arXiv subjects

Marcelo A. Dias

Publications and source records attributed to Marcelo A. Dias.

At least 19 recordsLinked to original sources

arXiv2026

Instability-induced bistable shape-morphing kirigami structures

Deployable shape-morphing structures that transform from flat sheets into stable three-dimensional configurations are highly desirable for applications ranging from soft robotics and biomedical devices to adaptive architecture and aerospace systems. Existing kirigami-based morphing systems primarily rely on isotropic deployment, compliant soft materials, or external constraints to maintain deployed shapes, which limits geometric programmability, structural integrity, and applicability in rigid-material systems. Here, we present an inverse design framework for anisotropic bistable kirigami structures that enables programmable shape morphing through controlled geometric frustration and instability-induced deployment. The framework combines a semi-analytical mechanical model with geometry to establish a direct connection between geometric transformation and the underlying energy landscape. We show that instability-induced shape morphing leads to tunable bistability and directional deployment in anisotropic kirigami structures. The results are validated through finite element simulations and experiments, demonstrating stable deployed configurations and programmable anisotropic morphing. The proposed framework further provides a general design strategy that can be integrated with various active actuation systems, enabling broader engineering applications.

cond-mat.soft↗

arXiv2026

Nonlinear Mechanics and Predictable Bifurcation of Multi-Cell Kresling Origami Chains

Meta-structures that display axial-twist coupling can be achieved through the emerging kinematics in Kresling origami patterns. A central challenge in these structures is understanding their nonlinear mechanical behaviour, specifically their equilibrium branches and bifurcation diagrams. This involves identifying relationships between desired responses and the geometric variables that define the design space, including the Kresling polygon count, initial twist angle, height, radius, and crease lengths. As the number of constituent units increases in an n-layer chain, we track complex equilibrium branches extending into the post-critical regime under successive instabilities, including branch-point bifurcations and limit-point instabilities. This work begins by establishing the relationship between the geometric design variables and the response curves of the assembled chain by modelling the crease lines as axial-load-carrying elements. Subsequently, equilibrium branches and instabilities are systematically investigated via continuation and bifurcation analysis, beginning with the single-layer system and progressively extending to two- and three-layer configurations. Finally, a generalisation strategy is proposed to extend these findings to an n-layer Kresling chain. This strategy enables the predictive construction of equilibrium paths and the inverse design of multi-layer meta-structures, using prescribed critical points to control post-critical behaviour. It provides a foundation for the inverse design and optimisation of architected mechanical metamaterials with programmable responses.

cond-mat.soft↗

arXiv2026

How Geometry Tames Disorder in Lattice Fracture

We investigate the fracture behavior of pre-cracked triangular beam-lattices whose elements have failure stresses drawn from a Weibull distribution. Through a statistical analysis and numerical simulations, we identify and verify the existence of three distinct failure regimes: (i) disorder is effectively suppressed, (ii) disorder manifests locally near the crack tip, modifying the crack morphology, and (iii) disorder manifests globally, leading to initially diffuse failure. Our model naturally reveals the key parameters governing this behavior: the Weibull modulus, quantifying the spread in failure thresholds, and a geometric quantity termed the Slenderness Ratio. We also reproduce the disorder-induced toughening reported in previous experimental and numerical studies, further demonstrating that its manifestation depends non-monotonically on disorder. Crucially, our results indicate that this toughening cannot be simply connected to the amount of damage in the lattice, challenging interpretations that attribute increased fracture energy solely to enhanced crack tortuosity or diffuse failure. Overall, our results establish geometry as a powerful control parameter for regulating how disorder is expressed during fracture in beam-lattices, with broader implications for the disorder-induced toughening in engineered materials.

cond-mat.mtrl-sci↗

arXiv2025

Architecting mechanisms of damage in topological metamaterials

Architecting mechanisms of damage in metamaterials by leveraging lattice topology and geometry poses a vital yet complex challenge, essential for engineering desirable mechanical responses. Of these metamaterials, Maxwell lattices, which are on the verge of mechanical stability, offer significant potential for advanced functionality. By leveraging their robust topological features, they enable precise control of effective elastic properties, manipulation of stress localisation and delocalisation across specific domains, and targeted global damage that follows local fracture events. In this work, we identify topology and geometry-dependent parameters that establish a simple, yet precise, framework for designing the behaviour of non-idealised Maxwell lattices and their damage processes. We numerically explore the underlying phenomenology to demonstrate how this framework can guide or arrest damage in lattices, both with and without domain walls and additional boundary constraints. Our approach uncovers a robust way to manipulate the mechanisms of damage and the path they follow in metamaterials, with further insight into crack arrest, diversion, and shielding.

