arXiv subjects

Oscar Lopez-Pamies

Publications and source records attributed to Oscar Lopez-Pamies.

At least 19 recordsLinked to original sources

arXiv2026

Fracture under body forces: An accessible test and analysis

Fracture in large-scale structures --- from failing concrete dams to calving glaciers --- is dominated by self-weight. Yet, owing to their immense scale, directly studying when and where cracks nucleate and propagate in these systems under gravity is unfeasible. To date, experimental investigations have largely relied on mimicking self-weight in scaled-down specimens via centrifugal forces, necessitating specialized centrifuge facilities. In this Letter, we introduce a simple benchtop test that bypasses the need for this infrastructure. The method utilizes a cantilever beam containing a downward-pointing V-notch, loaded solely by its self-weight. Through appropriate selection of the notch geometry and placement and the beam dimensions, the setup forces a crack to nucleate at the notch tip and propagate through the specimen in a measurable manner. We demonstrate the utility of this self-weight fracture test on a 3D-printable mortar and analyze the results using the fracture theory recently introduced in (\citeauthor{LPKFG2026}, 2026). \emph{Inter alia}, the findings provide a first validation of the theory for fracture driven by body forces.

cond-mat.other↗

arXiv2026

Nucleation and propagation of brittle fracture as a constrained energy minimization problem

This paper presents a macroscopic, or continuum, theory aimed at describing when, where, and why cracks nucleate and propagate in nominally elastic brittle materials under monotonic, quasi-static, but otherwise arbitrary mechanical loads. Motivated by recent insights, the proposed sharp theory posits that: \emph{cracks nucleate and propagate exclusively in regions where the strength surface of the material is exceeded, with their evolution dictated by the minimization of the sum of the potential --- the elastic energy minus the work done by the externally applied forces --- and surface energies.} While the theory applies to materials with any elasticity (linear or nonlinear) and any material symmetry (isotropic or anisotropic), attention is restricted here to the most basic case of isotropic elastic brittle materials. For demonstration purposes, the theory is confronted with a set of nine tests that span the entire range of well-settled experimental knowledge on fracture nucleation and propagation --- the so-called ``Nine Circles of Elastic Brittle Fracture'' --- on both a hard material (a silicate glass) and a soft material (a synthetic rubber).

cond-mat.mtrl-sci↗

arXiv2026

The single edge notch fracture test for viscoelastic elastomers

Making use of the Griffith criticality condition recently introduced by Shrimali and Lopez-Pamies (Extreme Mechanics Letters 58: 101944, 2023), this work presents a comprehensive analysis of the single edge notch fracture test for viscoelastic elastomers. The results -- comprised of a combination of a parametric study and direct comparisons with experiments -- reveal how the non-Gaussian elasticity, the nonlinear viscosity, and the intrinsic fracture energy of elastomers interact and govern when fracture nucleates from the pre-existing crack in these tests. The results also serve to quantify the limitations of existing analyses, wherein viscous effects and the actual geometries of the pre-existing cracks and the specimens are neglected.

cond-mat.soft↗

arXiv2026

A Guide to Fully Characterize the Fracture Properties of Cementitious Materials from Simple Experiments

Guided by recent advances in the understanding of nucleation and propagation of fracture in elastic brittle materials, this paper proposes a suite of three simple experiments that permit the measurement of the three macroscopic material properties governing when and where cracks nucleate and propagate in structures made of cementitious materials that are subjected to arbitrary monotonic quasi-static loading conditions. The first experiment is that of the uniaxial compression of a cylindrical specimen, which enables the extraction of the elastic properties -- namely, the Young's modulus and Poisson's ratio -- as well as the uniaxial compressive strength. The second experiment is the Brazilian fracture test, performed with flat platens on a material disk to determine the uniaxial tensile strength. Having knowledge of the uniaxial compressive and uniaxial tensile strengths then allows for the estimation of the strength surface of the material via interpolation (e.g., a Drucker-Prager fit). Finally, the third experiment is the wedge split test on a notched cube, which yields the fracture toughness. We demonstrate by means of direct comparisons with four-point and three-point bending tests on both unnotched and notched beams made of a 3D-printable mortar mixture that the elasticity, strength, and toughness properties obtained from the proposed tests are sufficient to predict the nucleation and propagation of fracture for any structure (granted separation of length scales) made of cementitious materials under any monotonic quasi-static loading condition.

