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Giuseppe Zurlo

Publications and source records attributed to Giuseppe Zurlo.

16 recordsLinked to original sources
arXiv2025

Active chemo-mechanical solitons

In many biological systems localized mechanical information is transmitted by mechanically neutral chemical signals. Typical examples include contraction waves in acto-myosin cortex at cellular scale and peristaltic waves at tissue level. In such systems, chemical activity is transformed into mechanical deformation by distributed motor-type mechanisms represented by continuum degrees of freedom. To elucidate the underlying principles of chemo-mechanical coupling, we here present the simplest example, involving directional motion of a localized solitary wave in a distributed mechanical system, guided by a purely chemical cue. Our main result is that mechanical signals can be driven by chemical activity in a highly efficient manner.

cond-mat.soft↗
arXiv2025

Micro-displacement tensor

We propose an extended kinematics of nominally elastic continuum solids allowing one to describe their mechanical interaction with micro-scale loading devices. The main new ingredient is the concept of a micro-displacement tensor which extends the conventional description of the deforming elastic solids in terms of macroscopic displacement vectors. We show that micro-displacement tensors are particularly useful in dealing with active incompatibility acquisition and its subsequent passive relaxation. We use the proposed approach to describe the energetics of surface deposition while accounting for the presence of micro-mechanical controls.To illustrate the effectiveness of the new conceptual scheme we present two case studies: crystallization from a melt resulting in pre-stress, and winding of a coil with controlled pre-stretch.

cond-mat.soft↗
arXiv2025

Programmable wrinkling for functionally-graded auxetic circular membranes

Materials with negative Poisson's ratio, also known as auxetic materials, display exotic properties such as expansion in all directions under uni-axial tension. For their unique properties, these materials find a broad range of applications in robotic, structural, aerospace, and biomedical engineering. In this work we study the wrinkling behavior of thin and soft auxetic membranes, subjected to edge tractions. We show that spatial inhomogeneities of the Young modulus and of the Poisson ratio can be suitably tailored to produce non-trivial wrinkling patterns, with wrinkled regions that can appear, broaden, merge, and eventually disappear again, as the magnitude of applied tractions is increased monotonically. To model wrinkling in a functionally graded membrane, we employ the mathematically elegant and physically transparent tension field theory, an approximated method that we implement in commercially available software. Beyond unveiling the challenging technological potential to achieve non-standard wrinkling on-demand in auxetic membranes, our study also confirms the potential of using tension field theory to study, analytically and numerically, instabilities in functionally graded materials.

cond-mat.soft↗
arXiv2025

The geometric nature of homeostatic stress in biological growth

Morphogenesis, the process of growth and shape formation in biological tissues, is driven by complex interactions between mechanical, biochemical, and genetic factors. Traditional models of biological growth often rely on the concept of homeostatic Eshelby stress, which defines an ideal target state for the growing body. Any local deviation from this state triggers growth and remodelling, aimed at restoring balance between mechanical forces and biological adaptation. Despite its relevance in the biomechanical context, the nature of homeostatic stress remains elusive, with its value and spatial distribution often chosen arbitrarily, lacking a clear biological interpretation or understanding of its connection to the lower scales of the tissue. To bring clarity on the nature of homeostatic stress, we shift the focus from Eshelby stress to growth incompatibility, a measure of geometric frustration in the tissue that is the primary source of residual stresses in the developing body. Incompatibility, measured by the Ricci tensor of the growth metric at the continuous level, can be potentially regulated at the cell level through connections with the surrounding cells, making it a more meaningful concept than homeostatic stress. In this geometric perspective, achieving a homeostatic state corresponds to the establishment of a physiological level of frustration in the body, a process leading to the generation and maintenance of the mechanical stresses that are crucial to tissue functionality. In this work we present a formulation of biological growth that penalises deviations from a desired state of incompatibility, similar to the way the Einstein-Hilbert action operates in General Relativity. The proposed framework offers a clear and physically grounded approach that elucidates the regulation of size and shape, while providing a means to link cellular and tissue scales in biological systems.

