arXiv subjects

Davide Bigoni

Publications and source records attributed to Davide Bigoni.

At least 19 recordsLinked to original sources

arXiv2026

Tensile wrinkling and creasing of an elastic half-space under a suction load

A famous and thoroughly investigated instability set-up, susceptible to wrinkling and creasing, consists of an elastic half-space being prestressed under a dead load, applied at infinity and, possibly, on its surface. We consider the case of a pressure or a suction applied on the surface and show that wrinkling and creasing occur in a surprising way, completely different from dead load. With reference to incompressible neo-Hookean elasticity and assuming the prevalence of a uniaxial prestress state induced by the application of a uniform pressure, no wrinkling or creasing is foreseen, whereas -- unexpectedly -- they do when reversing the sign of pressure, which is then a suction, thus leading to tensile creasing and tensile wrinkling. When a biaxial prestress state is considered, it is shown that some loading paths can be envisaged, able to grow to infinity without causing any instability. Consequently, we suggest that, according to its sign, pressure can promote or delay surface instabilities, a finding which may have implications for mechanobiology or microfluidic fluid-structure interaction.

physics.class-ph↗

arXiv2026

Shear band patterns by boundary integral equations

Boundary integral equations are presented to analyze perturbations in terms of small elastic deformations superimposed upon an arbitrary, homogeneous strain. Plane strain deformations of an incompressible, prestressed, anisotropic, elastic solid are considered assuming the Biot constitutive framework. The special case of perturbations of stress/deformation incident wave fields, caused by a shear band of finite length formed inside the material at a certain stage of the deformation path, is formulated.

physics.class-ph↗

arXiv2026

The strange mechanics of an elastic rod under null-resultant transverse loads

Two equal and opposite distributed dead loads are applied orthogonally to the axis of an elastic rod in its rectilinear reference configuration, one at the extrados and the other at the intrados, such that the resultant applied force per unit length is uniformly zero. In this configuration, the rod is subjected to a transverse (tensile or compressive) stress, which is usually believed to have no significant effect on the structural response and has therefore not been considered so far. Contrary to this common belief, the asymptotic behavior of an incrementally deformed elastic layer and three different rod models (the first derived as an asymptotic approximation of the elastic layer; the second based on Euler elastica; and the third obtained by homogenization of a discrete model) reveal that this loading condition produces the same deformation in the rod as an axial load. In particular, the transverse load adds to the axial load in a generalized version of the Euler elastica, leading to buckling and nontrivial postcritical deformations when compressive. The critical transverse stress for buckling is found to have the same form as the Euler critical stress under axial force and tends to zero in the limit of vanishing rod inertia. For this reason, instability induced by transverse loading persists even when the rod thickness tends to zero. These theoretical predictions are confirmed by numerical simulations of a slender elastic layer, which show that increasing transverse load can induce buckling and drive the layer along a deformation path that closely follows that predicted by the generalized Euler elastica throughout the entire postcritical regime, even beyond self-intersection. To show that this behavior can be realized in practice, a dedicated experimental setup is developed, and the experimental results fully confirm the theoretical and numerical predictions.

physics.class-ph↗

arXiv2025

Homogenization of architected materials incorporating shearable beams

Two-dimensional architected materials are often realized as periodic grids of elastic beams. Conventional homogenization methods represent these structures as equivalent elastic solids but neglect shear deformation in the constituent beams. This article addresses this limitation by incorporating shear deformability through Timoshenko beam theory, enabling accurate modeling of stubby beams. Moreover, shearable beams with extreme mechanical characteristics can be obtained through the design of appropriate microstructures. Introducing shearable beams into the grid expands the design space, allowing, for instance, the control of the effective Poisson's ratio beyond the limits achievable with slender beams.

physics.class-ph↗

arXiv2025

Material instability and subsequent restabilization from homogenization of periodic elastic lattices