cond-mat.soft↗

arXiv2026

Breaking Four-Point and Three-Point Bending Tests

Since their initial standardizations in the 1930s and 1950s, the so-called four-point and three-point bending tests on unnotched beams have been embraced by practitioners as two popular methods to indirectly measure the tensile strength of concrete, ceramics, and other materials with a large compressive strength relative to their tensile strength. This is because of the ease that the tests afford in both the preparation of the specimen (a beam of rectangular cross section) and the application of the loads (simple supports pressing on the specimen). Yet, this practical advantage has to be tempered by the fact that the observations from both of these tests -- being \emph{indirect} experiments in the sense that they involve \emph{not} uniform uniaxial tension but non-uniform triaxial stress states throughout the specimen -- have to be appropriately interpreted to be useful. By making use of the phase-field fracture theory initiated by Kumar, Francfort, and Lopez-Pamies (2018), which has been recently established as a complete theory of fracture capable of accurately describing the nucleation and propagation of cracks in elastic brittle materials under arbitrary quasistatic loading conditions, the main objective of this paper is to carry out a thorough 3D quantitative analysis of when and where fracture nucleates and propagates in four-point and three-point bending tests and thereby establish how to appropriately interpret their results. As a corollary, the analysis provides an explanation for why four-point bending tests typically yield smaller flexural strengths than three-point bending tests, a source of constant headaches for practitioners who have been left to wonder which test -- if any -- would be more appropriate for their purposes.

cond-mat.mtrl-sci↗

arXiv2025

Nine circles of elastic brittle fracture: A series of challenge problems to assess fracture models

Since the turn of the millennium, capitalizing on modern advances in mathematics and computation, a slew of computational models have been proposed in the literature with the objective of describing the nucleation and propagation of fracture in materials subjected to mechanical, thermal, and/or other types of loads. By and large, each new proposal focuses on a particular aspect of the problem, while ignoring others that have been well-established. This approach has resulted in a plethora of models that are, at best, descriptors of fracture only under a restricted set of conditions, while they may predict grossly incorrect and even non-physical behaviors in general. In an attempt to address this predicament, this paper introduces a vetting process in the form of nine challenge problems that any computational model of fracture must convincingly handle if it is to potentially describe fracture nucleation and propagation in general. The focus is on the most basic of settings, that of isotropic elastic brittle materials subjected to quasi-static mechanical loads. The challenge problems have been carefully selected so that: $i$) they can be carried out experimentally with standard testing equipment; $ii$) they can be unambiguously analyzed with a sharp description of fracture; and, most critically, $iii$) in aggregate they span the entire range of well settled experimental knowledge on fracture nucleation and propagation that has been amassed for over a century. For demonstration purposes, after their introduction, each challenge problem is solved with two phase-field models of fracture.

physics.comp-ph↗

arXiv2025

Nucleation and propagation of fracture in viscoelastic elastomers: A complete phase-field theory

This paper presents a macroscopic theory, alongside its numerical implementation, aimed at describing, explaining, and predicting the nucleation and propagation of fracture in viscoelastic materials subjected to quasistatic loading conditions. The focus is on polymers, in particular, on elastomers. To this end, the starting point of this work is devoted to summarizing the large body of experimental results on how elastomers deform, nucleate cracks, and propagate cracks when subjected to mechanical loads. When viewed collectively, the experiments make it plain that there are three basic ingredients that any attempt at a complete macroscopic theory of fracture in elastomers ought to account for: i) the viscoelasticity of the elastomer; ii) its strength; and iii) its fracture energy. A theory is then introduced that accounts for all these three basic ingredients by extending the phase-field theory initiated by Kumar, Francfort, and Lopez-Pamies (J. Mech. Phys. Solids 112 (2018), 523--551) for elastic brittle materials to seamlessly incorporate viscous energy dissipation by deformation, a generalized strength surface that is a hypersurface in stress-deformation space (and not just in stress space as for elastic brittle materials), and the pertinent Griffith criticality condition for materials that dissipate energy not just by the creation of surface but also by deformation, in this case, by viscous deformation (Shrimali and Lopez-Pamies (2023) Extreme Mech. Lett. 58, 101944). From an applications point of view, the proposed theory amounts to solving an initial-boundary-value problem comprised of two nonlinear PDEs coupled with a nonlinear ODE for the deformation field, a tensorial internal variable, and the phase field. A robust scheme is presented to generate solutions for these equations.

