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See detailFinite deformations govern the anisotropic shear-induced area reduction of soft elastic contacts
Lengiewicz, Jakub UL; de Souza, Mariana; Lahmar, Mohamed A. et al

in Journal of the Mechanics and Physics of Solids (2020), 143

Solid contacts involving soft materials are important in mechanical engineering or biomechanics. Experimentally, such contacts have been shown to shrink significantly under shear, an effect which is ... [more ▼]

Solid contacts involving soft materials are important in mechanical engineering or biomechanics. Experimentally, such contacts have been shown to shrink significantly under shear, an effect which is usually explained using adhesion models. Here we show that quantitative agreement with recent high-load experiments can be obtained, with no adjustable parameter, using a non-adhesive model, provided that finite deformations are taken into account. Analysis of the model uncovers the basic mechanisms underlying anisotropic shear-induced area reduction, local contact lifting being the dominant one. We confirm experimentally the relevance of all those mechanisms, by tracking the shear-induced evolution of tracers inserted close to the surface of a smooth elastomer sphere in contact with a smooth glass plate. Our results suggest that finite deformations are an alternative to adhesion, when interpreting a variety of sheared contact experiments involving soft materials. [less ▲]

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See detailRate-dependent phase-field damage modeling of rubber and its experimental parameter identification
Loew, Pascal Juergen UL; Peters, Bernhard UL; Beex, Lars UL

in Journal of the Mechanics and Physics of Solids (2019)

Phase-field models have the advantage in that no geometric descriptions of cracks are required, which means that crack coalescence and branching can be treated without additional effort. Miehe and ... [more ▼]

Phase-field models have the advantage in that no geometric descriptions of cracks are required, which means that crack coalescence and branching can be treated without additional effort. Miehe and Schänzel (2014) introduced a rate-independent phase-field damage model for finite strains in which a viscous damage regularization was proposed. We extend the model to depend on the loading rate and time by incorporating rubber’s strain-rate dependency in the constitutive description of the bulk, as well as in the damage driving force. The parameters of the model are identified using experiments at different strain rates. Local strain fields near the crack tip, obtained with digital image correlation (DIC), are used to help identify the length scale parameter. Three different degradation functions are assessed for their accuracy to model the rubber’s rate-dependent fracture. An adaptive time-stepping approach with a corrector scheme is furthermore employed to increase the computational efficiency with a factor of six, whereas an active set method guarantees the irreversibility of damage. Results detailing the energy storage and dissipation of the different model constituents are included, as well as validation results that show promising capabilities of rate-dependent phase-field modeling. [less ▲]

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See detailEquilibrium morphology of misfit particles in elastically stressed solids under chemo-mechanical equilibrium conditions
Zhao, X.; Bordas, Stéphane UL; Qu, J.

in Journal of the Mechanics and Physics of Solids (2015), 81

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See detailCentral summation in the quasicontinuum method
Beex, Lars UL; Peerlings, Ron; Geers, Marc

in Journal of the Mechanics and Physics of Solids (2014), 70

The quasicontinuum (QC) method [Tadmor, E.B., Phillips, R., Ortiz, M., 1996. Mixed atomistics and continuum models of deformation in solids. Langmuir 12, 4529–4534] is a multiscale methodology to ... [more ▼]

The quasicontinuum (QC) method [Tadmor, E.B., Phillips, R., Ortiz, M., 1996. Mixed atomistics and continuum models of deformation in solids. Langmuir 12, 4529–4534] is a multiscale methodology to significantly reduce the computational cost of atomistic simulations. The method ensures an accurate incorporation of small-scale atomistic effects in large-scale models. It essentially consists of an interpolation of the displacements of large numbers of atoms between representative atoms (repatoms) and an estimation of the total potential energy of the atomistic lattice by a so-called summation (or sampling) rule. In this paper a novel energy-based summation rule is presented for the QC method that allows for a seamless coupling between coarse domains and fully resolved domains. In the presented summation rule only the repatoms are used in combination with one extra sampling atom in the center of each interpolation triangle. The presented summation rule is therefore straightforward and computationally efficient. The performance of the proposed summation rule is evaluated for a number of two-dimensional and three-dimensional multiscale atomistic test problems. [less ▲]

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See detailA multiscale quasicontinuum method for dissipative lattice models and discrete networks
Beex, Lars UL; Peerlings, Ron; Geers, Marc

in Journal of the Mechanics and Physics of Solids (2014), 64

Lattice models and discrete networks naturally describe mechanical phenomena at the mesoscale of fibrous materials. A disadvantage of lattice models is their computational cost. The quasicontinuum (QC ... [more ▼]

Lattice models and discrete networks naturally describe mechanical phenomena at the mesoscale of fibrous materials. A disadvantage of lattice models is their computational cost. The quasicontinuum (QC) method is a suitable multiscale approach that reduces the computational cost of lattice models and allows the incorporation of local lattice defects in large-scale problems. So far, all QC methods are formulated for conservative (mostly atomistic) lattice models. Lattice models of fibrous materials however, often require non-conservative interactions. In this paper, a QC formulation is derived based on the virtual-power of a non-conservative lattice model. By using the virtual-power statement instead of force-equilibrium, errors in the governing equations of the force-based QC formulations are avoided. Nevertheless, the non-conservative interaction forces can still be directly inserted in the virtual-power QC framework. The summation rules for energy-based QC methods can still be used in the proposed framework as shown by two multiscale examples. [less ▲]

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See detailEffects of elastic strain energy and interfacial stress on the equilibrium morphology of misfit particles in heterogeneous solids
Zhao, X.; Duddu, R.; Bordas, Stéphane UL et al

in Journal of the Mechanics and Physics of Solids (2013), 61(6), 1433-1445

This paper presents an efficient sharp interface model to study the morphological transformations of misfit particles in phase separated alloys. Both the elastic anisotropy and interfacial energy are ... [more ▼]

This paper presents an efficient sharp interface model to study the morphological transformations of misfit particles in phase separated alloys. Both the elastic anisotropy and interfacial energy are considered. The geometry of the material interface is implicitly described by the level set method so that the complex morphological transformation of microstructures can be accurately captured. A smoothed extended finite element method is adopted to evaluate the elastic field without requiring remeshing. The equilibrium morphologies of particles are shown to depend on the elastic anisotropy, interfacial energy as well as the particle size. Various morphological transformations, such as shape changes from spheres to cuboids, directional aligned platelets and particle splitting, are observed. The simulated results are in good agreement with experimental observations. The proposed model provides a useful tool in understanding the morphological transformation of precipitates, which will facilitate the analysis and design of metallic alloys. © 2013 Elsevier Ltd. [less ▲]

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