physics.bio-ph↗
arXiv2024

Local and Global Dynamics of a Functionally Graded Dielectric Elastomer Plate

We investigate the nonlinear vibrations of a functionally graded dielectric elastomer plate subjected to electromechanical loads. We focus on local and global dynamics in the system. We employ the Gent strain energy function to model the dielectric elastomer. The functionally graded parameters are the shear modulus, mass density, and permittivity of the elastomer, which are formulated by a common through-thickness power-law scheme. We derive the equation of motion using the Euler-Lagrange equations and solve it numerically with the Runge-Kutta method and a continuation-based method. We investigate the influence of the functionally graded parameters on equilibrium points, natural frequencies, and static/dynamic instability. We also establish a Hamiltonian energy method to detect safe regions of operating gradient parameters. Furthermore, we explore the effect of the functionally graded parameters on chaos and resonance by plotting several numerical diagrams, including time histories, phase portraits, Poincaré maps, largest Lyapunov exponent criteria, bifurcation diagram of Poincaré maps, and frequency-stretch curves. The results provide a benchmark for developing functionally graded soft smart materials.

cond-mat.soft↗
arXiv2024

Designing necks and wrinkles in inflated auxetic membranes

This article presents the potentiality of inflatable, functionally-graded auxetic membranes to produce wrinkles and necks. We obtain elastic instabilities at desired locations in axisymmetric membranes and with prescribed patterns in square membranes. First, we use an analytical approach to obtain a series of universal results providing insights into the formation of wrinkles and necks in inflated, axisymmetric membranes. For example, we prove analytically that necks and wrinkles may never overlap in pressurized, axially symmetric membranes. Second, we implement the relaxed strain energy of tension field theory into a Finite Element solver (COMSOL). By tuning spatial inhomogeneities of the material moduli, we corroborate our universal results, describe the onset of wrinkling in an averaged way, and also generate non-trivial instabilities at desired locations. This study on membranes with morphing or corrugation on demand has potential applications in Braille reading and haptics.

cond-mat.soft↗
arXiv2023

A discrete model for layered growth

In this work we present a discrete model that captures the fundamental properties of additively manufactured solids in a minimal setting. The model is based on simplified kinematics and allows for the onset of incompatible deformations between discrete layers of an additively manufactured stack. Thanks to the discrete nature of the model, we obtain an averaged formulation of mechanical equilibrium for the growing stack, leading to closed-form solutions that are both analytically simple and physically transparent. In particular, we are able to explain the origin of residual stresses by the accumulation of incompatible deformations between adjacent layers. At the same time, we are able to formulate the technologically relevant inverse problem that provides the deposition protocol required to produce a desired state of internal stress in the manufactured stack. Another important aspect analyzed in the work is the role played by an ideal ``glue'' between the layers, whose presence is fundamental to prevent their sliding and whose mechanical behavior can quantitatively influence the final stress distribution in the stack. Although the model is an elementary approximation of additive manufacturing, its simplicity makes it possible to highlight how the controls exerted during deposition will have qualitative or quantitative effects on the final stress state of the stack. This understanding is crucial in shedding light on the complex mechanical behavior of additive manufactured solids.

cond-mat.soft↗
arXiv2020

Mechanical behavior of multi-cellular spheroids under osmotic compression

The internal and external mechanical environment plays an important role in tumorogenesis. As a proxy of an avascular early state tumor, we use multicellular spheroids, a composite material made of cells, extracellular matrix and permeating fluid. We characterize its effective rheology at the timescale of minutes to hours by compressing the aggregates with osmotic shocks and modeling the experimental results with an active poroelastic material that reproduces the stress and strain distributions in the aggregate. The model also predicts how the emergent bulk modulus of the aggregate as well as the hydraulic diffusion of the percolating interstitial fluid are modified by the preexisting active stress within the aggregate. We further show that the value of these two phenomenological parameters can be rationalized by considering that, in our experimental context, the cells are effectively impermeable and incompressible inclusions nested in a compressible and permeable matrix.

physics.bio-ph↗
arXiv2020

Strain incompatibility as a source of residual stress in welding and additive manufacturing

The accumulation of residual stress during welding and additive manufacturing is an important effect that can significantly anticipate the workpiece failure. In this work we exploit the physical and analytical transparency of a 1.5D model to show that the deposition of thermally expanded material onto an elastic substrate leads to the accumulation of strain incompatibility. This field, which is the source of residual stress in the system, introduces memory of the construction history even in the absence of plastic deformations. The model is then applied to describe the onset and the progression of residual stresses during deposition, their evolution upon cooling, and the fundamental role played by the velocity of the moving heat source.