cond-mat.soft↗

arXiv2025

Cracking Down on Fracture to Functionalise Damage

In this work we propose a novel relationship between topology and damage propagation in Maxwell lattices that redefines fracture as a functional design feature rather than mere degradation. We demonstrate that topologically protected modes, inherently robust against perturbations, localise along lattice discontinuities and govern the mechanical response. By precisely engineering the microstructure, we direct these modes to control stress distributions and trigger predictable, controlled damage. Our findings -- validated through comprehensive numerical simulations and experiments -- advance our understanding of nontrivial mechanical responses in Maxwell lattices and establish a clear framework for designing materials with improved fracture energy. This work paves the way for further exploration of topology-driven phenomena in mechanical systems and promises a new direction in the design of robust materials.

cond-mat.soft↗

arXiv2024

Inverse design of programmable shape-morphing kirigami structures

Shape-morphing structures have the capability to transform from one state to another, making them highly valuable in engineering applications. In this study, it is propose a two-stage shape-morphing framework inspired by kirigami structures to design structures that can deploy from a compacted state to a prescribed state under certain mechanical stimuli -- although the framework may also be extended to accommodate various physical fields, such as magnetic, thermal, and electric fields. The framework establishes a connection between the geometry and mechanics of kirigami structures. The proposed approach combines the finite element analysis (FEA), genetic algorithm (GA), and an analytical energy-based model to obtain kirigami designs with robustness and efficiency.

cond-mat.soft↗

arXiv2024

On Micropolar Elastic Foundations

The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar elasticity. Conversely, elastic foundation theory is widely employed in fracture mechanics and the analysis of delamination propagation in composite materials. This study aims to amalgamate these two frameworks, enhancing the elastic foundation theory to accommodate materials exhibiting micropolar behaviour. Specifically, we present a novel theory of elastic foundation for micropolar materials, employing stress potentials formulation and a unique normalisation approach. Closed-form solutions are derived for stress and couple stress reactions inherent in such materials, along with the associated restoring stiffness. The validity of the proposed theory is established through verification using the double cantilever beam configuration. Concluding our study, we elucidate the benefits and limitations of the developed theory by quantifying the derived parameters for materials known to exhibit micropolar behaviour. This integration of micropolar elasticity into the elastic foundation theory not only enhances our understanding of material responses but also provides a versatile framework for the analysis of heterogeneous materials in various engineering applications.

cond-mat.soft↗

arXiv2024

Toughening mechanisms and damage propagation in Architected-Interfaces

We investigate fracture toughness of architected interfaces and their ability to maintain structural integrity and provide stable damage propagation conditions beyond the failure load. We propose theoretical and numerical frameworks to evaluate the fracture properties of architected interfaces sandwiched between two (face) materials. The microscopic geometries of these interfaces are chosen as 2D cells--pillar, tetrahedron, and hexagon--as well as their 3D counterparts--namely, pillar array, octet truss, and Kelvin cell. Our model, both numerical and analytical, exhibits a high level of accuracy in predicting the compliance before failure and failure loads. Novel results are obtained during the damage propagation regime, indicating fulfilment of the so-called fail-safe design. Some of the cell geometries unfold during fracture, thus increasing the failure load and ensuring stable and controlled damage propagation conditions.

physics.app-ph↗

arXiv2024

Frictional contact of soft polymeric shells

The classical Hertzian contact model establishes a monotonic correlation between contact force and area. Here, we showed that the interplay between local friction and structural instability can deliberately lead to unconventional contact behavior when a soft elastic shell comes into contact with a flat surface. The deviation from Hertzian contact first arises from bending within the contact area, followed by the second transition induced by buckling, resulting in a notable decrease in the contact area despite increased contact force. Friction delays both transitions and introduces hysteresis during unloading. However, a high amount of friction suppresses both buckling and dissipation. Different contact regimes are discussed in terms of rolling and sliding mechanisms, providing insights for tailoring contact behaviors in soft shells.