cond-mat.soft↗

arXiv2024

The nonlinear elastic deformation of liquid inclusions embedded in elastomers

Elastomers filled with liquid inclusions -- as opposed to conventional solid fillers -- are a recent trend in the soft matter community because of their unique range of mechanical and physical properties. Such properties stem, in part, from the very large deformations that the underlying liquid inclusions are capable of undergoing. With the objective of advancing the understanding of the mechanics of this emerging class of materials, this paper presents a combined experimental/theoretical study of the nonlinear elastic deformation of initially spherical liquid inclusions embedded in elastomers that are subjected to quasistatic mechanical loads. The focus is on two fundamental problems, both within the limit regime when elasto-capillarity effects are negligible: ($i$) the problem of an isolated inclusion and ($ii$) that of a pair of closely interacting inclusions. Experimentally, specimens made of a polydimethylsiloxane (PDMS) elastomer filled with either isolated or pairs of initially spherical liquid glycerol inclusions are subjected to uniaxial tension. For the specimens with pairs of inclusions, three orientations of the two inclusions with respect to the direction of the applied macroscopic tensile load are considered, $0^\circ$, $45^\circ$, and $90^\circ$. The liquid glycerol is stained with a fluorescent dye that permits to measure the local deformation of the inclusions \emph{in situ} via confocal laser scanning fluorescent microscopy. Theoretically, a recently developed framework -- wherein the elastomer is considered to be a nonlinear elastic solid, the liquid comprising the inclusions is considered to be a nonlinear elastic fluid, and the interfaces separating the elastomer from the liquid inclusions can feature their own nonlinear elastic behavior (e.g., surface tension) -- is utilized to carry out full-field simulations of the experiments.

cond-mat.soft↗

arXiv2024

On the effects of material strength in dynamic fracture: A phase-field study

Over the past seven years, full-field analyses of a wide range of classical as well as modern quasi-static fracture experiments on nominally elastic brittle materials -- ranging from hard ceramics to soft elastomers -- have repeatedly identified the material strength surface as one of the key material properties that governs not only the nucleation of cracks, but also their propagation. Central to these analyses are the results generated by the Griffith phase-field fracture theory with material strength introduced in [21,23,20]. The first of two objectives of this paper is to extend this theory to account for inertia, this for the basic case of isotropic linear elastic brittle materials. From an applications point of view, the theory amounts to solving an initial-boundary-value problem comprised of a hyperbolic PDE coupled with an elliptic PDE for the displacement field $\mathbf{u}(\mathbf{X},t)$ and the phase field $d(\mathbf{X},t)$. A robust scheme is presented to generate solutions for these equations that is based on an adaptive finite-element discretization of space and an implicit finite-difference discretization of time. %At every time increment $t_m$, the resulting discretized equations are solved separately in a staggered manner for $\mathbf{u}(\mathbf{X},t_m)$ and $d(\mathbf{X},t_m)$ by means of Newton-Raphson schemes. The second objective is to illustrate the descriptive and predictive capabilities of the proposed theory via simulations of benchmark problems and experiments. These include problems involving fracture nucleation from large pre-existing cracks, such as the classical Kalthoff-Winkler experiments, as well as problems involving fracture nucleation within the bulk, such as the dynamic Brazilian fracture experiments.

cond-mat.mtrl-sci↗

arXiv2024

Nucleation of fracture: The first-octant evidence against classical variational phase-field models

As a companion work to [1], this Note presents a series of simple formulae and explicit results that illustrate and highlight why classical variational phase-field models cannot possibly predict fracture nucleation in elastic brittle materials. The focus is on ``tension-dominated'' problems where all principal stresses are non-negative, that is, problems taking place entirely within the first octant in the space of principal stresses.

