arXiv subjects

Valentina Balbi

Publications and source records attributed to Valentina Balbi.

9 recordsLinked to original sources

arXiv2026

The Role of Compressibility in Modified Quasi-Linear Viscoelasticity: A Comparison of Simple Shear and Torsion

We investigate the role of compressibility in the modified quasi-linear viscoelastic (MQLV) constitutive framework for soft solids at finite strain, where shear and bulk responses are governed by distinct relaxation functions. Analytical and semi-analytical results are derived for simple shear and torsion, under incompressible and slightly compressible assumptions. We show that compressibility affects the response only when volume changes occur: under isochoric deformations, the bulk contribution vanishes, while even small deviations from isochoricity significantly alter the normal response. Shear stress and torque are largely insensitive to compressibility, whereas normal stress and axial force exhibit pronounced sensitivity due to the coupling between shear and bulk relaxation. We further demonstrate that volumetric effects interact with the Poynting effect: in simple shear they oppose each other, reducing relaxation, while in torsion they reinforce each other, enhancing it. These trends agree with brain tissue experiments but reveal limitations of the slightly compressible model for highly compressible materials, such as agarose gels. Overall, the results emphasise the importance of accounting for compressibility in modelling normal stress responses and motivate the development of fully compressible formulations and numerical implementations.

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↗

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↗

arXiv2024

Wrinkling instability of 3D auxetic bilayers in tension

Bilayers, soft substrates coated with stiff films, are commonly found in nature with examples including skin tissue, vesicles, and organ membranes. They exhibit different types of instabilities when subjected to compression, depending on the contrast in material properties between the two components. In this work, we unravel the mechanisms behind wrinkling instabilities in auxetic bilayer systems under uniaxial tension. We find that a soft bilayer in tension can experience significant lateral contraction, and with sufficient contrast in Poisson ratios, compressive stresses may induce wrinkles aligned with the tensile direction. We analytically model the onset of wrinkles and validate our predictions using Finite Element simulations in ABAQUS. Our findings reveal that wrinkles occur when the Poisson ratio of the substrate is greater than that of the film. As the two Poisson ratios converge to a common value, the critical stretch for instability shoots up rapidly and the wrinkles disappear. We also confirm these results through asymptotic analysis. Using inverse analysis, we design film microstructures to achieve desired effective Poisson ratios and further validate the effective properties with the Finite Element code FEAP. We show that the critical stretch ratio for buckling in auxetic structures with microstructural patterns is in strong agreement with the homogenized model predictions. The proposed method has significant potential for controlling surface patterns in auxetic skin grafts and hydrogel organ patches under mechanical loads. Moreover, the asymptotic expressions for compressible bilayers developed in this work can also be applied under finite strain for buckling-based metrology.

cond-mat.mtrl-sci↗

arXiv2023

Tensor decomposition for modified quasi-linear viscoelastic models: towards a fully nonlinear theory

We discuss the decomposition of the tensorial relaxation function for isotropic and transversely isotropic Modified Quasi-Linear Viscoelastic models. We show how to formulate the constitutive equation by using a convenient decomposition of the relaxation tensor into scalar components and tensorial bases. We show that the bases must be symmetrically additive, i.e they must sum up to the symmetric fourth-order identity tensor. This is a fundamental property both for isotropic and anisotropic bases that ensures the constitutive equation is consistent with the elastic limit. We provide two robust methods to obtain such bases. Furthermore, we show that, in the transversely isotropic case, the bases are naturally deformation-dependent for deformation modes that induce rotation or stretching of the fibres. Therefore, the Modified Quasi-Linear Viscoelastic framework allows to capture the non-linear phenomenon of strain-dependent relaxation, which has always been a criticised limitation of the original Quasi-Linear Viscoelastic theory. We illustrate this intrinsic non-linear feature, unique to the Modified Quasi-Linear Viscoelastic model, with two examples (uni-axial extension and perpendicular shear).

cond-mat.soft↗

arXiv2021

Foundations of viscoelasticity and application to soft tissues mechanics

Soft tissues are complex media, they display a wide range of mechanical properties such as anisotropy and non-linear stress-strain behaviour. They undergo large deformations and they exhibit a time-dependent mechanical behaviour, i.e. they are viscoelastic. In this chapter we review the foundations of the linear viscoelastic theory and the theory of Quasi-Linear Viscoelasticity (QLV) in view of developing new methods to estimate the viscoelastic properties of soft tissues through model fitting. To this aim, we consider the simple torsion of a viscoelastic Mooney-Rivlin material in two different testing scenarios: step-strain and ramp tests. These tests are commonly performed to characterise the time-dependent properties of soft tissues and allow to investigate their stress relaxation behaviour. Moreover, commercial torsional rheometers measure both the torque and the normal force, giving access to two sets of data. We show that for a step test, the linear and the QLV models predict the same relaxation curves for the torque. However, when the strain history is in the form of a ramp function, the non-linear terms appearing in the QLV model affect the relaxation curve of the torque depending on the final strain level and on the rising time of the ramp. Furthermore, our results show that the relaxation curve of the normal force predicted by the QLV theory depends on the level of strain both for a step and a ramp tests. To quantify the effect of the non-linear terms, we evaluate the maximum and the equilibrium values of the relaxation curves. Our results provide useful guidelines to accurately fit QLV models in view of estimating the viscoelastic properties of soft tissues.

cond-mat.soft↗

arXiv2018

The mechanics of human brain organoids

Organoids are prototypes of human organs derived from cultured human stem cells. They provide a reliable and accurate experimental model to study the physical mechanisms underlying the early developmental stages of human organs morphogenesis and, in particular, the early morphogenesis of the cortex. Here, we propose a mathematical model to elucidate the role played by two mechanisms which have been experimentally proven to be crucial in shaping human brain organoids: the contraction of the inner core of the organoid and the microstructural remodeling of the outer cortex. Our results show that both mechanisms are crucial for the final shape of the organoid and can explain the origin of brain pathologies such as lissencephaly (smooth brain).

cond-mat.soft↗

arXiv2018

Poynting effect of brain matter in torsion

We investigate experimentally and model theoretically the mechanical behaviour of brain matter in torsion. Using a strain-controlled rheometer we perform torsion tests on fresh porcine brain samples. We quantify the torque and the normal force required to twist a cylindrical sample at constant twist rate. Data fitting gives a mean value for the shear modulus μ = 900 $\pm$ 312 Pa and for the second Mooney-Rivlin parameter $c_2$ = 297 $\pm$ 189 Pa, indicative of extreme softness. Our results show that brain always displays a positive Poynting effect; in other words, it expands in the direction perpendicular to the plane of twisting. We validate the experiments with Finite Element simulations and show that when a human head experiences a twisting motion in the horizontal plane, the brain can experience large forces in the axial direction.

cond-mat.soft↗

arXiv2018

A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation

The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation of nonlinear viscoelasticity, according to the physical mode of deformation. The theory is consistent with linear viscoelasticity in the small strain limit and makes use of relaxation functions that can be determined from small-strain experiments, given the time/deformation separability assumption. After considering the general constitutive form applicable to compressible materials, attention is restricted to incompressible media. This enables a compact form for the constitutive relation to be derived, which is used to illustrate the behaviour of the model under three key deformations: uniaxial extension, transverse shear and longitudinal shear. Finally, it is demonstrated that the Poynting effect is present in transversely isotropic, neo-Hookean, modified QLV materials under transverse shear, in contrast to neo-Hookean elastic materials subjected to the same deformation. Its presence is explained by the anisotropic relaxation response of the medium.

cond-mat.soft↗