Two classes of non-linear elastic materials are derived via two-dimensional homogenization. These materials are equivalent to a periodic grid of axially-deformable and axially-preloaded structural elements, subject to incremental deformations that involve bending, shear, and normal forces. The unit cell of one class is characterized by elements where deformations are lumped within a finite-degrees-of-freedom framework. In contrast, the other class involves smeared deformation, modelled as flexurally deformable rods with sufficiently high axial compliance. Under increasing compressive load, the elasticity tensor of the equivalent material loses positive definiteness and subsequently undergoes an ellipticity loss. Remarkably, in certain conditions, this loss of stability is followed by a subsequent restabilization; that is, the material re-enters the elliptic regime and even the positive definiteness domain and simultaneously, the underlying elastic lattice returns to a stable state. This effect is closely related to the axial compliance of the elements. Our results: (i.) demonstrate new possibilities for exploiting structural elements within the elastic range, characterized by a finite number of degrees of freedom, to create architected materials with tuneable instabilities, (ii.) introduce reconfigurable materials characterized by 'islands' of stability or instability.

physics.class-ph↗

arXiv2024

Necking of thin-walled cylinders via bifurcation of incompressible nonlinear elastic solids

Necking localization under quasi-static uniaxial tension is experimentally observed in ductile thin-walled cylindrical tubes, made of soft polypropylene. Necking nucleates at multiple locations along the tube and spreads throughout, involving higher-order modes, evidencing trefoil and fourthfoiled (but rarely even fifth-foiled) shaped cross-sections. No evidence of such a complicated necking occurrence and growth was found in other ductile materials for thin-walled cylinders under quasi-static loading. With the aim of modelling this phenomenon, as well as all other possible bifurcations, a twodimensional formulation is introduced, in which only the mean surface of the tube is considered, paralleling the celebrated Fl\"ugge treatment of axially-compressed cylindrical shells. This treatment is extended to include tension and a broad class of nonlinear-hyperelastic constitutive law for the material, which is also assumed to be incompressible. The theoretical framework leads to a number of new results, not only for tensile axial force (where necking is modelled and, as a particular case, the classic Consid\`ere formula is shown to represent the limit of very thin tubes), but also for compressive force, providing closed-form formulae for wrinkling (showing that a direct application of the Fl\"ugge equation can be incorrect) and for Euler buckling. It is shown that the J2-deformation theory of plasticity (the simplest constitutive assumption to mimic through nonlinear elasticity the plastic branch of a material) captures multiple necking and occurrence of higher-order modes, so that experiments are explained. The presented results are important for several applications, ranging from aerospace and automotive engineering to the vascular mechanobiology, where a thin-walled tube (for instance an artery, or a catheter, or a stent) may become unstable not only in compression, but also in tension.

cond-mat.soft↗

arXiv2024

Effects of different loading on the bifurcation of annular elastic rods: theory vs. experiments

The bifurcation problem of a circular Euler-Bernoulli rod subject to a uniform radial force distribution is investigated under three distinct loading conditions: (i.) hydrostatic pressure, (ii.) centrally-directed, and (iii.) dead load. Previous studies on this apparently 'familiar' structural problem have yielded controversial results, necessitating a comprehensive clarification. This study shows that results previously labelled as 'correct' or 'wrong' simply refer to different external constraints, whose presence becomes necessary only for the two latter loads, (ii.) and (iii.). Moreover, the paper presents the first experimental realization of a circular rod subjected to centrally-directed loads. The experimental findings align with the theoretical predictions and show the exploitation of a new type of load acting on a continuous structural element. The feasibility of this load is demonstrated through the use of inextensible cables and opens the way to applications in flexible robotics when cables are used for actuation.

physics.class-ph↗

arXiv2024

Elastic solids under frictionless rigid contact and configurational force

A homogeneous elastic solid, bounded by a flat surface in its unstressed configuration, undergoes a finite strain when in frictionless contact against a rigid and rectilinear constraint, ending with a rounded or sharp corner, in a two-dimensional formulation. With a strong analogy to fracture mechanics, it is shown that (i.) a path-independent $J$--integral can be defined for frictionless contact problems, (ii.) which is equal to the energy release rate $G$ associated with an infinitesimal growth in the size of the frictionless constraint, and thus gives the value of the configurational force component along the sliding direction. Furthermore, it is found that (iii.) such a configurational sliding force is the Newtonian force component exerted by the elastic solid on the constraint at the frictionless contact. Assuming the kinematics of an Euler-Bernoulli rod for an elastic body of rectangular shape, the results (i.)--(iii.) lead to a new interpretation from a nonlinear solid mechanics perspective of the configurational forces recently disclosed for one-dimensional structures of variable length. Finally, approximate but closed-form solutions (validated with finite element simulations) are exploited to provide further insight into the effect of configurational forces. In particular, two applications are presented which show that a transverse compression can lead to Eulerian buckling or to longitudinal dynamic motion, both realizing novel examples of soft actuation mechanisms. As an application to biology, our results may provide a mechanical explanation for the observed phenomenon of negative durotaxis, where cells migrate from stiffer to softer environments.

