Joel Marthelot

Self-Replicating Cracks: A Collaborative Fracture Mode in Thin Films

Straight cracks are observed in thin coatings under residual tensile stress, resulting into the classical network pattern observed in china crockery, old paintings, or dry mud. Here, we present a novel fracture mechanism where delamination and propagation occur simultaneously, leading to the spontaneous self-replication of an initial template. Surprisingly, this mechanism is active below the standard critical tensile load for channel cracks and selects a robust interaction length scale on the order of 30 times the film thickness. Depending on triggering mechanisms, crescent alleys, spirals, or long bands are generated over a wide range of experimental parameters. We describe with a simple physical model, the selection of the fracture path and provide a configuration diagram displaying the different failure modes.

The Geometric Role of Precisely Engineered Imperfections on the Critical Buckling Load of Spherical Elastic Shells

We study the effect of a dimple-like geometric imperfection on the critical buckling load of spherical elastic shells under pressure loading. This investigation combines precision experiments, finite element modeling and numerical solutions of a reduced shell theory, all of which are found to be in excellent quantitative agreement. In the experiments, the geometry and magnitude of the defect can be designed and precisely fabricated through a customizable rapid prototyping technique. Our primary focus is on predictively describing the imperfection sensitivity of the shell to provide a quantitative relation between its knockdown factor, as a function of the amplitude of the defect. In addition, we find that the buckling pressure becomes independent of the amplitude of the defect beyond a critical value. The level and onset of this plateau are quantified systematically and found to be affected by a single geometric parameter that depends on both the radius to thickness ratio of the shell and the angular width of the defect. To the best of our knowledge, this is the first time that experimental results on the knockdown factors of imperfect spherical shells have been accurately predicted, through both finite element modeling and shell theory solutions.

Fabrication of slender elastic shells by the coating of curved surfaces

Various manufacturing techniques exist to produce double-curvature shells, including injection, rotational and blow molding, as well as dip coating. However, these industrial processes are typically geared for mass production and are not directly applicable to laboratory research settings, where adaptable, inexpensive and predictable prototyping tools are desirable. Here, we study the rapid fabrication of hemispherical elastic shells by coating a curved surface with a polymer solution that yields a nearly uniform shell, upon polymerization of the resulting thin film. We experimentally characterize how the curing of the polymer affects its drainage dynamics and eventually selects the shell thickness. The coating process is then rationalized through a theoretical analysis that predicts the final thickness, in quantitative agreement with experiments and numerical simulations of the lubrication flow field. This robust fabrication framework should be invaluable for future studies on the mechanics of thin elastic shells and their intrinsic geometric nonlinearities.

Transforming architectures inspired by origami

Paper folding is found across cultures for both aesthetic and functional purposes, with its most widely recognized exponent being the ancient art form of origami. More recently, there has been an upsurge of interest for translating origami designs into mathematics, natural sciences, engineering, and architecture. Across these different fields, origami is becoming a fountain of inspiration for new reconfigurable and multifunctional materials and structures. However, the use of origami designs as engineering elements is typically compromised by limitations in structural performance. A new study by Filipov et al. (1) presents an innovative approach for the design of strikingly rigid deployable structures. Their strategy is based on tubular building blocks, which are themselves built on Miura-ori; a regular folding pattern that maps a flat sheet into a one degree-of-freedom deployable structure (2). Two neighboring Miura tubes can be set in a zig-zag (“zipper”) arrangement; together, the pair is remarkably stiff and effectively possesses a single degree of freedom by resisting other bending and twisting modes. These zipper tubes can then be combined to generate other structures, including more complex tubular systems and cellular assemblies. In Fig. 1 A and B, we present two particular examples from their study: a model bridge with load-bearing capacity and an architectural canopy that can be deployed to cover a wide span. Filipov et al. (1) borrow well-established tools from structural mechanics that are commonly used in civil and mechanical engineering and port them to this new emerging field of origami-inspired design.

Technical Brief: Knockdown Factor for the Buckling of Spherical Shells Containing Large-Amplitude Geometric Defects

We explore the effect of precisely defined geometric imperfections on the buckling load of spherical shells under external pressure loading, using finite element analysis that was previously validated through precision experiments. Our numerical simulations focus on the limit of large amplitude defects and reveal a lower bound that depends solely on the shell radius to thickness ratio and the angular width of the defect. It is shown that, in the large amplitude limit, the buckling load depends on an single geometric parameter, even for shells of moderate radius to thickness ratio. Moreover, numerical results on the knockdown factor are fitted to an empirical, albeit general, functional form that may be used as robust design guideline for the critical buckling conditions of pressurized spherical shells.

A new failure mechanism in thin film by collaborative fracture and delamination: Interacting duos of cracks

When a thin film moderately adherent to a substrate is subjected to residual stress, the cooperation between fracture and delamination leads to unusual fracture patterns, such as spirals, alleys of crescents and various types of strips, all characterized by a robust characteristic length scale. We focus on the propagation of a duo of cracks: two fractures in the film connected by a delamination front and progressively detaching a strip. We show experimentally that the system selects an equilibrium width on the order of 25 times the thickness of the coating and independent of both fracture and adhesion energies. We investigate numerically the selection of the width and the condition for propagation by considering Griffiths criterion and the principle of local symmetry. In addition, we propose a simplified model based on the criterion of maximum of energy release rate, which provides insights of the physical mechanisms leading to these regular patterns, and predicts the effect of material properties on the selected width of the detaching strip.

Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force

We study the buckling of hemispherical elastic shells subjected to the combined effect of pressure loading and a probing force. We perform an experimental investigation using thin shells of nearly uniform thickness that are fabricated with a well-controlled geometric imperfection. By systematically varying the indentation displacement and the geometry of the probe, we study the effect that the probe-induced deflections have on the buckling strength of our spherical shells. The experimental results are then compared to finite element simulations, as well as to recent theoretical predictions from the literature. Inspired by a nondestructive technique that was recently proposed to evaluate the stability of elastic shells, we characterize the nonlinear load-deflection mechanical response of the probe for different values of the pressure loading. We demonstrate that this nondestructive method is a successful local way to assess the stability of spherical shells. [DOI: 10.1115/1.4038063]