Macroscopic instabilities and domain formation in neo-Hookean laminates

Furer, J.; Castañeda, Pedro Ponte

doi:10.1016/j.jmps.2018.05.006

Cited by 13 publications

(12 citation statements)

References 26 publications

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“…Two types of instability may occur in the grid, classified as 'microscopic' and 'macroscopic'. Only the latter is captured by the homogenized material response and corresponds to its loss of ellipticity, which, in turn, coincides with the condition of strain localization, and, as a special case, shear band formation [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 89%

“…On the other hand, the bifurcation of an incrementally loaded periodic lattice can be analyzed with a Floquet-Bloch technique as shown in [15,23]. This analysis shows that both local and global bifurcation modes can occur and only the latter correspond to failure of ellipticity for the effective material evaluated from homogenization [18,20,22].…”

Section: Positive Definiteness Strong Ellipticity and Lattice Stabilitymentioning

confidence: 99%

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Tensile material instabilities in elastic beam lattices lead to a bounded stability domain

Bordiga,

Bigoni,

Piccolroaz

2022

Preprint

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Homogenization of the incremental response of grids made up of preloaded elastic rods leads to homogeneous effective continua which may suffer macroscopic instability, occurring at the same time in both the grid and the effective continuum. This instability corresponds to the loss of ellipticity in the effective material and the formation of localized responses as, for instance, shear bands. Using lattice models of elastic rods, loss of ellipticity has always been found to occur for stress states involving compression of the rods, as usually these structural elements only buckle under compression. In this way, the locus of material stability for the effective solid is unbounded in tension, i.e. the material is always stable for a tensile prestress. A rigorous application of homogenization theory is proposed to show that the inclusion of sliders (constraints imposing axial and rotational continuity, but allowing shear jumps) in the grid of rods leads to loss of ellipticity in tension, so that the locus for material instability becomes bounded. This result explains (i.) how to design elastic materials passible of localization of deformation and shear banding for all radial stress paths; (ii.) how for all these paths a material may fail by developing strain localization and without involving cracking.

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Section: Introductionmentioning

confidence: 89%

Section: Positive Definiteness Strong Ellipticity and Lattice Stabilitymentioning

confidence: 99%

Tensile material instabilities in elastic beam lattices lead to a bounded stability domain

Bordiga,

Bigoni,

Piccolroaz

2022

Preprint

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“…From a physical standpoint, as shown in [5], the onset of loss of ellipticity corresponds with the development of localised deformations, and it is an expected phenomenon related to the development of long wavelength diffuse modes in the microscale. Indeed, loss of ellipticity can occur in the solely mechanical case, even when (polyconvex) Neo-Hookean strain energies are considered for the constitutive models of the micro-constituents of layered composites (see Reference [24]). Suitable relaxation techniques, such as rank-one convexification, can be applied [24] in order to restore the mathematical well-posedness of the problem.…”

Section: Effective Constitutive Tensorsmentioning

confidence: 99%

“…Indeed, loss of ellipticity can occur in the solely mechanical case, even when (polyconvex) Neo-Hookean strain energies are considered for the constitutive models of the micro-constituents of layered composites (see Reference [24]). Suitable relaxation techniques, such as rank-one convexification, can be applied [24] in order to restore the mathematical well-posedness of the problem. Notwithstanding, the latter is out of the scope of this paper.…”

Section: Effective Constitutive Tensorsmentioning

confidence: 99%

A Convex Multi-Variable based computational framework for multilayered electro-active polymers

Marín

Martínez-Frutos

Ortigosa

et al. 2021

Computer Methods in Applied Mechanics and Engineering

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“…the largest quasiconvex function below W , which is generally not possible to obtain in a closed form except a few available examples; see [18], and this approach attains lots of attention also from the numerical point of view, cf. [21], for instance.…”

Section: Introductionmentioning

confidence: 99%

Gradient polyconvex material models and their numerical treatment

Horák

Kružík

2020

International Journal of Solids and Structures

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Gradient polyconvex materials are nonsimple materials where we do not assume smoothness of the elastic strain but instead regularity of minors of the strain is required. This allows for a larger class of admissible deformations than in the case of second-grade materials. We describe a possible implementation of gradient polyconvex elastic energies. Besides, a new geometric interpretation of gradient-polyconvexity is given and it is compared with standard second-grade materials. Finally, we demonstrate application of the proposed approach using two different models, namely, a St.-Venant Kirchhoff material and a double well stored energy density.

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Macroscopic instabilities and domain formation in neo-Hookean laminates

Cited by 13 publications

References 26 publications

Tensile material instabilities in elastic beam lattices lead to a bounded stability domain

Tensile material instabilities in elastic beam lattices lead to a bounded stability domain

A Convex Multi-Variable based computational framework for multilayered electro-active polymers

Gradient polyconvex material models and their numerical treatment

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