arXiv subjects

Mattia Bacca

Publications and source records attributed to Mattia Bacca.

At least 19 recordsLinked to original sources

arXiv2026

Deep Indentation of Hyperelastic Materials Reveals Tip Independent Parabolic Force Depth Response via Strain Energy Delocalization

Indentation is a practical route for probing soft materials when standard tests are difficult, destructive, or cannot be performed in situ. Conventional indentation is usually interpreted in the shallow-depth regime, where the indentation depth D is small compared with the indenter radius R. In this limit, the response is controlled by local contact geometry and primarily identifies the small-strain Young's modulus E. Here, we show that at deep indentation, D >> R, flat and spherical indenters converge to the same parabolic force-depth law, F = beta E D^2. The coefficient beta is independent of indenter radius and tip shape, only mildly affected by interfacial friction, and controlled by the hyperelastic strain-stiffening response. Finite-element simulations show that this scaling arises from strain-energy delocalization: the region where SED/mu > 0.01 expands into a spheroidal domain whose size scales with D. The activated volume therefore scales as D^3, giving stored elastic energy U ~ E D^3 and force F = dU/dD ~ E D^2. Far from contact, the strain-energy-density fields collapse toward the Boussinesq far-field solution when distances are normalized by a = sqrt(F/E), which scales as D in the deep-indentation regime. These results provide a mechanistic basis for tip-shape independence and link beta to the Ogden strain-stiffening parameter alpha, enabling hyperelastic parameter extraction from deep-indentation data.

cond-mat.soft↗

arXiv2026

Hollow Needle Puncture Mechanics for Biopsy Sampling

Biopsy sampling relies on hollow needles that puncture soft tissues by propagating and opening a cylindrical crack, yet the mechanics governing this coring process remain only partially understood. Motivated by this gap, we develop a simple, energy based model for puncture by blunt hollow needles, grounded in brittle fracture mechanics and extended to include frictional interactions at the needle tissue interface. The model describes puncture as the competition between the fracture energy and the elastic energy. This energetic balance is controlled by the interplay among needle geometry (radius and wall thickness), material properties (toughness and elastic modulus), and interfacial parameters (adhesion and friction). This model provides semi-analytical predictions for five key quantities: core size, frictionless force, frictional force slope, critical insertion depth, and critical insertion force. Model predictions are validated against experiments, demonstrating that friction significantly improves force estimation and alters the puncture regime. These results offer quantitative insight into the mechanics of tissue coring and force generation during biopsy, providing a predictive foundation for needle design, sampling performance, and real time control in robotic biopsy and needle insertion systems.

cond-mat.soft↗

arXiv2026

Membrane Tension Governs Particle Wrapping-Unwrapping Transitions and Stalling

Membrane wrapping controls nanoparticle uptake during endocytosis, whereas the reverse process of membrane unwrapping accompanies particle expulsion and membrane fusion events. Existing theoretical descriptions typically focus on adhesion and bending energies within the particle membrane contact region and often neglect the deformation energy of the membrane outside the contact zone. This approximation is valid only in the limit of vanishing membrane tension, where the non contact membrane assumes a catenoid like configuration with negligible bending energy. However, at finite tension the deformation of the non contact membrane becomes a dominant energetic contribution. Here we show that this tension dependent non contact energy governs the progression of particle wrapping. By analysing the variation of the total membrane energy with wrapping degree, we uncover a competition between particle adhesion, membrane tension and particle size that determines whether wrapping proceeds, stalls, or reverses into spontaneous unwrapping. This framework reveals a stalling boundary separating regimes of particle uptake and expulsion. To capture the non contact deformation efficiently, we derive a compact phenomenological approximation that accurately reproduces the full numerical solution of the membrane shape. The resulting energetic map provides a unified physical description of particle wrapping and unwrapping, with implications for endocytosis, membrane fusion, and nanoparticle design.

