On the modelling of highly elastic flows of amorphous thermoplastics

Two approaches to the kinematic structuring of constitutive models for highly elastic flows of polymer melts have been examined systematically, assuming either: (1) additivity of elastic and viscous velocity gradients or (2) multiplicability of elastic and viscous deformation gradients. A series of constitutive models were compared, with differing kinematic structure but the same linear responses in elastic and viscous limits. They were solved numerically and their predictions compared, and they were also compared to those of the Giesekus model. Several variants, previously proposed as separate models, are shown to be equivalent and qualitatively in agreement with experiment, and therefore a sound basis for construction of models. But the assignment of viscous spin is critical: if it is assumed equal to the total spin with approach (1), or equal to zero with approach (2), then unphysical viscoelastic behaviour is predicted. © 2008 Elsevier Ltd. All rights reserved

Nonlinear multiscale modelling of quasi-solid state behaviour of PET/MWCNT nanocomposites : 3D RVE-based approach

Nonlinear 3D RVE-based computational multiscale model for prediction of the quasi-solid state behaviour of PET/MWCNT nanocomposites is proposed in this work. The model links the time and length scale of representative morphology of the nanocomposite with the corresponding macroscopic scales via the numerical homogenisation. Finite Element simulations of the uniaxial extension of the nanocomposite near the glass transition show that the addition of MWCNTs leads to significant stiffening of PET. It is caused by an excellent reinforcing ability of the nanotubes, which on average are found to carry the load around two orders of magnitude larger than the matrix. A significant decrease of nanocomposite stresses with increasing processing temperature in its narrow range near the glass transition is also predicted by the model

A numerical method for finite-strain mechanochemistry with localised chemical reactions treated using a Nitsche approach

In this paper, a novel finite-element based method for finite-strain mechanochemistry with moving reaction fronts, which separate the chemically transformed and the untransformed phases, is proposed. The reaction front cuts through the finite elements and moves independently of the finite-element mesh, thereby removing the necessity for remeshing. The proposed method solves the coupled mechanics-diffusion–reaction problem. In the mechanical part of the problem, the force equilibrium and the displacement continuity conditions at the reaction front are enforced weakly using a Nitsche-like method. The formulation is applicable to the case of large deformations and arbitrary constitutive behaviour, and is also consistent with the minimisation of the total potential energy

Microscale diffusion-mechanics model for a polymer-based solid-state battery cathode

A non-linear microscale diffusion-mechanics model combining mass transport and linear momentum balance equations, with elasto-viscoplastic polymer constitutive law and interfacial traction-separation law is proposed to provide a new insight into the effects of viscoplasticity and interfacial damage on the in situ diffusive-mechanical behaviour of a polymer-based cathode for a solid-state battery (SSB). Diffusion and mechanics are coupled through two mechanisms: (1) active particle (AP) volumetric change dependence on Li concentration, and (2) interfacial flux dependence on mechanical opening. The model is resolved for a simple cathode microstructure using an axisymmetric unit cell concept, and integrated with the non-linear finite-element solver ABAQUS with the help of its user subroutines (UMAT and UINTER). Finite-element simulations reveal that plastic deformations of the polymer due to volumetric changes of the AP reduce the value of the interfacial opening displacement, which is desirable for maintaining interfacial flux. The results also demonstrate that slower battery charging rates may lead to a softer polymer response, and thus a smaller interfacial gap. Moreover, a comparison between the linear elastic and current elasto-viscoplastic models for the polymer electrolyte shows that even 5% volumetric shrinkage of the AP leads to an overprediction of the interfacial opening with the linear elastic material law, which limits its validity in modelling polymer-based SSBs

Modelling stress-affected chemical reactions in non-linear viscoelastic solids with application to lithiation reaction in spherical Si particles

This paper aims at modelling stress-affected chemical reactions in spherical particles by adopting the chemomechanical framework based on the chemical affinity tensor and combining it with the finite-strain non-linear viscoelastic constitutive model. The model is applied to the chemical reaction between lithium (Li) ions and silicon (Si), which has been considered as promising successor to graphite for use as active material in lithium-ion battery (LIB) anodes. However, during charging of LIBs, Si enters into the chemical reaction with Li ions, causing large volumetric expansion of Si particles, which leads to the emergence of mechanical stresses, which, in turn, can affect the kinetics of the chemical reaction even up to the reaction arrest. In this paper, the propagation of the reaction front separating the chemically transformed and the untransformed phases is modelled, and the coupled stress-diffusion-reaction problem is solved using the finite element approach. The model predicts the retardation and the locking of the chemical reaction in Si depending on the values of the chemical energy parameter, which corresponds to experimental observations

Size-dependent dynamic characteristics of graphene based multi-layer nano hetero-structures