cond-mat.soft↗

arXiv2024

Effects of prestress in the coating of an elastic disk

An elastic disk is coated with an elastic rod, uniformly prestressed with a tensile or compressive axial force. The prestress state is assumed to be induced by three different models of external radial load or by 'shrink-fit' forcing the coating onto the disk. The prestressed coating/disk system, when loaded with an additional and arbitrary incremental external load, experiences incremental displacement, strain, and stress, which are solved via complex potentials. The analysis incorporates models for both perfect and imperfect bonding at the coating/disk interface. The derived solution highlights the significant influence not only of the prestress but also of the method employed to generate it. These two factors lead, in different ways, to a loss or an increase in incremental stiffness for compressive or tensile prestress. The first bifurcation load of the structure (which differs for different prestress generations) is determined in a perturbative way. The results emphasize the importance of modelling the load and may find applications in flexible electronics and robot arms subject to pressure or uniformly-distributed radial forces.

physics.class-ph↗

arXiv2024

Bifurcations of an elastic disc coated with an elastic inextensible rod

An analytical solution is derived for the bifurcations of an elastic disc that is constrained on the boundary with an isoperimetric Cosserat coating. The latter is treated as an elastic circular rod, either perfectly or partially bonded (with a slip interface in the latter case) and is subjected to three different types of uniformly distributed radial loads (including hydrostatic pressure). The proposed solution technique employs complex potentials to treat the disc's interior and incremental Lagrangian equations to describe the prestressed elastic rod modelling the coating. The bifurcations of the disc occur with modes characterized by different circumferential wavenumbers, ranging between ovalization and high-order waviness, as a function of the ratio between the elastic stiffness of the disc and the bending stiffness of its coating. The presented results find applications in various fields, such as coated fibres, mechanical rollers, and the growth and morphogenesis of plants and fruits.

physics.class-ph↗

arXiv2024

Homogenization of elastic grids containing rigid elements

The inclusion of rigid elements into elastic composites may lead to superior mechanical properties for the equivalent elastic continuum, such as, for instance, extreme auxeticity. To allow full exploitation of these properties, a tool for the homogenization of two-dimensional elastic grids containing rigid elements is developed and tested on elaborate geometries, such as, for instance, Chinese lattices. The rigid elements are assumed to be either jointed with full continuity of displacement or hinged to the elastic rods. It is shown that the two different constraints induce strongly different mechanical characteristics of the equivalent elastic solid. The presented results open the way to the design of architected materials or metamaterials containing both elastic and rigid parts.

physics.class-ph↗

arXiv2024

Bimodal buckling governs human fingers luxation

Equilibrium bifurcation in natural systems can sometimes be explained as a route to stress shielding for preventing failure. Although compressive buckling has been known for a long time, its less-intuitive tensile counterpart was only recently discovered and yet never identified in living structures or organisms. Through the analysis of an unprecedented all-in-one paradigm of elastic instability, it is theoretically and experimentally shown that coexistence of two curvatures in human finger joints is the result of an optimal design by nature that exploits both compressive and tensile buckling for inducing luxation in case of traumas, so realizing a unique mechanism for protecting tissues and preventing more severe damage under extreme loads. Our findings might pave the way to conceive complex architectured and bio-inspired materials, as well as next generation artificial joint prostheses and robotic arms for bio-engineering and healthcare applications.

physics.bio-ph↗

arXiv2024

Flutter instability in solids and structures, with a view on biomechanics and metamaterials

The phenomenon of oscillatory instability called \lq flutter' was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving nonconservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing a new renaissance. A review is presented of the most notable applications and recent advances in fundamentals, both theoretical and experimental aspects, of flutter instability and Hopf bifurcation. Open problems, research gaps, and new perspectives for investigations are indicated.

physics.class-ph↗

arXiv2023

Stabilization against gravity and self-tuning of an elastic variable-length rod through an oscillating sliding sleeve