cond-mat.mtrl-sci↗

arXiv2024

Classical variational phase-field models cannot predict fracture nucleation

Notwithstanding the evidence against them, classical variational phase-field models continue to be used and pursued in an attempt to describe fracture nucleation in elastic brittle materials. In this context, the main objective of this paper is to provide a comprehensive review of the existing evidence against such a class of models as descriptors of fracture nucleation. To that end, a review is first given of the plethora of experimental observations of fracture nucleation in nominally elastic brittle materials under quasi-static loading conditions, as well as of classical variational phase-field models, without and with energy splits. These models are then confronted with the experimental observations. The conclusion is that they cannot possibly describe fracture nucleation in general. This because classical variational phase-field models cannot account for material strength as an independent macroscopic material property. The last part of the paper includes a brief summary of a class of phase-field models that can describe fracture nucleation. It also provides a discussion of how pervasively material strength has been overlooked in the analysis of fracture at large, as well as an outlook into the modeling of fracture nucleation beyond the basic setting of elastic brittle materials.

cond-mat.mtrl-sci↗

arXiv2024

A Griffith description of fracture for non-monotonic loading with application to fatigue

With the fundamental objective of establishing the universality of the Griffith energy competition to describe the growth of large cracks in solids \emph{not} just under monotonic but under general loading conditions, this paper puts forth a generalization of the classical Griffith energy competition in nominally elastic brittle materials to arbitrary \emph{non-monotonic} quasistatic loading conditions, which include monotonic and cyclic loadings as special cases. Centered around experimental observations, the idea consists in: $i$) viewing the critical energy release rate $\mathcal{G}_c$ \emph{not} as a material constant but rather as a material function of both space $\textbf{X}$ and time $t$, $ii$) one that decreases in value as the loading progresses, this solely within a small region $Ω_\ell(t)$ around crack fronts, with the characteristic size $\ell$ of such a region being material specific, and $iii$) with the decrease in value of $\mathcal{G}_c$ being dependent on the history of the elastic fields in $Ω_\ell(t)$. By construction, the proposed Griffith formulation is able to describe any Paris-law behavior of the growth of large cracks in nominally elastic brittle materials for the limiting case when the loading is cyclic. For the opposite limiting case when the loading is monotonic, the formulation reduces to the classical Griffith formulation. Additional properties of the proposed formulation are illustrated via a parametric analysis and direct comparisons with representative fatigue fracture experiments on a ceramic, mortar, and PMMA.

cond-mat.other↗

arXiv2024

The poker-chip experiments of synthetic elastomers

In a recent study, Kumar and Lopez-Pamies (J. Mech. Phys. Solids 150: 104359, 2021) have provided a complete quantitative explanation of the famed poker-chip experiments of Gent and Lindley (Proc. R. Soc. Lond. Ser. A 249: 195--205, 1959) on natural rubber. In a nutshell, making use of the fracture theory of Kumar, Francfort, and Lopez-Pamies (J. Mech. Phys. Solids 112: 523--551, 2018), they have shown that the nucleation of cracks in poker-chip experiments in natural rubber is governed by the strength -- in particular, the hydrostatic strength -- of the rubber, while the propagation of the nucleated cracks is governed by the Griffith competition between the bulk elastic energy of the rubber and its intrinsic fracture energy. The main objective of this paper is to extend the theoretical study of the poker-chip experiment by Kumar and Lopez-Pamies to synthetic elastomers that, as opposed to natural rubber: ($i$) may feature a hydrostatic strength that is larger than their uniaxial and biaxial tensile strengths and ($ii$) do not exhibit strain-induced crystallization. A parametric study, together with direct comparisons with recent poker-chip experiments on a silicone elastomer, show that these two different material characteristics have a profound impact on where and when cracks nucleate, as well as on where and when they propagate. In conjunction with the results put forth earlier for natural rubber, the results presented in this paper provide a complete description and explanation of the poker-chip experiments of elastomers at large. As a second objective, this paper also introduces a new fully explicit constitutive prescription for the driving force that describes the material strength in the fracture theory of Kumar, Francfort, and Lopez-Pamies.

