Coupled thermoviscoplasticity of glassy polymers in the logarithmic strain space based on the free volume theory

Miehé, Christian; Diez, Joel Méndez; Göktepe, Serdar; Schänzel, Lisa‐Marie

doi:10.1016/j.ijsolstr.2011.01.030

Cited by 42 publications

(13 citation statements)

References 41 publications

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“…For the definition of constitutive relations and a linear evolution equation to determine the internal variables, we work entirely in the logarithmic strain space. This concept was initially developed and applied in the context of plasticity [35, 34, 33, 36, 19] and allows for an additive split in logarithmic elastic and viscous strains.…”

Section: Introductionmentioning

confidence: 99%

Modeling and simulation of viscous electro-active polymers

Vogel

Göktepe

Steinmann

et al. 2014

European Journal of Mechanics - A/Solids

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Electro-active materials are capable of undergoing large deformation when stimulated by an electric field. They can be divided into electronic and ionic electro-active polymers (EAPs) depending on their actuation mechanism based on their composition. We consider electronic EAPs, for which attractive Coulomb forces or local re-orientation of polar groups cause a bulk deformation. Many of these materials exhibit pronounced visco-elastic behavior. Here we show the development and implementation of a constitutive model, which captures the influence of the electric field on the visco-elastic response within a geometrically non-linear finite element framework. The electric field affects not only the equilibrium part of the strain energy function, but also the viscous part. To adopt the familiar additive split of the strain from the small strain setting, we formulate the governing equations in the logarithmic strain space and additively decompose the logarithmic strain into elastic and viscous parts. We show that the incorporation of the electric field in the viscous response significantly alters the relaxation and hysteresis behavior of the model. Our parametric study demonstrates that the model is sensitive to the choice of the electro-viscous coupling parameters. We simulate several actuator structures to illustrate the performance of the method in typical relaxation and creep scenarios. Our model could serve as a design tool for micro-electro-mechanical systems, microfluidic devices, and stimuli-responsive gels such as artificial skin, tactile displays, or artificial muscle.

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Section: Introductionmentioning

confidence: 99%

Modeling and simulation of viscous electro-active polymers

Vogel

Göktepe

Steinmann

et al. 2014

European Journal of Mechanics - A/Solids

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“…\scrL 1 and \scrL 2 := \partial 2 \bfitE (0) /\partial\bfitC \otimes \partial\bfitC are needed for the calculation of \bfitS and its corresponding elasticity tensor, which appears in the FE stiffness matrix 7 . There is a high computational cost for the calculation of \scrL 1 and \scrL 2 [56,57,58,2,1] due to double and quadruple contraction with the logarithmic stress \bfitS (0) := \partialW/\partial\bfitE (0) and its tangent \partial\bfitS (0) /\partial\bfitE (0) (see Kumar and Parks [2]). This computational cost can be reduced for isotropic material models [59,60] but this is not possible for anisotropic material models.…”

Section: Finite Element Formulation For Kirchhoff-love Shellsmentioning

confidence: 99%

A new efficient hyperelastic finite element model for graphene and its application to carbon nanotubes and nanocones

Ghaffari

Sauer

2018

Finite Elements in Analysis and Design

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A new hyperelastic material model is proposed for graphene-based structures, such as graphene, carbon nanotubes (CNTs) and carbon nanocones (CNC). The proposed model is based on a set of invariants obtained from the right surface Cauchy-Green strain tensor and a structural tensor. The model is fully nonlinear and can simulate buckling and postbuckling behavior. It is calibrated from existing quantum data. It is implemented within a rotation-free isogeometric shell formulation. The speedup of the model is 1.5 relative to the finite element model of Ghaffari et al. [1], which is based on the logarithmic strain formulation of Kumar and Parks [2]. The material behavior is verified by testing uniaxial tension and pure shear. The performance of the material model is illustrated by several numerical examples. The examples include bending, twisting, and wall contact of CNTs and CNCs. The wall contact is modeled with a coarse grained contact model based on the Lennard-Jones potential. The buckling and post-buckling behavior is captured in the examples. The results are compared with reference results from the literature and there is good agreement.properties of single-walled CNCs. A second approach is based on the quasi-continuum method [35]. Yan et al. [36] apply the quasi-continuum to simulate buckling and post-buckling of CNCs. A temperature-related quasi-continuum model is proposed by Wang et al.[37] to model the behavior of CNCs under axial compression. A third approach is based on classical continuum material models. Those are popular for graphene in the context of isotropic linear material models. Firouz-Abadi et al. [38] obtain the natural frequencies of nanocones by using a nonlocal continuum theory and linear elasticity assumptions. Their work is extended to the stability analysis under external pressure and axial loads by Firouz-Abadi et al. [39] and the stability analysis of CNCs conveying fluid by Gandomani et al. [40]. Lee and Lee [29] use the finite element (FE) method to obtain the natural frequencies of CNTs and CNCs. The interaction of carbon atoms is modeled as continuum frame elements. Graphene has an anisotropic behavior under large strains. There are several continuum material models for anisotropic behavior of graphene. Sfyris et al. [41] and Sfyris et al. [42] use Taylor expansion and a set of invariants to propose strain energy functionals for graphene based on its lattice structure. Delfani et al. [43] and Delfani and Shodja [44, 45] use a similar Taylor expansion for the strain energy and apply symmetry operators to the elasticity tensors in order to reduce the number of independent variables. Nonlinear membrane material models are proposed by Xu et al. [46] and Kumar and Parks [2]. They use ab-initio results to calibrate their models. The model of Kumar and Parks [2] is based on the logarithmic strain and the symmetry group of the graphene lattice [47, 48, 49]. This symmetry group reduces the number of parameters in the model of Xu et al. [46] by a half. The membrane model of Kumar and Parks [2...

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“…The reader is referred to [198] for a finite element approach in thermoviscoplasticity involving operator splitting. Furthermore, in order to derive a rather complete model of a geothermal reservoir, fluid and heat flow models have to be coupled with a stress field model [176,286].…”

Section: Future Research Perspectivesmentioning

confidence: 99%

A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs

Augustin¹

2015

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Coupled thermoviscoplasticity of glassy polymers in the logarithmic strain space based on the free volume theory

Cited by 42 publications

References 41 publications

Modeling and simulation of viscous electro-active polymers

Modeling and simulation of viscous electro-active polymers

A new efficient hyperelastic finite element model for graphene and its application to carbon nanotubes and nanocones

A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs

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