A nonlinear thermomechanical formulation for anisotropic volume and surface continua

Shirazian

et al. 2019

Proc. R. Soc. A.

Self Cite

A new hyperelastic membrane material model is proposed for single layer blue phosphorus ( β -P), also known as blue phosphorene. The model is fully nonlinear and captures the anisotropy of β -P at large strains. The material model is calibrated from density functional theory (DFT) calculations considering a set of elementary deformation states. Those are pure dilatation and uniaxial stretching along the armchair and zigzag directions. The DFT calculations are performed with the Quantum ESPRESSO package. The material model is compared and validated with additional DFT results and existing DFT results from the literature, and the comparison shows good agreement. The new material model can be directly used within computational shell formulations that are, for example, based on rotation-free isogeometric finite elements. This is demonstrated by simulations of the indentation and vibration of single layer blue phosphorus sheets at micrometer scales. The elasticity constants at small deformations are also reported.

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

A nonlinear hyperelasticity model for single layer blue phosphorus based on ab initio calculations

Shirazian

et al. 2019

Proc. R. Soc. A.

Self Cite

“…So far, it seems that only elasto-plasticity and isotropic thermoelasticity have been analyzed with multiplicatively split isogeometric shell FE (Ambati et al, 2018;Vu-Bac et al, 2019). But the authors are currently applying the present theory to extend the hyperelastic graphene FE model of Ghaffari and Sauer (2018) to anisotropic thermoelasticity (Ghaffari and Sauer, 2019), and to study the growth of fluid films using the FE model of Sauer (2014) and Roohbakhshan and Sauer (2019).…”

Section: Discussionmentioning

confidence: 99%

The multiplicative deformation split for shells with application to growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity

Sauer

International Journal of Solids and Structures

Gupta

2019

Self Cite

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various kinematical quantities, such as area change and curvature, on the elastic and inelastic strains is discussed. This is essential for the development of general constitutive models. In order to fully explore the coupling between elastic and different inelastic deformations, the surface balance laws for mass, momentum, energy and entropy are examined in the context of the multiplicative decomposition. Based on the second law of thermodynamics, the general constitutive relations are then derived. Two cases are considered: Independent inelastic strains, and inelastic strains that are functions of temperature and concentration. The constitutive relations are illustrated by several nonlinear examples on growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity of shells. The formulation is fully expressed in curvilinear coordinates leading to compact and elegant expressions for the kinematics, balance laws and constitutive relations. (183) and consider only inelastic dilatation (â αβ = J in A αβ ) according to Sec. 3.3. Contracting (184) with a αβ and using the relations from Sec. 3.3 thus yields the evolution laẇfor J in . For a generalized viscoelastic solid, see Fig. 2b, evolution law (184) needs to be solved forâ αβ

“…The material constants \varepsi , \\alpha , \mu 0 , \mu 1 , \\beta , \eta 0 , \eta 1 and c \mathrm{ are given in Tables 2 and 3. J is the surface area change, and \kappa 1 and \kappa 2 are the principal surface curvatures [64]. \scrJ 1 and \scrJ 2 capture isotropic dilatation and shear deformation, respectively, while \scrJ 3 captures anisotropic shear deformation.…”

Section: Continuum Modelmentioning

confidence: 99%

Comparing quantum, molecular and continuum models for graphene at large deformations

Mokhalingam

Sauer

et al. 2020

Carbon

Self Cite

In this paper, the validity and accuracy of three interatomic potentials, commonly used to study carbon nanostructures in molecular dynamics, and the continuum shell model of Ghaffari and Sauer [1] are investigated. The mechanical behavior of single-layered graphene sheets (SLGSs) near zero Kelvin is studied for this comparison. The validity of the molecular and continuum models is assessed by direct comparison with density functional theory (DFT) data available in the literature. The molecular simulations are carried out employing the MM3, Tersoff and REBO+LJ potentials. The continuum formulation uses an anisotropic hyperelastic material model in the framework of the geometrically exact Kirchhoff-Love shell theory and isogeometric finite elements. For the comparison, the nonlinear response of a square graphene sheet under uniaxial stretching, biaxial stretching and pure bending is studied. Results from the continuum model are in good agreement with those of DFT. The results from the MM3 potential agree well with the DFT results up to the instability point, whereas those from the REBO+LJ and Tersoff potentials agree with the DFT results only within the range of small deformations. In contrast to the other potentials, the Tersoff potential yields auxetic response in SLGSs under uniaxial stretch. Additionally, the transverse vibration frequencies of a pre-stretched graphene sheet and a carbon nanocone are obtained using the continuum model and molecular simulations with the MM3 potential. The variations of the frequencies obtained from these two approaches agree within an accuracy of about 95\%.