A micro–macro approach to rubber-like materials. Part II: The micro-sphere model of finite rubber viscoelasticity

Miehé, Christian; Göktepe, Serdar

doi:10.1016/j.jmps.2005.04.006

Cited by 181 publications

(119 citation statements)

References 46 publications

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“…Having understood the origins of elasticity and viscosity, it was only a technical challenge to develop theoretical and thermodynamically consistent constitutive models for the viscoelasticity of polymeric materials, with all the relevant physical mechanisms considered [19,[29][30][31][32][33]. However, the predictions and/or assumptions made in these theoretical models should be checked against computer simulations and experimental observations, to either accept, reject or refine the models as a whole or subsets of their basic assumptions.…”

Section: Introductionmentioning

confidence: 99%

Challenges in Multiscale Modeling of Polymer Dynamics

et al. 2013

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The mechanical and physical properties of polymeric materials originate from the interplay of phenomena at different spatial and temporal scales. As such, it is necessary to adopt multiscale techniques when modeling polymeric materials in order to account for all important mechanisms. Over the past two decades, a number of different multiscale computational techniques have been developed that can be divided into three categories: (i) coarse-graining methods for generic polymers; (ii) systematic coarse-graining methods and (iii) multiple-scale-bridging methods. In this work, we discuss and compare eleven different multiscale computational techniques falling under these categories and assess them critically according to their ability to provide a rigorous link between polymer chemistry and rheological material properties. For each technique, the fundamental ideas and equations are introduced, and the most important results or predictions are shown and discussed. On the one hand, this review provides a comprehensive tutorial on multiscale computational techniques, which will be of interest to readers newly entering this field; on the other, it presents a critical discussion of the future opportunities and key challenges in the multiscale geometric mapping matrix between all-atomistic and coarse-grained models N number of monomers per chain N e entanglement length, which is the number of monomers between two entanglements n v number of polymer chains per unit volume n ij (n 0 (r ij )) entanglement number (at equilibrium) between particle pairs i and j p r , P R configurational probability distributions in all-atomistic and coarse-grained models, respectively R ee end-to-end distance of polymer chain R G radius of gyration of polymer chain s segment index/contour length variable along primitive chain S(q) single chain coherent dynamic scattering function Z number of entanglements per chain, defined as Z = N/N e α exponent in standard Mittag-Leffler function σ

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Section: Introductionmentioning

confidence: 99%

Challenges in Multiscale Modeling of Polymer Dynamics

et al. 2013

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“…Menzel and Waffenschmidt (2009) reported a work related to remodeling processes, while Göktepe and Miehe (2005) and Miehe and Göktepe (2005) developed other inelastic models on the microsphere framework for isotropic materials. Moreover, the incorporation of the von Mises ODF could allow, in a more realistic way, the development of remodeling models such as those reported by Kuhl et al (2005) or Menzel et al (2008), with the preferential orientation direction evolving during the simulation.…”

Section: Discussionmentioning

confidence: 99%

“…It is in this context where the microsphere-based approach acquires considerable relevance. Miehe et al (2004), Miehe and Göktepe (2005) and Göktepe and Miehe (2005) used the microsphere approach with emphasis on elastomers. Caner and Carol (2006) were the first to apply this approach to soft biological tissues.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic microsphere-based approach to damage in soft fibered tissue

Saéz

Alastrué²,

Peña

et al. 2011

Biomech Model Mechanobiol

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An anisotropic damage model for soft fibered tissue is presented in this paper, using a multi scale scheme and focusing on the directionally-dependent behavior of these materials. For this purpose, a microstructural or, more precisely, a microsphere-based approach is used to model the contribution of the fibers. The link between micro-structural contribution and macroscopic response is achieved by means of computational homogenization, involving numerical integration over the surface of the unit sphere. In order to deal with the distribution of the fibrils within the fiber, a von Mises probability function is incorporated, and the mechanical (phenomenological) behavior of the fibrils is defined by an exponential-type model. We will restrict ourselves to affine deformations of the network, neglecting any cross-link between fibrils and sliding between fibers and the surrounding ground matrix. Damage in the fiber bundles is introduced through a thermodynamic formulation, which is directly included in the hyperelastic model. When the fibers are stretched far from their natural state, they become damaged. The damage increases gradually due to the progressive failure of the fibrils that make up such a structure. This model has been implemented in a finite element code, and different boundary value problems are solved and

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“…Structural damage models for fibrous biological soft tissues. Int J Solids Struct 44 (18)(19), 5894-5911.…”

Section: Acknowledgementsmentioning

confidence: 99%

“…This methodology, together with the computational homogenisation technique based on the integration of the microscopic contributions over the surface of the unit sphere -or rather the micro-sphere approach-, has revealed to be effective for the implementation of these models within a numerical framework. Considering the isotropic case, Miehe and co-workers presented a series of papers modelling damage and viscoelasticity in polymers [18,10]. Nevertheless, not much work has been done in the numerical study of this approach accounting for anisotropy.…”

Section: Introductionmentioning

confidence: 99%

On the use of the Bingham statistical distribution in microsphere-based constitutive models for arterial tissue

Alastrué

Saéz

Martı́nez

et al. 2010

Mechanics Research Communications

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Constitutive models for arterial tissue have been an active research field during the last years. The main micro-constituents of blood vessels are different types of cells and the extra-cellular matrix formed by an isotropic high water content ground substance and a network composed of elastin and collagen fibres. Usually the arterial tissue has been modelled as a hyperelastic material within the framework of continuum mechanics, whereas inclusion of structural tensors into constitutive laws is the most widely used technique to introduce the anisotropy induced by the fibres. Though the different existing fibre bundles present a clear preferential direction, the dispersion inherent to biological tissue advices using of constitutive models including representative structural information associated to the spatial probabilistic distribution of the fibres. Lately, microsphere-based models have demonstrated to be a powerful tool to incorporate this information. The fibre dispersion is incorporated by means of an Orientation Density Function (ODF) that weights the contribution of each fibre in each direction of the micro-sphere. In previous works the rotationally symmetric von Mises ODF was successfully applied to the modelling of blood vessels. In this study the inclusion of the Bingham ODF into microsphere-based model is analysed. This ODF exhibits some advantages with respect to the von Mises one, like a greater versatility and a comparable response to uniaxial and equibiaxial tension tests.

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A micro–macro approach to rubber-like materials. Part II: The micro-sphere model of finite rubber viscoelasticity

Cited by 181 publications

References 46 publications

Challenges in Multiscale Modeling of Polymer Dynamics

Challenges in Multiscale Modeling of Polymer Dynamics

Anisotropic microsphere-based approach to damage in soft fibered tissue

On the use of the Bingham statistical distribution in microsphere-based constitutive models for arterial tissue

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