physics.bio-ph↗

arXiv2025

Hyperelastic characterization via deep indentation

Hyperelastic material characterization is crucial for understanding the behavior of soft materials -- such as tissues, rubbers, hydrogels, and polymers -- under quasi-static loading before failure. Traditional methods typically rely on uniaxial tensile tests, which require the cumbersome preparation of dumbbell-shaped samples for clamping in a uniaxial testing machine. In contrast, indentation-based methods, which can be conducted \textit{in-situ} without sample preparation, have been underexplored. To characterize the hyperelastic behavior of soft materials, deep indentation is required, where the material response extends beyond linear elasticity. In this study, we perform finite element analysis to link the force ($F$) versus indentation depth ($D$) curve with the hyperelastic behavior of a soft incompressible material, using a one-term Ogden model for simplicity. We identify three indentation regimes based on the ratio between indentation depth and the radius ($R$) of the spherical-tipped cylindrical indenter: the Hertzian regime ($D < 0.1R$), where $F = \frac{16}{9} E R^{0.5} D^{1.5}$; the parabolic regime ($D > 10R$), where $F = E D^2 \beta$ and the indenter radius becomes irrelevant; and an intermediate regime ($0.1R < D < 10R$) bridging the two extremes. We find that the Ogden strain-stiffening coefficient ($\alpha$) increases the parabolic indentation coefficient ($\beta$), allowing for the estimation of $\alpha$ from $\beta$. Furthermore, we observe that Coulomb friction increases $\beta$, potentially masking the effect of strain-stiffening for small $\alpha$. However, for $\alpha > 3$, friction has a negligible effect. Finally, our results show good agreement with experimental data, demonstrating that deep indentation can be an effective method for extracting hyperelastic properties from soft materials through \textit{in-situ} testing.

cond-mat.soft↗

arXiv2024

Piercing soft solids: A mechanical theory for needle insertion

In this paper we investigate the mechanical problem of piercing a soft solid body with a needle. This phenomenon is controlled by the critical condition of needle insertion. Needle insertion involves physical and geometrical nonlinearities and a complex failure mechanism. To overcome the complexity of the problem, we describe needle insertion as a sharp transition between two needle-specimen configurations, namely "indentation" and "penetration". The sharp configurational change emerges from a mechanical instability and follows the principle of energy minimum. We describe the needle-specimen system in terms of the force applied to the back of the needle and the axial displacement of the needle tip toward the material. At small needle displacements, the energetically favoured configuration is indentation. Conversely, when the needle displaces beyond a critical threshold, it penetrates the specimen by rupturing its surface. This creates a new energetically favoured configuration: penetration. Our analysis considers a cylindrical needle with a spherical tip, neglects friction and adhesion between the needle and the material, and assumes quasi-static conditions. Despite the mathematical simplicity of our analysis, our theoretical predictions on the needle insertion force have been validated against experiments with surprising accuracy. Our method provides an effective predictive tool, which can be extended to account for different indenter geometry and material behaviour.

cond-mat.soft↗

arXiv2024

How friction and adhesion affect the mechanics of deep penetration in soft solids

The mechanics of puncture and soft solid penetration is commonly explored with the assumption of frictionless contact between the needle (penetrator) and the specimen. This leads to the hypothesis of a constant penetration force. Experimental observations, however, report a linear increment of penetration force with needle tip depth. This force increment is due to friction and adhesion, and this paper provides its correlation with the properties of the cut material. Specifically, the force-depth slope depends on the rigidity and toughness of the soft material, the radius of the penetrator and the interfacial properties (friction and adhesion) between the two. We observe that adhesion prevails at relatively low toughness, while friction is dominant at high toughness. Finally, we compare our results with experiments and observe good agreement. Our model provides a valuable tool to predict the evolution of penetration force with depth and to measure the friction and adhesion characteristics at the needle-specimen interface from puncture experiments.

cond-mat.soft↗

arXiv2024

Cutting Soft Matter: Scaling relations controlled by toughness, friction, and wear

Cutting mechanics of soft solids is gaining rapid attention thanks to its promising benefits in material characterization and other applications. However, a full understanding of the physical phenomena is still missing, and several questions remain outstanding. E.g.: How can we directly and reliably measure toughness from cutting experiments? What is the role of blade sharpness? In this paper, we explore the simple problem of wire cutting, where blade sharpness is only defined by the wire radius. Through finite element analysis, we obtain a simple scaling relation between the wire radius and the steady-state cutting force per unit sample thickness. The cutting force is independent of the wire radius if the latter is below a transition length, while larger radii produce a linear force-radius correlation. The minimum cutting force, for small radii, is given by cleavage toughness, i.e., the surface energy required to break covalent bonds in the crack plane. The force-radius slope is instead given by the wear shear strength in the material. Via cutting experiments on polyacrylamide gels, we find that the magnitude of shear strength is close to the work of fracture of the material, i.e., the critical strain energy density required to break a pristine sample in uniaxial tension. The work of fracture characterizes the toughening contribution from the fracture process zone (FPZ), which adds to cleavage toughness. Our study provides two important messages, that answer the above questions: Toughness can be estimated from wire-cutting experiments from the intercept of the force-radius linear correlation, as previously explored. However, as we discovered, this only estimates cleavage toughness. Additionally, the force-radius slope is correlated with the work of fracture, giving an estimation of the dissipative contributions from the FPZ.

