A Comparison of Atomistic and Enhanced Continuum Approaches at Finite Temperature - Davydov, Denis; Javili, Ali; Steinmann, Paul; McBride, Andrew (Surface effects in solid mechanics, 2012)
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.acompa_7

A Deformational and Configurational Framework for Geometrically Nonlinear Continuum Thermomechanics Coupled to Diffusion - Steinmann, Paul; McBride, Andrew; Bargmann, Swantje; Javili, Ali (International Journal of Non-Linear Mechanics, 2011)
A general framework encompassing both the (conventional) deformational and configurational settings of continuum mechanics is presented. A systematic application of balance principles over a migrating control volume in the undeformed configuration of the continuum body yields the system of governing equations in the bulk, on the surface and on a coherent interface within the continuum. The equations governing the response of the bulk agree with those of the conventional deformational approach. The localised balance equations are expressed in the configurational setting using a pull-back operator and reformulated in terms of the Eshelby stress. The configurational expression of the dissipation elucidates the energy loss associated with configurational changes. The general framework is introduced by considering the problem of coupled deformation, heat conduction and species diffusion within a geometrically non-linear continuum body intersected by a coherent interface. The nature of the coupling is emphasised throughout the presentation and via an example.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.adefor

A geometrically exact formulation of peridynamics - Javili, Ali; McBride, Andrew; Steinmann, Paul (Theoretical and Applied Fracture Mechanics, 2021)
The main objective of this contribution is to develop a geometrically exact peridynamics (PD) formulation wherein the basic elements of continuum kinematics are preserved. The proposed formulation accounts for large deformations and is variationally consistent. We distinguish between one-, two- and three-neighbour interactions. One-neighbour interactions recover the original (bond-based) PD formalism. Two- and three-neighbour interactions are fundamentally different to state-based PD. We account for material frame indifference and provide a set of appropriate arguments for objective interaction potentials accordingly. This contribution is presented in a manner such that the established theory is immediately suitable for computational implementation. From a computational perspective, the proposed strategy is fully implicit and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed. Finally, we demonstrate the capability of our proposed framework via a series of numerical examples at large deformations.
CRIS-Team Scopus Importer:2020-12-25
Keywords: Continuum kinematics; Geometrically exact; Large deformations; Peridynamics; Variationally consistent

Computational aspects of thermomechanical solids with Kapitza interfaces - Javili, Ali; McBride, Andrew; Steinmann, Paul (Computational Materials Science, 2012)
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.comput_6

Computational modeling of case II diffusion in polymeric materials - Bargmann, Swantje; McBride, Andrew; Steinmann, Paul (Proceedings of the 24th Nordic Seminar on Computational Mechanics, 2011)
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.comput_9

Geometrically nonlinear continuum thermomechanics coupled to diffusion: a framework for case II diffusion - McBride, Andrew; Bargmann, Swantje; Steinmann, Paul (Advances in Extended and Multifield Theories for Continua, 2011)
This chapter introduces a geometrically nonlinear, continuum thermomechanical framework for case II diffusion: a type of non-Fickian diffusion characterized by the wave-like propagation of a low-molecular weight solvent in a polymeric solid. The key objective of this contribution is to derive the coupled system of governing equations describing case II diffusion from fundamental balance principles. A general form for the Helmholtz energy is proposed and the resulting constitutive laws are derived from logical, thermodynamically consistent argumentation. The chapter concludes by comparing the model developed here to various others in the literature. The approach adopted to derive the governing equations is not specific to case II diffusion, rather it encompasses a wide range of applications wherein heat conduction, species diffusion and finite inelastic effects are coupled. The presentation is thus applicable to the generality of models for non-Fickian diffusion: an area of increasing research interest. © 2011 Springer-Verlag Berlin Heidelberg.
UnivIS-Import:2015-04-20:Pub.2011.tech.FT.FT-TM.geomet

Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion - McBride, Andrew; Javili, Ali; Steinmann, Paul; Bargmann, Swantje (Journal of the Mechanics and Physics of Solids, 2011)
Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad hoc manner. This work is concerned with a nonlinear continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion and viscoelasticity. The formulation is presented within a thermodynamically consistent framework and elucidates the nature of the coupling between the various fields, and the surface and the bulk. Conservation principles are used to determine the form of the constitutive relations and the evolution equations. Restrictions on the jump in the temperature and the chemical potential between the surface and the bulk are not a priori assumptions, rather they arise from the reduced dissipation inequality on the surface and are shown to be satisfiable without imposing the standard assumptions of thermal and chemical slavery. The nature of the constitutive relations is made clear via an example wherein the form of the Helmholtz energy is explicitly given. © 2011 Elsevier Ltd.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.geomet_1
Keywords: Constitutive behaviour; Diffusion; bulk and surface; Finite strain; Thermomechanical process

Macroscopic modelling of the selective beam melting process - Riedlbauer, Daniel-Rouven; Mergheim, Julia; Steinmann, Paul; McBride, Andrew (Proceedings in Applied Mathematics and Mechanics, 2012)
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.macros_9

Micro-to-macro transitions for heterogeneous material layers accounting for in-plane stretch - McBride, Andrew; Mergheim, Julia; Javili, Ali; Steinmann, Paul; Bargmann, Swantje (Journal of the Mechanics and Physics of Solids, 2012)
The computational micro-to-macro transition framework couples heterogeneities on the microscopic scale to the macroscopic response of a continuum. The objective here is to apply this framework to macroscopic material layers capable of undergoing an in-plane stretch in addition to the normal opening mode. This is achieved using the continuum interface theory of Gurtin and Murdoch (1975) which endows the interface with its own energetic structure. The relation of the macroscopic kinematic descriptors of the interface deformation to the averaged underlying microscopic quantities is consistently derived using the Hill-type averaging theorem. Key features of the theory are elucidated using a series of three-dimensional numerical examples.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.microt
Keywords: Micro-to-macro transitions; Microstructures; Constitutive behaviour; Finite elements

Models of Solvent Penetration in Glassy Polymers With an Emphasis on Case II Diffusion. A Comparative Review - Bargmann, Swantje; McBride, Andrew; Steinmann, Paul (Applied Mechanics Reviews, 2011)
The objective of this review is to provide an overview and a classification of the key literature on models of non-Fickian case II type diffusion. Several extensive review articles concerning non-Fickian diffusion exist in the literature; our objective is not to reproduce these worthy contributions. Rather, we focus on a limited number of, seemingly disparate, notable models and attempt to unify them using the language of thermodynamics and continuum mechanics. This attempted unification of selected models arising from various modeling communities serves to elucidate the key strengths and potential weaknesses of the model
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.models
Keywords: Deformation; Diffusion (Physics); Polymers; Equations; Stress

Numerical modelling of thermomechanical solids with highly conductive energetic interfaces - Javili, Ali; McBride, Andrew; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2013)
Interfaces within a solid can play a significant role in the overall response of a body. The influence of an interface increases as the scale of the problem decreases. Furthermore, the thermomechanical properties of the interface can differ significantly from those of the surrounding bulk. Such effects are described here using interface elasticity theory. The objective of this contribution is to detail the computational aspects of modelling thermomechanical solids with highly conductive energetic interfaces. The interface is termed energetic in the sense that it possesses its own energy, entropy, constitutive relations and dissipation. The equations governing the fully nonlinear, transient problem are given. They are then solved using an efficient finite element scheme. Full details of the consistent linearisation of the nonlinear governing equations are provided. Key features of highly conductive energetic interfaces are then elucidated via a series of three-dimensional numerical examples. In particular and in contrast to highly conductive thermal interfaces, it is clearly shown that a jump in the heat flux across the interface is possible even in the absence of a heat flux along the interface. © 2012 John Wiley & Sons, Ltd.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.numeri
Keywords: Energetic interfaces; Finite element method; Highly conductive interfaces; Nanomaterials; Thermomechanics