cond-mat.mtrl-sci↗
arXiv2019

Nonlinear elasticity of incompatible surface growth

Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility leading to residual stresses and triggering various instabilities. In a recent paper (PRL, 119, 048001, 2017) we developed a linearized elasticity theory of incompatible surface growth which quantitatively linked deposition protocols with post-growth states of stress. Here we extend this analysis to account for both physical and geometrical nonlinearities of an elastic solid. The new development reveals the shortcomings of the linearized theory, in particular, its inability to describe kinematically confined surface growth and to account for growth-induced elastic instabilities.

cond-mat.soft↗
arXiv2018

Fine tuning the electro-mechanical response of dielectric elastomers

We propose a protocol to model accurately the electromechanical behavior of dielectric elastomer membranes using experimental data of stress-stretch and voltage-stretch tests. We show how the relationship between electric displacement and electric field can be established in a rational manner from this data. Our approach demonstrates that the ideal dielectric model, prescribing linearity in the purely electric constitutive equation, is quite accurate at low-to-moderate values of the electric field and that, in this range, the dielectric permittivity constant of the material can be deduced from stress-stretch and voltage-stretch data. Beyond the linearity range, more refined couplings are required, possibly including a non-additive decomposition of the electro-elastic energy. We also highlight that the presence of vertical asymptotes in voltage-stretch data, often observed in the experiments just prior to failure, should not be associated with strain stiffening effects, but instead with the rapid development of electrical breakdown.

cond-mat.soft↗
arXiv2017

Inelastic Surface Growth

Inelastic surface growth associated with continuous creation of incompatibility on the boundary of an evolving body is behind a variety of natural and technological processes, including embryonic development and 3D printing. In this paper we extend the recently proposed stress-space-centered theory of surface growth (PRL 119, 048001, 2017) by shifting the focus towards growth induced strains. To illustrate the new development we present several analytically tractable examples.

cond-mat.soft↗
arXiv2017

Printing non-Euclidean solids

Geometrically frustrated solids with non-Euclidean reference metric are ubiquitous in biology and are becoming increasingly relevant in technological applications. Often they acquire a targeted con- figuration of incompatibility through surface accretion of mass as in tree growth or dam construction. We use the mechanics of incompatible surface growth to show that geometrical frustration develop- ing during deposition can be fine-tuned to ensure a particular behavior of the system in physiological (or working) conditions. As an illustration, we obtain an explicit 3D printing protocol for arteries, which guarantees stress uniformity under inhomogeneous loading, and for explosive plants, allowing a complete release of residual elastic energy with a single cut. Interestingly, in both cases reaching the physiological target requires the incompatibility to have a topological (global) component.

cond-mat.soft↗
arXiv2016

Catastrophic thinning of dielectric elastomers

We provide a clear energetic insight into the catastrophic nature of the so-called creasing and pull-in instabilities in soft electro-active elastomers. These phenomena are ubiquitous for thin electro-elastic plates and are a major obstacle to the development of giant actuators; yet they are not completely understood nor modelled accurately. Here, in complete agreement with experiments, we give a simple formula to predict the voltage thresholds for these instability patterns and model their shape, and show that equilibrium is impossible beyond their onset. Our analysis is fully analytical, does not require finite element simulations, and can be extended to include pre-stretch and to encompass any material behaviour.

cond-mat.soft↗
arXiv2010

Compression-induced failure of electro-active polymeric thin films

The insurgence of compression induces wrinkling in actuation devices based on EAPs thin films leading to a sudden decrease of performances up to failure. Based on the classical tension field theory for thin elastic membranes, we provide a general framework for the analysis of the insurgence of in-plane compression in membranes of electroactive polymers (EAPs). Our main result is the deduction of a (voltage-dependent) domain in the stretch space which represents tensile configurations. Under the assumption of Mooney-Rivlin materials, we obtain that for growing values of the applied voltage the domain contracts, vanishing at a critical voltage above which the polymer is wrinkled for any stretch configuration. Our approach can be easily implemented in numerical simulations for more complex material behaviors and provides a tool for the analysis of compression instability as a function of the elastic moduli.

math-ph↗