cond-mat.soft↗

arXiv2024

Machine Learning Based Optimal Design of Fibrillar Adhesives

Fibrillar adhesion, observed in animals like beetles, spiders, and geckos, relies on nanoscopic or microscopic fibrils to enhance surface adhesion via 'contact splitting.' This concept has inspired engineering applications across robotics, transportation, and medicine. Recent studies suggest that functional grading of fibril properties can improve adhesion, but this is a complex design challenge that has only been explored in simplified geometries. While machine learning (ML) has gained traction in adhesive design, no previous attempts have targeted fibril-array scale optimization. In this study, we propose an ML-based tool that optimizes the distribution of fibril compliance to maximize adhesive strength. Our tool, featuring two deep neural networks (DNNs), recovers previous design results for simple geometries and introduces novel solutions for complex configurations. The Predictor DNN estimates adhesive strength based on random compliance distributions, while the Designer DNN optimizes compliance for maximum strength using gradient-based optimization. Our method significantly reduces test error and accelerates the optimization process, offering a high-performance solution for designing fibrillar adhesives and micro-architected materials aimed at fracture resistance by achieving equal load sharing (ELS).

cs.LG↗

arXiv2024

Cutting Mechanics of Soft Compressible Solids: Force-radius scaling versus bulk modulus

Cutting mechanics in soft solids present a complex mechanical challenge due to the intricate behavior of soft ductile materials as they undergo crack nucleation and propagation. Recent research has explored the relationship between the cutting force needed to continuously cut a soft material and the radius of the wire (blade). A typical simplifying assumption is that of material incompressibility, albeit no material in nature is really incompressible. In this study, we relax this assumption and examine how material (in)compressibility influences the correlation between cutting forces and material properties like toughness and modulus. The ratio μ/\k{appa}, where μ and \k{appa} are the shear and bulk moduli, indicates the material's degree of compressibility, where incompressible materials have μ/\k{appa}=0, and larger μ/\k{appa} provide higher volumetric compressibility. Following previous observations, we obtain two cutting regimes: (i) high toughness or small wire radius, and (ii) low toughness or large wire radius. Regime (i) is dominated by frictional dissipation, while regime (ii) is dominated by adhesive debonding and/or the wear resistance of the material. These regimes are controlled by the ratio between the wire radius and the elasto-cohesive length of the material: the critical crack opening displacement at fast fracture under uniaxial tension. In the large radius, regime (ii), our theoretical findings reveal that incompressible materials require larger forces. Notably, however, the elasto-cohesive length of the material, defining the transition wire radius between regimes (i) and (ii), is larger for compressible materials, which are therefore more likely to be cut in regime (i), and thus requiring larger cutting forces.

cond-mat.soft↗

arXiv2023

Making the cut: end effects and the benefits of slicing

Cutting mechanics in soft solids have been a subject of study for several decades, an interest fuelled by the multitude of its applications, including material testing, manufacturing, and biomedical technology. Wire cutting is the simplest model system to analyze the cutting resistance of a soft material. However, even for this simple system, the complex failure mechanisms that underpin cutting are still not completely understood. Several models that connect the critical cutting force to the radius of the wire and the key mechanical properties of the cut material have been proposed. An almost ubiquitous simplifying assumption is a state of plane (and anti-plane) strain in the material. In this paper, we show that this assumption can lead to erroneous conclusions because even such a simple cutting problem is essentially three-dimensional. A planar approximation restricts the analysis to the stress distribution in the mid-plane. However, through finite element modeling, we reveal that the maximal tensile stress - and thus the likely location of cut initiation - is in fact located in the front plane. Friction reduces the magnitude of this stress, but this detrimental effect can be counteracted by large slice-to-push (shear-to-indentation) ratios. The introduction of these end effects helps reconcile a recent controversy around the role of friction in wire cutting, for it implies that slicing can indeed reduce required cutting forces, but only if the slice-push ratio and the friction coefficient are sufficiently large. Material strain-stiffening reduces the critical indentation depth required to initiate the cut further and thus needs to be considered when cutting non-linearly elastic materials.

cond-mat.soft↗

arXiv2023

Multi-material topology optimization of adhesive backing layers via J-integral and strain energy minimizations