Numerical modelling of thermomechanical solids with mechanically energetic (generalised) Kapitza interfaces - Javili, Ali; McBride, Andrew; Steinmann, Paul (Computational Materials Science, 2012)
Interfaces within a solid can play a significant role in the overall response of the body. The influence of the interface increases as the scale of the problem decreases. Furthermore, the properties of the interface can differ significantly from those of the surrounding bulk. Such effects are described here using interface elasticity theory. The objective of this presentation is to detail the computational aspects of modelling thermomechanical solids with mechanically energetic interfaces. The interface is termed energetic in the sense that it possesses its own energy, entropy, constitutive relations, and dissipation. A mechanically energetic interface does not possess a thermal structure, and thus lacks its own heat capacity, heat conduction and heat expansion coefficient. For a mechanically energetic interface within a thermomechanical solid, the jump of the normal heat flux across the interface is zero while a temperature jump is allowed. In this sense, a mechanically energetic interface can be understood as a generalised Kapitza interface. Therefore the concept of Kapitza thermal resistance is used to control the temperature jump across the interface. The equations governing the fully-nonlinear, transient problem are given. They are then solved using an efficient finite element scheme. Key features of mechanically energetic interfaces are elucidated via a series of three-dimensional numerical examples. © 2012 Elsevier B.V. All rights reserved.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Finite element method; Kapitza interface; Nanomaterials; Thermoelasticity

Relationships between the admissible range of surface material parameters and stability of linearly elastic bodies - Javili, Ali; McBride, Andrew; Steinmann, Paul; Reddy, Batmanathan Dayanand (Philosophical Magazine, 2012)
This work focuses on the problem of an elastic bulk encased by an energetic elastic surface. The key contribution of this work is a study of the admissible range for the surface material parameters. In particular, the validity of negative surface parameters, which have been reported in the literature, is assessed. The balance equations for a continuum with a coherent energetic surface are stated. The local bifurcation conditions for the system (i.e. the bulk and the surface) are analysed using a standard ansatz for stationary waves. Under the reasonable assumption that the bulk is pointwise stable, the analysis concludes that pointwise stability of the surface elasticity tensor excludes any possible bifurcations; the weaker condition of surface strong ellipticity does not. The stability of the approximation of the governing equations using the finite element method is shown to be mesh-dependent for the case where the surface elasticity tensor loses pointwise stability. This is clearly illustrated via a series of numerical examples. Critically, it appears that the admissible range for the surface material properties differs for inherently non-local atomistic models and classical continuum formulations, both of which are used to model surface effects at the nanometre-scale. A key conclusion based on this observation is that care should be taken when fitting material properties obtained from atomistic models to classical continuum formulations that inherently lack a length-scale. The length-scale provided by the spatial discretisation can add stability, albeit artificially. © 2012 Copyright Taylor and Francis Group, LLC.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.relati
Keywords: bifurcation; mesh dependency; stability; surface elasticity

Thermomechanics of Solids with Lower-Dimensional Energetics: On the Importance of Surface, Interface and Curve Structures at the Nanoscale. A Unifying Review - Javili, Ali; McBride, Andrew; Steinmann, Paul (Applied Mechanics Reviews, 2012)
Surfaces and interfaces can significantly influence the overall response of a solid body. Their behavior is well described by continuum theories that endow the surface and interface with their own energetic structures. Such theories are becoming increasingly important when modeling the response of structures at the nanoscale. The objectives of this review are as follows. The first is to summarize the key contributions in the literature. The second is to unify a select subset of these contributions using a systematic and thermodynamically consistent procedure to derive the governing equations. Contributions from the bulk and the lower-dimensional surface, interface, and curve are accounted for. The governing equations describe the fully nonlinear response (geometric and material). Expressions for the energy and entropy flux vectors, and the admissible constraints on the temperature field, all subject to the restriction of non-negative dissipation, are explored. A particular emphasis is placed on the structure of these relations at the interface. A weak formulation of the governing equations is then presented that serves as the basis for their approximation using the finite element method. Various forms for a Helmholtz energy that describes the fully coupled thermomechanical response of the system are given. They include the contribution from surface tension. The vast majority of the literature on surface elasticity is framed in the infinitesimal deformation setting. The finite deformation stress measures are, thus, linearized and the structure of the resulting stresses discussed. The final objective is to elucidate the theory using a series of numerical example problems.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.thermo_8