An elastic rod, straight in its undeformed state, has a mass attached at one end and a variable length, due to a constraint at the other end by a frictionless sliding sleeve. The constraint is arranged with the sliding direction parallel to a gravity field, in a way that the rod can freely slip inside of the sleeve, when the latter is not moving. In this case, the free fall of the mass continues until the rod is completely injected into the constraint. However, when the sliding sleeve is subject to a harmonic transverse vibration, it is shown that the fall of the mass and the rod injection are hindered by the presence of a configurational force developing at the sliding sleeve and acting oppositely to gravity. During the dynamic motion, such a configurational force is varying in time because it is associated with the variable bending moment at the sleeve entrance. It is (experimentally, analytically, and numerically) demonstrated that, in addition to the states of complete injection or ejection of the elastic rod (for which the mass falls down or is thrown out), a stable sustained oscillation around a finite height can be realized. This 'suspended motion' is the signature of a new attractor, that arises by the constraint oscillation. This behaviour shares similarities with parametric oscillators, as for instance the Kapitza inverted pendulum. However, differently from the classical parametric oscillators, the 'suspended' configuration of the rod violates equilibrium and the stabilization occurs through a transverse mechanical input, instead of a longitudinal one. By varying the sliding sleeve oscillation amplitude and frequency within specific sets of values, the system spontaneously adjusts the sustained motion through a self-tuning of the rod's external length. This self-tuning property opens the way to the design of vibration-based devices with extended frequency range.

physics.class-ph↗

arXiv2023

Phase-field modelling of failure in ceramics with multiscale porosity

Many stiff biological materials exhibiting outstanding compressive strength/weight ratio are characterized by high porosity, spanning different size-scales, typical examples being bone and wood. A successful bio-mimicking of these materials is provided by a recently-obtained apatite, directly produced through a biomorphic transformation of natural wood and thus inheriting its highly hierarchical structure. This unique apatite (but also wood and bone) is characterized by two major distinct populations of differently-sized cylindrical voids, a porosity shown in the present paper to influence failure, both in terms of damage growth and fracture nucleation and propagation. This statement follows from failure analysis, developed through in-silico generation of artificial samples (reproducing the two-scale porosity of the material) and subsequent finite element modelling of damage, implemented with phase-field treatment for fracture growth. It is found that small voids promote damage nucleation and enhance bridging of macro-pores by micro-crack formation, while macro-pores influence the overall material response and drive the propagation of large fractures. Our results explain the important role of multiscale porosity characterizing stiff biological materials and lead to a new design paradigm, by introducing an in-silico tool to implement bio-mimicking in new artificial materials with brittle behaviour, such as carbide or ceramic foams.

cond-mat.mtrl-sci↗

arXiv2023

Fusion of two stable elastic structures resulting in an unstable system

It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of freedom and is made up of a rigid rod connected with two springs to a smooth support, which evidences a jump in the curvature at the equilibrium configuration. Instability is proven in a linearized context and is related to the application of a non-conservative load of the follower type, so that the instability disappears under dead loads. In the fully nonlinear range, the instability is also confirmed through numerical simulations. The obtained results may be useful in the design of new mechanical sensors, or devices for energy harvesting, or architected materials. In addition, our findings have conceptual implications on piecewise-linear theories of mechanics such as for instance plasticity or frictional contact.

physics.class-ph↗

arXiv2022

Configurational forces on elastic structures

The discovery of configurational forces acting on elastic structures and its initial applications are reviewed. Configurational forces are related to the possibility that an elastic structure can change its configuration, thus inducing a variation in the potential energy. This concept has already led to several applications (the elastica arm scale, the dripping of an elastic rod, and the torsional actuator), has been shown to strongly affect stability, and to be related to limbless locomotion. It is believed that these results will open a new research territory in mechanics.

cond-mat.soft↗

arXiv2022

Configurational Forces in Penetration Processes

With a loose reference to problems of penetration in biomechanics (for instance, a nanoparticle penetrating through a cell's membrane or a cell sucked with a pipette), the role of configurational forces is investigated during the process in which a compliant intruder is inserted into an elastic structure. For insertion into a rigid constraint, a configurational force proportional to the square of the strain needed to deform the body, which is penetrating, is found. This force has a more complex structure when the compliance of the constraint is kept into account, but in all cases, it tends to expel the penetrating body.

cond-mat.soft↗