cond-mat.soft↗

arXiv2023

Cavitation in elastomers: A review of the evidence against elasticity

In spite of the growing body of evidence against it, the elasticity view of the phenomenon of cavitation in elastomers continues to be utilized in numerous studies. In this context, the main objective of this paper is to provide a comprehensive review of the existing evidence that settles that cavitation in elastomers is \emph{not} a purely elastic phenomenon. To that end, a review is first given of the experimental observations of cavitation in elastomers -- gathered since the 1930s until present times -- as well as of its theoretical description as an elastic phenomenon -- whose development started in the 1950s and was substantially completed by the 2010s. The latter is then confronted to the former to pinpoint the reasons why the elastic behavior of elastomers cannot possibly explain the experimental observations. The last part of the paper includes a brief summary of the current view of cavitation as a fracture phenomenon and an outlook for the field in that direction.

cond-mat.soft↗

arXiv2023

Abaqus implementation of a large family of finite viscoelasticity models

In this paper, we introduce an Abaqus UMAT subroutine for a family of constitutive models for the viscoelastic response of isotropic elastomers of any compressibility -- including fully incompressible elastomers -- undergoing finite deformations. The models can be chosen to account for a wide range of non-Gaussian elasticities, as well as for a wide range of nonlinear viscosities. From a mathematical point of view, the structure of the models is such that the viscous dissipation is characterized by an internal variable $\textbf{C}^v$, subject to the physically-based constraint $\det\textbf{C}^v=1$, that is solution of a nonlinear first-order ODE in time. This ODE is solved by means of an explicit Runge-Kutta scheme of high order capable of preserving the constraint $\det\textbf{C}^v=1$ identically. The accuracy and convergence of the code is demonstrated numerically by comparison with an exact solution for several of the Abaqus built-in hybrid finite elements, including the simplicial elements C3D4H and C3D10H and the hexahedral elements C3D8H and C3D20H. The last part of this paper is devoted to showcasing the capabilities of the code by deploying it to compute the homogenized response of a bicontinuous rubber blend.

math.NA↗

arXiv2023

The nonlinear elastic response of bicontinuous rubber blends

Rubber blends are ubiquitous in countless technological applications. More often than not, rubber blends exhibit complex interpenetrating microstructures, which are thought to have a significant impact on their resulting macroscopic mechanical properties. As a first step to understand this potential impact, this paper presents a bottom-up or homogenization study of the nonlinear elastic response of the prominent class of bicontinuous rubber blends, that is, blends made of two immiscible constituents or phases segregated into an interpenetrating network of two separate but fully continuous domains that are perfectly bonded to one another. The focus is on blends that are isotropic and that contain an equal volume fraction (50/50) of each phase. The microstructures of these blends are idealized as microstructures generated by level cuts of Gaussian random fields that are suitably constrained to be periodic so as to allow for the construction of unit cells over which periodic homogenization can be carried out. The homogenized or macroscopic elastic response of such blends are determined both numerically via finite elements and analytically via a nonlinear comparison medium method. The numerical approach makes use of a novel meshing scheme that leads to conforming and periodic simplicial meshes starting from a voxelized representation of the microstructures. Results are presented for the fundamental case when both rubber phases are Neo-Hookean, as well as when they exhibit non-Gaussian elasticity. Remarkably, irrespective of the elastic behavior of the phases, the results show that the homogenized response of the blends is largely insensitive to the specific morphologies of the phases.

cond-mat.soft↗

arXiv2023

Liquid Filled Elastomers: From Linearization to Elastic Enhancement

Surface tension at cavity walls can play havoc with the mechanical properties of perforated soft solids when the cavities are filled with a fluid. This study is an investigation of the macroscopic elastic properties of elastomers embedding spherical cavities filled with a pressurized liquid in the presence of surface tension, starting with the linearization of the fully nonlinear model and ending with the enhancement properties of the linearized model when many such liquid filled cavities are present.

math.AP↗

arXiv2023

The trousers fracture test for viscoelastic elastomers

Shrimali and Lopez-Pamies (2023) have recently shown that the Griffith criticality condition that governs crack growth in viscoelastic elastomers can be reduced to a fundamental form that involves exclusively the intrinsic fracture energy $G_c$ of the elastomer and, in so doing, they have brought resolution to the complete description of the historically elusive notion of critical tearing energy $T_c$. The purpose of this paper -- which can be viewed as the third installment of the series started by Shrimali and Lopez-Pamies (2023) -- is to make use of this fundamental form to explain one of the most popular fracture tests for probing the growth of cracks in viscoelastic elastomers, the trousers test.

cond-mat.soft↗