cs.CE↗

arXiv2021

On local kirigami mechanics II: Stretchable creased solutions

Following on Part I of this work series on local kirigami mechanics, we present a study of a discretely creased mechanism as a model to investigate the mechanics of the basic geometric building block of kirigami--the e-cone. We consider an annular disk with a single radial slit discritised by a series of radial creases connecting kinematically flat rigid panels. The creases allow both relative rotation and separation between panels, capturing both bending and stretching deformations. Admissible equilibrium configurations are obtained by penalising these deformations using elastic springs with stiffnesses derived from compatible continuum plate deformations. This provides a tool to study both inextensible and extensible e-cone configurations due to opening of the slit and rotation of its lips. This creased model hence offers the possibility to study the e-cone away from its isometric limit, i.e., for plates with finite thickness, and explore the full range of post-buckling (far-from-threshold) behaviour as well as initial buckling (near-threshold) instability. Our local approach provides a fundamental understanding of kirigami phenomenology, underpinned by a proper theoretical approach to geometry and mechanics.

cond-mat.soft↗

arXiv2021

Can confined mechanical metamaterials replace adhesives?

The subject of mechanical metamaterials has been gaining significant attention, however, their widespread application is still halted. Such materials are usually considered as stand-alone, vis-à-vis all characteristic length scales being associated solely with geometry of material itself. In this work we propose novel application of mechanical metamaterials as interface regions joining two materials with potential of replacing bulk adhesives. This idea leads into paradigm shifts for both metamaterials and adhesive joints. In specific, we outline methodology for testing and evaluating confined lattice materials within fracture mechanics framework. The theoretical and numerical approaches are inter-winded, revealing a set of critical parameters that needs to be considered during design process. Lattices that are stretching and bending dominated are explored and failure maps are proposed, indicating susceptibility to a certain failure mode depending on level of confinement and characteristic dimension of each lattice's unit cells.

cond-mat.mtrl-sci↗

arXiv2021

Re-entrant tensegrity: A three-periodic, chiral, tensegrity structure that is auxetic

We present a three-periodic, chiral, tensegrity structure and demonstrate that it is auxetic. Our tensegrity structure is constructed using the chiral symmetry Π+ cylinder packing, transforming the cylinders themselves to the elastic elements and cylinder contacts to incompressible rods. The resulting structure displays local re-entrant geometry at its vertices, and is shown to be auxetic when modelled as an equilibrium configuration of spatial constraints subject to a quasi-static deformation. When the tensegrity structure is subsequently modelled as a lattice material with elastic elements, the auxetic behaviour is again confirmed through finite element modelling as well as demonstrated with a 3d printed example. The cubic symmetry of the structure means that the behaviour is independent of the chosen stretching direction and the auxetic behaviour is observed in both perpendicular directions. This structure could be the simplest three-dimensional analogue to the two-dimensional re-entrant honeycomb. This, alongside the chirality of the structure, make it an interesting design target for multifunctional materials.

cond-mat.mtrl-sci↗

arXiv2021

On Local Kirigami Mechanics I: Isometric Conical Solutions

Over the past decade, kirigami--the Japanese art of paper cutting--has been playing an increasing role in the emerging field of mechanical metamaterials and a myriad of other mechanical applications. Nonetheless, a deep understanding of the mathematics and mechanics of kirigami structures is yet to be achieved in order to unlock their full potential to pioneer more advanced applications in the field. In this work, we study the most fundamental geometric building block of kirigami: a thin sheet with a single cut. We consider a reduced two-dimensional plate model of a circular thin disk with a radial slit and investigate its deformation following the opening of the slit and the rotation of its lips. In the isometric limit--as the thickness of the disk approaches zero--the elastic energy has no stretching contribution and the thin sheet takes a conical shape known as the e-cone. We solve the post-buckling problem for the e-cone in the geometrically nonlinear setting assuming a Saint Venant-Kirchhoff constitutive plate model; we find closed-form expressions for the stress fields and show the geometry of the e-cone to be governed by the spherical elastica problem. This allows us to fully map out the space of solutions and investigate the stability of the post-buckled e-cone problem assuming mirror symmetric boundary conditions on the rotation of the lips on the open slit.

cond-mat.soft↗

arXiv2019

Tunable wrinkling of thin nematic liquid crystal elastomer sheets

Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control of these instabilities through direct coupling between microscopic degrees of freedom, resulting from orientational ordering of rod-like molecules, and macroscopic strain. By a standard method of dimensional reduction, we construct a plate theory for thin sheets of nematic elastomer. We then apply this theory to the study of the formation of wrinkles due to compression of a thin sheet of nematic liquid crystal elastomer atop an elastic or fluid substrate. We find the scaling of the wrinkle wavelength in terms of material parameters and the applied compression. The wavelength of the wrinkles is found to be non-monotonic in the compressive strain owing to the presence of the nematic. Finally, due to soft modes, the critical stress for the appearance of wrinkles can be much higher than in an isotropic elastomer and depends nontrivially on the manner in which the elastomer was prepared.

