experimentally calibrated cohesive zone model to model the soft phase is proposed. The model is successfully validated against experimental results for an interlocking brick-and-mortar structure and allows to unveil unique failure mechanisms which enhance the toughness of such structures.image (c) 2024 WILEY-VCH GmbH

Discrete Network (DN) models are a useful tool to investigate structure–property relationships in rubbery networks such as elastomers and hydrogels. In a DN model, polymer chains are represented by entropic springs connected at crosslinking points, and the partitioning of stretches among the chains is dictated by the condition of mechanical equilibrium at each crosslink. A key feature of these models is that springs have a zero natural length, and are therefore pre-stretched in the reference configuration. However, the role of chain pre-stretch distribution on the emerging mechanical properties has often been overlooked. In this work we investigate the elastic properties of DNs where the average chain pre-stretch, chain density and chain length distribution can be prescribed independently via a novel network generation algorithm. We show that increasing the average pre-stretch increases the network stiffness and decreases its extensibility limit. We also compare predictions of semi-analytical micromechanical models of rubber elasticity to DN predictions taken as reference. Deviations between analytical model and DN predictions are attributed to the combination of two factors: the loss of affinity at large strain and the initial pre-stretch distribution, which is not taken into account in analytical estimates. DN simulations further show that the assumption of one-to-one mapping between chain stretch and chain orientation on which microsphere models rely is not satisfied.

Hydrolytic degradation of polymers involves the scission of long chain molecules, leading to molecu-lar weight reduction and mass loss. The precise degradation response however depends on the scission probability of individual bonds along the polymer backbone. In particular, bonds near the chain ends are considered to be more susceptible to hydrolysis than inner bonds. In this paper, we incorporate a discrete chain scission model that can handle arbitrary bond scission probabilities within a continuum reaction -diffusion framework. Overall hydrolysis kinetics (including autocatalysis) is described independently of the chain scission model. By decoupling the description of the chain scission mechanism from kinetics, our framework enables the identification of the chain scission mechanism from molecular weight reduc-tion and mass loss curves commonly reported in experimental degradation studies. We further propose a reduced continuum model which is better suited for large-scale simulations while retaining the predic-tive capability of the full discrete-continuum model. The model capability is illustrated in representative case studies based on experimental data from the literature for different materials and geometries. Statement of significance Many models have been proposed to predict the evolution of molecular weight and mass loss in biodegradable polymers undergoing hydrolytic degradation. However, existing models remain limited in their ability to describe the degradation mechanism, autocatalytic kinetics and short chains diffusion si-multaneously. Moreover, existing models often rely on empirical relations and a large number of fitting parameters. Here, we propose a conceptually simple discrete-continuum mathematical framework with a small number of parameters which all have a clear physical meaning. Model calibration against experi-mental data is simplified, and further provides insights into the degradation mechanisms at play, namely random scission, chain-end scission, or a combination of both. The framework can serve as a basis for future generalisations, including a description of evolving crystallinity, or other degradation mechanisms, such as thermal oxidation or photo-degradation. & COPY; 2023 The Authors. Published by Elsevier Ltd on behalf of Acta Materialia Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Understanding the inelastic, rate-dependent mechanical response of biodegradable polymers is important for the design of load-bearing biodegradable structures with controlled deformation and failure response. In this study, we investigate the mechanical response of amorphous polylactic acid (PLA) in dry and wet conditions prior to the onset of degradation at body temperature. The presence of water decreases the glass transition temperature by 4.5 °C, the storage modulus by 21%, and the compressive and tensile yield strengths by about 10%, despite a small water uptake of 0.93 wt%. The tensile response of PLA is dominated by craze yielding, rather than shear plasticity, and is stable against necking despite pronounced strain softening and local strain heterogeneities measured by Digital Image Correlation (DIC). Further analysis of the DIC strain fields in dry and wet samples suggests a transition from pure craze yielding in dry samples to a coexistence of craze yielding and shear plasticity in wet samples. The mechanism shift between tension and compression behaviour of dry and wet PLA has implications for the design of load-bearing structures and for constitutive modelling.

Brick-and-Mortar structures are of high interest because their staggered multi-material arrangement can result in a remarkable combination of high strength and high toughness. Synthetic replication of these structures with high geometric control has been made possible recently with the advances in multi-material Additive Manufacturing (AM). However, very little is known on how inherent material variation in the constituent materials, which can be significant in AM, affects the structure response. In this work, we use a semi-analytical model to theoretically show that a variation in the strength of the layers in a Brick-and-Mortar structure has a significant effect on the failure response of the structure. It can lead to changes in failure regimes and negatively impact the mechanical properties, such as decrease the strain to failure or decrease the yield stress. This is particularly pronounced when the material behaviour is situated close to the transition point between failure regimes. We then present an experimental method to capture strength variability in the layer material and demonstrate that the incorporation of this variability into the semi-analytical model improves our prediction of the failure response of the structure, as compared to experiments.