A micro-macro approach to rubber-like materials?Part I: the non-affine micro-sphere model of rubber elasticity

Miehe, C
Göktepe, Serdar
Lulei, F.
The contribution presents a new micro-mechanically based network model for the description of the elastic response of rubbery polymers at large strains and considers details of its numerical implementation. The approach models a rubber-like material based on a micro-structure that can be symbolized by a micro-sphere where the surface represents a continuous distribution of chain orientations in space. Core of the model is a new two-dimensional constitutive setting of the micro-mechanical response of a single polymer chain in a constrained environment defined by two micro-kinematic variables: the stretch of the chain and the contraction of the cross section of a micro-tube that contains the chain. The second key feature is a new non-affine micro-to-macro transition that defines the three-dimensional overall response of the polymer network based on a characteristic homogenization procedure of micro-variables defined on the micro-sphere of space orientations. It determines a stretch fluctuation field on the micro-sphere by a principle of minimum averaged free energy and links the two micro-kinematic variables in a non-affine format to the line-stretch and the area-stretch of the macro-continuum. Hence, the new model describes two superimposed contributions resulting from free chain motions and their topological constraints in an attractive dual geometric structure on both the micro- and the macro-level. Averaging operations on the micro-sphere are directly evaluated by an efficient numerical integration scheme. The overall model contains five effective material parameters obtained from the single chain statistics and properties of the network with clearly identifiable relationships to characteristic phenomena observed in stress-strain experiments. The approach advances features of the affine full network and the eight chain models by a substantial improvement of their modeling capacity. The excellent predictive performance is illustrated by comparative studies with previously developed network models and by fitting of various available experimental data of homogeneous and non-homogeneous tests.
Journal of the Mechanics and Physics of Solids


A micro macro approach to rubber like materials Part II The micro sphere model of finite rubber viscoelasticity
Christian, Miehe; Göktepe, Serdar (Elsevier BV, 2005-10-01)
A micromechanically based non-affine network model for finite rubber elasticity incorporating topological constraints was discussed in Part 1 (2004. J. Mech. Phys. Solids 52, 2617-2660) of this work. In this follow-up contribution we extend the non-affine microsphere model towards the description of time-dependent viscoelastic effects. The viscoelastic network model is constructed by an additive split of the overall response into elastic equilibrium-stress and viscoelastic overstress contributions. The equi...
A theoretical study on the simplest fullerene, C-20 - an AM1 treatment
Türker, Burhan Lemi (Elsevier BV, 2003-05-05)
Within the constraints of AM1 (UHF) type semiempirical quantum chemical treatment, C-20 and its cationic and anionic forms were considered for their stabilities. The results revealed that C-20 has a greater tendency to act as electron acceptor than a donor. C-20(-) and C-20(-2) were found to be even more stable than C-20.
A robust optimization approach for the breast cancer targeted design of PEtOx-b-PLA polymersomes
Oz, Umut Can; Bolat, Zeynep Busra; Ozkose, Umut Ugur; Gulyuz, Sevgi; Kucukturkmen, Berrin; Khalily, Melek Parlak; Özçubukçu, Salih; Yilmaz, Ozgur; Telci, Dilek; ESENDAĞLI, GÜNEŞ; Sahin, Fikrettin; Bozkir, Asuman (2021-04-01)
© 2021 Elsevier B.V.The equipping of nanoparticles with the peptide moiety recognizing a particular receptor, enables cell or tissue-specific targeting, therefore the optimization of the targeted nanoparticles is a key factor in the formulation design process. In this paper, we report the optimization concept of Doxorubicin encapsulating PEtOx-b-PLA polymersome formulation equipped with Peptide18, which is a breast cancer recognizing tumor homing peptide, and the unveiling of the cell-specific delivery pote...
A micro-macro approach to rubber-like materials. Part III: The micro-sphere model of anisotropic Mullins-type damage
Göktepe, Serdar (Elsevier BV, 2005-10-01)
A micromechanically based non-affine network model for finite rubber elasticity and viscoelasticity was discussed in Parts I and II [Miehe, C., Goktepe, S., Lulei, F., 2004. A micro-macro approach to rubber-like materials. Part I: The non-affine micro-sphere model of rubber elasticity. J. Mech. Phys. Solids 52, 2617-2660; Miehe, C., Goktepe, S., 2005. A micro-macro approach to rubber-like materials. Part II: Viscoelasticity model for polymer networks. J. Mech. Phys. Solids, published on-line, doi:10.1016/j....
A computational framework of configurational-force-driven brittle fracture based on incremental energy minimization
MIEHE, CHRISTIAN; Gürses, Ercan; BIRKLE, MANUEL (Springer Science and Business Media LLC, 2007-06-01)
A variational formulation of quasi-static brittle fracture in elastic solids at small strains is proposed and an associated finite element implementation is presented. On the theoretical side, a consistent thermodynamic framework for brittle crack propagation is outlined. It is shown that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius-Planck inequality. Here, the canonical direction of the crack propagation associate...
Citation Formats
C. Miehe, S. Göktepe, and F. Lulei, “A micro-macro approach to rubber-like materials?Part I: the non-affine micro-sphere model of rubber elasticity,” Journal of the Mechanics and Physics of Solids, pp. 2617–2660, 2004, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/28582.