Strong adhesives rely on reduced stress concentrations, often obtained via specific geometry or composition of materials. In many examples in nature and engineering prototypes, the adhesive performance relies on structural rigidity being placed in specific locations. A few design principles have been formulated, based on parametric optimization, while a general design tool is still missing. We propose to use topology optimization to achieve optimal stiffness distribution in a multi-material adhesive backing layer, reducing stress concentration at specified locations. The method involves the minimization of a linear combination of J-integral and strain energy. While the J-integral minimization is aimed at reducing stress concentration, we observe that the combination of these two objectives ultimately provides the best results. We analyze three cases in plane strain conditions, namely (i) double-edged crack and (ii) center crack in tension and (iii) edge crack under shear. Each case evidences a different optimal topology with (i) and (ii) providing similar results. The optimal topology allocates stiffness in regions that are far away from the crack tip, intuitively, but the allocation of softer materials over stiffer ones can be non-trivial. To test our solutions, we plot the contact stress distribution across the interface. In all observed cases, we eliminate the stress singularity at the crack tip. Stress concentrations might arise in locations far away from the crack tip, but the final results are independent of crack size. Our method ultimately provides optimal, flaw tolerant, adhesives where the crack location is known.

cond-mat.mtrl-sci↗

arXiv2023

A model for the contraction kinetics of cytoskeletal gel slabs

Cytoskeletal gels are engineered prototypes that mimic the contractile behavior of a cell in-vitro. They are composed of an active polymer matrix and a liquid solvent. Their contraction kinetics is governed by two dynamic phenomena: mechanotransduction (molecular motor activation), and solvent diffusion. In this paper, we solve the transient problem for the simple case of a thin gel slab in uniaxial contraction under two extreme conditions: motor-limited or slow motor activation (SM) regime, and diffusion-limited or fast motor activation (FM) regime. The former occurs when diffusion is much faster than mechanotransduction, while the latter occurs in the opposite case. We observe that in the SM regime, the contraction time scales as t/t_0 ~ (l/l_0)^(-3), with t_0 the nominal contraction time, and l and l_0 are the final and initial stretches of the slab. t_0 is proportional to 1/w, where w is the average mechanical power generated by the molecular motors per unit reference (dry polymer) volume. In the FM regime, the contraction time scales as t/t_1 ~ (1-l/l_0)^2, with t_1 the nominal contraction time, here proportional to the ratio L^2/D, where L is the reference (dry polymer) thickness, and D is the diffusivity of the solvent in the gel. The transition between the SM and FM regimes is defined by a characteristic power density w^*, where w << w^* gives the SM regime and w >> w^* gives the FM regime. Intuitively, w^* is proportional to D/L^2, where, at a given power density w, a thinner gel slab (smaller L) or including smaller solvent molecules (higher D) is more likely to be in the SM regime given that solvent diffusion will occur faster than motor activation.

cond-mat.soft↗

arXiv2023

Theoretical Puncture Mechanics of Soft Compressible Solids

Accurate prediction of the force required to puncture a soft material is critical in many fields like medical technology, food processing, and manufacturing. However, such a prediction strongly depends on our understanding of the complex nonlinear behavior of the material subject to deep indentation and complex failure mechanisms. Only recently we developed theories capable of correlating puncture force with material properties and needle geometry. However, such models are based on simplifications that seldom limit their applicability to real cases. One common assumption is the incompressibility of the cut material, albeit no material is truly incompressible. In this paper we propose a simple model that accounts for linearly elastic compressibility, and its interplay with toughness, stiffness, and elastic strain-stiffening. Confirming previous theories and experiments, materials having high-toughness and low-modulus exhibit the highest puncture resistance at a given needle radius. Surprisingly, in these conditions, we observe that incompressible materials exhibit the lowest puncture resistance, where volumetric compressibility can create an additional (strain) energy barrier to puncture. Our model provides a valuable tool to assess the puncture resistance of soft compressible materials and suggests new design strategies for sharp needles and puncture-resistant materials.

cond-mat.soft↗

arXiv2022

Energetics of Cytoskeletal Gel Contraction

Cytoskeletal gels are prototyped to reproduce the mechanical contraction of the cytoskeleton in-vitro. They are composed of a polymer network (backbone), swollen by the presence of a liquid solvent, and active molecules (molecular motors, MMs) that transduce chemical energy into the mechanical work of contraction. These motors attach to the polymer chains to shorten them and/or act as dynamic crosslinks, thereby constraining the thermal fluctuation of the chains. We describe both mechanisms thermodynamically as a microstructural reconfiguration, where the backbone stiffens to motivate solvent (out)flow and accommodate contraction. Via simple steady-state energetic analysis, under the simplest case of isotropic contraction, we quantify the mechanical energy required to achieve contraction as a function of polymer chain density and molecular motor density. We identify two limit cases, (fm) fast MM activation for which MMs provide all the available mechanical energy instantaneously and leave the polymer in a stiffened state, i.e. their activity occurs at a time scale that is much smaller than solvent diffusion, and (sm) slow MM activation for which the MM activation timescale is much longer. To achieve the same final contracted state, fm requires the largest amount of work per unit reference volume, while sm requires the least. For all intermediate cases where the timescale of MM activation is comparable with that of solvent flow, the required work ranges between the two cases. We provide all these quantities as a function of chain density and MM density. Finally, we compare our results with experiments and observe good agreement.