Carbon-based nano hetero-structures are receiving increasing attention due their ability in multi-synchronous modulation of a range of mechanical and other critically desirable properties. In this paper, the vibration characteristics of two different graphene based heterostructures, graphene-hexagonal boron nitride (hBN) and graphene-molybdenum disulfide (MoS2), are explored based on atomistic finite element approach. Such vibrational characteristics of nanostructures are of utmost importance in order to access their suitability as structural members for adoption in various nano-scale devices and systems. In the current analysis, the developed atomistic finite element model for nano-heterostructures is extensively validated first with the results available in literature considering elastic responses and natural frequencies. Thereafter a range of insightful new results are presented for the dynamic behaviour of various configurations of graphene-hBN and graphene-MoS2 heterostructures including their size, chirality and boundary dependence. The investigation of tunable vibrational properties along with simultaneous modulation of other mechanical, electronic, optical, thermal and chemical attributes of such nano-heterostructures would accelerate their application as prospective candidates for manufacturing nanosensors, electromechanical resonators, and a wide range of other devices and systems across the length-scales

A two-scale framework for coupled mechanics-diffusion-reaction processes

There is a wide range of industrially-relevant problems where mechanical stresses directly affect kinetics of chemical reactions. For example, this includes formation of oxide layers on parts of micro-electro-mechanical systems (MEMS) and lithiation of Si in Li-ion batteries. Detailed understanding of these processes requires thermodynamically-consistent theories describing the coupled thermo-chemo-mechanical behaviour of those systems. Furthermore, as the majority of materials used in those systems have complex microstructures, multiscale modelling techniques are required for efficient simulation of their behaviour. Hence, the purpose of the present paper is two-fold: (1) to derive a thermodynamically-consistent thermo-chemo-mechanical theory; and (2) to propose a two-scale modelling approach based on the concept of computational homogenisation for the considered theory. The theory and the two-scale computational approach are implemented and tested using a number of computational examples, including the case of the reaction locking due to mechanical stresses

Modeling non-linear rheology of PLLA : comparison of Giesekus and Rolie-Poly constitutive models

Rheological models for biobased plastics can assist in predicting optimum processing parameters in industrial forming processes for biobased plastics and their composites such as film blowing, or injection stretch-blow molding in the packaging industry. Mathematical descriptions of polymer behavior during these forming processes are challenging, as they involve highly nonlinear, time-, temperature-, and strain-dependent physical deformation processes in the material, and have not been sufficiently tested against experimental data in those regimes. Therefore, the predictive capability of two polymer models, a classical Giesekus and a physically-based Rolie-Poly, is compared here for extensional and shear rheology data obtained on a poly(L-lactide) (PLLA) across a wide range of strain rates of relevance to those forming processes. Generally, elongational and shear melt flow behavior of PLLA was predicted to a satisfactory degree by both models across a wide range of strain rates (for strain rates 0.05–10.0 s−1), within the strain window up to 1.0. Both models show a better predictive capability for smaller strain rates, and no significant differences between their predictions were found. Hence, as the Giesekus model generally needs a smaller number of parameters, this class of models is more attractive when considering their use in computationally demanding forming simulations of biobased thermoplastics

Correlation between MWCNT aspect ratio and the mechanical properties of composites of PMMA and MWCNTs

The correlation between MWCNT aspect ratio and the quasi-static and dynamic mechanical properties of composites of MWCNTs and PMMA was studied for relatively long MWCNT lengths, in the range 0.3mm to 5mm (aspect ratios up to 5 x 105) and at low loading (0.15wt%). The height of the MWCNTs prepared were modulated by controlling the amount of water vapour introduced in the reactor limiting Ostwald ripening of the catalyst, the formation of amorphous carbon and any increase in CNT diameter. The Tg of PMMA increased by up to 4 ºC on addition of the longest tubes as they have the ability to form physical junctions with the polymer chains which lead to enhanced PMMA-MWCNTs interactions and increased mechanical properties, Young's modulus by 20% on addition of 5mm long MWCNTs. Predictions of the Young's modulus of the composites of PMMA and MWCNT with the Mori-Tanaka theory show that future micromechanical models should account for MWCNT agglomeration and polymer-nanotube interactions as a function of CNT length

Improving damage resistance of solid-state battery cathodes with block copolymers : a non-linear diffusion-mechanics study at the microscale

Minimizing interfacial failure in the composite cathode remains a crucial challenge to unravel the full potential of all solid-state batteries (ASSBs). Polymer-based ASSBs offer promising means of minimizing those damage effects due to their high ductility. However, multicomponent polymers such as block copolymers (BCPs) are needed to meet requirements for both ionic conductivity and mechanical resistance. This study aims to provide a new insight into the combined effects of block copolymer composition (soft-to-hard phase ratio) and interfacial strength on the coupled diffusion-mechanics response of an ASSB cathode, achieved by proposing a non-linear computational micromechanics approach. The approach combines a pressure-dependent diffusion process, interfacial gap-dependent diffusivity, and advanced elasto-viscoplastic constitutive model for a BCP, and it is implemented numerically within a non-linear finite element framework. Two cathode design concepts are explored here, with and without the BCP coating. Results from these case studies suggest that there is a strong interplay between the interface strength (between active particles and the BCP matrix), the BCP material composition, and the interfacial diffusivity. It is found that interfacial damage can be minimized by increasing both the interfacial strength and the amount of the soft component in the BCP system. If the diffusivity across the interface is damage-dependent, the latter is reduced when the BCP is predominantly made of the hard phase. Ultimately, a simple sensitivity analysis reveals that interfacial strength plays a vital role in minimizing interfacial damage, while the coating thickness is the least influential design parameter