cond-mat.soft↗

arXiv2018

Multistable Kirigami for Tunable Architected Materials

In nature, materials such as ferroelastics and multiferroics can switch their microstructure in response to external stimuli, and this reconfiguration causes a simultaneous modulation of its material properties. Rapid prototyping technologies have enabled origami and kirigami-inspired architected materials to provide a means for designing shape-shifting structures, and here we show how multistable structures inspired by kirigami provide novel design criteria for preparing mechanical metamaterials with tunable properties. By changing the geometry of kirigami unit cells, we obtain multistable kirigami lattice structures endowed with a bistable snap-through mechanism. We demonstrate the precise control of material stiffness, along with the ability to tune this property in situ by locally and reversibly switching the unit cell configurations. We anticipate these mechanical metamaterials will provide a platform to achieve in situ tunable electrical, optical, and mechanical properties for a variety of applications in multifunctional materials, two-dimensional materials, and soft robotics.

physics.app-ph↗

arXiv2018

Overcurvature induced multistability of linked conical frusta: How a `bendy straw' holds its shape

We study the origins of multiple mechanically stable states exhibited by an elastic shell comprising multiple conical frusta, a geometry common to reconfigurable corrugated structures such as `bendy straws'. This multistability is characterized by mechanical stability of axially extended and collapsed states, as well as a partially inverted `bent' state that exhibits stability in any azimuthal direction. To understand the origin of this behavior, we study how geometry and internal stress affect the stability of linked conical frusta. We find that tuning geometrical parameters such as the frustum heights and cone angles can provide axial bistability, whereas stability in the bent state requires a sufficient amount of internal pre-stress, resulting from a mismatch between the natural and geometric curvatures of the shell. We analyze the latter effect through curvature analysis during deformation using X-ray computed tomography (CT), and with a simple mechanical model that captures the qualitative behavior of these highly reconfigurable systems.

cond-mat.soft↗

arXiv2017

Kirigami Actuators

Thin elastic sheets bend easily and, if they are patterned with cuts, can deform in sophisticated ways. Here we show that carefully tuning the location and arrangement of cuts within thin sheets enables the design of mechanical actuators that scale down to atomically-thin 2D materials. We first show that by understanding the mechanics of a single, non-propagating crack in a sheet we can generate four fundamental forms of linear actuation: roll, pitch, yaw, and lift. Our analytical model shows that these deformations are only weakly dependent on thickness, which we confirm with experiments at centimeter scale objects and molecular dynamics simulations of graphene and MoS$_{2}$ nanoscale sheets. We show how the interactions between non-propagating cracks can enable either lift or rotation, and we use a combination of experiments, theory, continuum computational analysis, and molecular dynamics simulations to provide mechanistic insights into the geometric and topological design of kirigami actuators.

cond-mat.soft↗

arXiv2017

Stiffness of the human foot and evolution of the transverse arch

Foot stiffness underlies its mechanical function, and is central to the evolution of human bipedal locomotion. The stiff and propulsive human foot has two distinct arches, the longitudinal and transverse. By contrast, the feet of non-human primates are flat and softer. Current understanding of foot stiffness is based on studies that focus solely on the longitudinal arch, and little is known about the mechanical function of the transverse arch. However, common experience suggests that transverse curvature dominates the stiffness; a drooping dollar bill stiffens significantly upon curling it along the transverse direction, not the longitudinal. We derive a normalized curvature parameter that encapsulates the geometric principle underlying the transverse curvature-induced stiffness. We show that the transverse arch accounts for almost all the difference in stiffness between human and monkey feet (vervet monkeys and pig-tailed macaques) by comparing transverse curvature-based predictions against published data on foot stiffness. Using this functional interpretation of the transverse arch, we trace the evolution of hominin feet and show that a human-like stiff foot likely predates Homo by $\sim 1.5$ million years, and appears in the $\sim 3.4$ million year old fossil from Burtele. A distinctly human-like transverse arch is also present in early members of Homo, including Homo naledi, Homo habilis, and Homo erectus. However, the $\sim 3.2$ million year old Australopithecus afarensis is estimated to have possessed a transitional foot, softer than humans and stiffer than other extant primates. A foot with human-like stiffness probably evolved around the same time as other lower limb adaptations for regular bipedality, and well before the emergence of Homo, the longitudinal arch, and other adaptations for endurance running.

physics.bio-ph↗