cond-mat.soft↗

arXiv2022

Mechanics of diffusion-mediated budding and implications for virus replication and infection

Budding allows virus replication and macromolecular secretion in cells. It involves the formation of a bud, i.e. an outgrowth from the cell membrane that evolves into an envelope. The largest energetic barrier to bud formation is membrane deflection and is trespassed primarily thanks to nucleocapsid-membrane adhesion. Transmembrane proteins (TPs), which later form the virus ligands, are the main promotors of adhesion and can accommodate membrane bending thanks to an induced spontaneous curvature. Adhesive TPs must diffuse across the membrane from remote regions to gather on the bud surface, thus, diffusivity controls the kinetics. This paper proposes a simple model to describe diffusion-mediated budding unraveling important size limitations and size-dependent kinetics. The predicted optimal virion radius, giving the fastest budding, is validated against experiments for Coronavirus, HIV, Flu, and Hepatitis. Assuming exponential replication of virions and hereditary size, the model can predict the size distribution of a virus population. This is verified against experiments for SARS-CoV-2. All the above comparisons rely on the premise that budding poses the tightest size constraint. This is true in most cases, as demonstrated in this paper, where the proposed model is extended to describe virus infection via receptor- and clathrin-mediated endocytosis, and via membrane fusion.

physics.bio-ph↗

arXiv2021

Theoretical limits in detachment strength for axisymmetric bi-material adhesives

Dry adhesives rely on short-ranged intermolecular bonds, hence requiring a low elastic modulus to conform to the surface roughness of the adhered material. Under external loads, however, soft adhesives accumulate strain energy, which release drives the propagation of interfacial flaws prompting detachment. The ideal adhesive is then soft but rigid. The solution to this controversial requirement is a bi-material adhesive having a soft tip, for surface conformation, and a rigid backing, for reduced strain energy release, hence, better adhesive strength. This design strategy is widely observed in nature across multiple species. However, the detachment mechanisms of these adhesives are poorly understood and quantitative analysis of their adhesive strength is still missing. Based on linear elastic fracture mechanics, we analyze the strength of axisymmetric bi-material adhesives. We observed two main detachment mechanisms, namely (i) center crack propagation and (ii) edge crack propagation. If the soft tip is sufficiently thin, mechanism (i) dominates and provides stable crack propagation, thereby toughening the interface. We ultimately provide the maximum theoretical strength of these adhesives obtaining closed form estimates for the detachment stress independent of the crack size, rendering the interface flaw tolerant.

cond-mat.soft↗

arXiv2019

Optimal load sharing in bioinspired fibrillar adhesives: Asymptotic solution

We propose here an asymptotic solution defining the optimal compliance distribution for a fibrillar adhesive to obtain maximum theoretical strength. This condition corresponds to that of equal load sharing (ELS) among fibrils, i.e. all the fibrils are carrying the same load at detachment, hence they all detach simultaneously. We model the array of fibrils as a continuum of linear elastic material that cannot laterally transmit load (analogous to a Winkler soil). Ultimately, we obtain the continuum distribution of fibril's compliance in closed-form solution and compare it with previously obtained data for a discrete model for fibrillar adhesives. The results show improving accuracy for an incremental number of fibrils and smaller center-to-center spacing. Surprisingly, the approximation introduced by the asymptotic model show reduced sensitivity of the adhesive strength with respect to misalignment and improved adhesive strength for large misalignment angles.

cond-mat.soft↗

arXiv2019

Contraction of polymer gels created by the activity of molecular motors

We propose a theory based on non-equilibrium thermodynamics to describe the mechanical behavior of an active polymer gel created by the inclusion of molecular motors in its solvent. When activated, these motors attach to the chains of the polymer network and shorten them creating a global contraction of the gel, which mimics the active behavior of a cytoskeleton. The power generated by these motors is obtained by ATP hydrolysis reaction, which transduces chemical energy into mechanical work. The latter is described by an increment of strain energy in the gel due to an increased stiffness. This effect is described with an increment of the cross-link density in the polymer network, which reduces its entropy. The theory then considers polymer network swelling and species diffusion to describe the transient passive behavior of the gel. We finally formulate the problem of uniaxial contraction of a slab of gel and compare the results with experiments, showing good agreement.

cond-mat.soft↗