arXiv subjects

Oscar Lopez-Pamies

Publications and source records attributed to Oscar Lopez-Pamies.

23 records · Page 2Linked to original sources

arXiv2023

Homogenization of elastomers filled with liquid inclusions: The small-deformation limit

This paper presents the derivation of the homogenized equations that describe the macroscopic mechanical response of elastomers filled with liquid inclusions in the setting of small quasistatic deformations. The derivation is carried out for materials with periodic microstructure by means of a two-scale asymptotic analysis. The focus is on the non-dissipative case when the elastomer is an elastic solid, the liquid making up the inclusions is an elastic fluid, the interfaces separating the solid elastomer from the liquid inclusions are elastic interfaces featuring an initial surface tension, and the inclusions are initially $n$-spherical ($n=2,3$) in shape. Remarkably, in spite of the presence of local residual stresses within the inclusions due to an initial surface tension at the interfaces, the macroscopic response of such filled elastomers turns out to be that of a linear elastic solid that is free of residual stresses and hence one that is simply characterized by an effective modulus of elasticity $\bar{\textbf{L}}$. What is more, in spite of the fact that the local moduli of elasticity in the bulk and the interfaces do not possess minor symmetries (due to the presence of residual stresses and the initial surface tension at the interfaces), the resulting effective modulus of elasticity $\bar{\textbf{L}}$ does possess the standard minor symmetries of a conventional linear elastic solid, that is, $\bar{L}_{ijkl}=\bar{L}_{jikl}=\bar{L}_{ijlk}$. As a first application, numerical results are worked out and analyzed for the effective modulus of elasticity of isotropic suspensions of incompressible liquid $2$-spherical inclusions of monodisperse size embedded in an isotropic incompressible elastomer.

cond-mat.soft↗

arXiv2023

The delayed fracture test for viscoelastic elastomers

In a recent contribution, Shrimali and Lopez-Pamies (2023) have shown that the Griffith criticality condition that governs crack growth in viscoelastic elastomers can be reduced -- from its ordinary form involving a historically elusive loading-history-dependent critical tearing energy $T_c$ -- to a fundamental form that involves exclusively the intrinsic fracture energy $G_c$ of the elastomer. The purpose of this paper is to make use of this fundamental form to explain one of the most distinctive fracture tests for viscoelastic elastomers, the so-called delayed fracture test.

cond-mat.mtrl-sci↗

arXiv2022

The "pure-shear" fracture test for viscoelastic elastomers and its revelation on Griffith fracture

Strikingly, "pure-shear" fracture tests have repeatedly shown that fracture nucleation in (common hydrocarbon and other types of) viscoelastic elastomers occurs at a critical stretch that is independent of the stretch rate at which the test is carried out. In this Letter, we demonstrate that this remarkable -- yet overlooked -- experimental finding implies that the Griffith criticality condition that governs nucleation of fracture from large pre-existing cracks in viscoelastic elastomers can be written in fact as an expression not in terms of an elusive loading-history-dependent critical tearing energy Tc, as ordinarily done, but as one exclusively in terms of the intrinsic fracture energy Gc of the elastomer.

cond-mat.soft↗

arXiv2022

The revisited phase-field approach to brittle fracture: Application to indentation and notch problems

In a recent contribution, Kumar, Bourdin, Francfort, and Lopez-Pamies (J. Mech. Phys. Solids 142:104027, 2020) have introduced a comprehensive macroscopic phase-field theory for the nucleation and propagation of fracture in linear elastic brittle materials under arbitrary quasistatic loading conditions. The theory can be viewed as a natural generalization of the phase-field approximation of the variational theory of brittle fracture of Francfort and Marigo (J. Mech. Phys. Solids 46:1319--1342, 1998) to account for the material strength at large. This is accomplished by the addition of an external driving force -- which physically represents the macroscopic manifestation of the presence of inherent microscopic defects in the material -- in the equation governing the evolution of the phase field. The main purpose of this paper is to continue providing validation results for the theory by confronting its predictions with direct measurements from three representative types of experimentally common yet technically challenging problems: $i$) the indentation of glass plates with flat-ended cylindrical indenters and the three-point bending of $ii$) U-notched and $iii$) V-notched PMMA beams.

cond-mat.mtrl-sci↗

arXiv2021

Enhancement of elasto-dielectrics by homogenization of active charges

We investigate the PDE system resulting from even electromechanical coupling in elastomers. Assuming a periodic microstructure and a periodic distribution of micro-charges of a prescribed order, we derive the homogenized system. The results depend crucially on periodicity (or adequate randomness) and on the type of microstructure under consideration. We also show electric enhancement if the charges are carefully tailored to the homogenized electric field and explicit that enhancement, as well as the corresponding electrostrictive enhancement in a dilute regime.

math.AP↗