1,720,989 research outputs found
Emerging anisotropy and tethering with memory effects in fibrous materials
No full textFibrous materials may undergo an internal reorganization, which turns out in the emergence of preferential directions. This is a peculiar behavior of many biological tissues, which drive reorientation by external stimuli at chemo-mechanical levels. In particular, it is detected that contractile cells can reorganize fibrous extracellular matrices and form dense tracts of aligned fibers (tethers), that guide the development of tubular tissue structures and may provide paths for the invasion of cancer cells. Tether formation is caused by buckling instability of network fibers under cell-induced compression. We present a simple mechanical model, within a variational framework, that captures the essential aspects of these phenomena. The model qualitatively describes: (i) the emergence, induced by local compressive strain, of anisotropy, where fibrous materials exhibit directional preferences; (ii) the occurrence of micro-buckling, which leaves a lasting plastic deformation in the material; and (iii) the formation of localized field patterns, which contribute to the overall behavior of the material. By considering these fundamental aspects, our model provides insights into the mechanical response of fibrous materials and sheds light on the underlying mechanisms driving their behavior
An atomistic-based Föppl–von Kármán model for graphene
No full textWe deduce a non-linear continuum model of graphene for the case of finite out-of-plane displacements and small in-plane deformations. On assuming that the lattice interactions are governed by the Brenner's REBO potential of 2nd generation and that self-stress is present, we introduce discrete strain measures accounting for up-to-the-third neighbor interactions. The continuum limit turns out to depend on an average (macroscopic) displacement field and a relative shift displacement of the two Bravais lattices that give rise to the hexagonal periodicity. On minimizing the energy with respect to the shift variable, we formally determine a continuum model of Föppl–von Kármán type, whose constitutive coefficients are given in terms of the atomistic interactions
A phase-field model for the brittle fracture of Euler–Bernoulli beams coupling stretching and bending
Full text linkDamage gradient models seek to simulate fracture mechanics by modulating the material stiffness. Within this framework, a singular scalar field representing damage is commonly utilized to globally decrease elastic energy. However, when considering structural models like beams and plates, this approach often fails to adequately capture important aspects due to the interaction between stretching and bending contributions. In this work, we propose a model for planar Euler–Bernoulli beams that incorporates the following features: firstly, we utilize two phase-field damage parameters to describe material damaging, specifically addressing the ‘erosion’ occurring above and below the original, undamaged beam; secondly, we assume a simple linear dependence of the axial stress field on the thickness coordinate, along with linear dependence on the axial force and bending moment. By appropriately identifying the constitutive response, our model effectively considers the coupling between stretching and bending induced during through-the-thickness damage, demonstrating good agreement with 2D observations
A coarse-grained constitutive law for fracturing beams based on a sharp interface crack representation
No full textDamage gradient models approximate fracture mechanics using a modulation of the material stiffness. To this aim a single scalar field, the damage, is used to degrade as a whole the elastic energy. If applied to the structural models of beams and shells, where the elastic energy is the sum of the stretching and bending contributions, a similar approach is not able to capture some important features. For instance, the coupling between axial and bending strains induced by cracks non-symmetric with respect to the center line is completely missed. In this contribution, we deduce a constitutive law for a beam having a crack non-symmetric with respect to the center line. To achieve this, we perform an asymptotic coarse-grained procedure from a 2D problem, using a sharp interface model. We deduce a homogenized 1D elastic energy, coupling the axial and bending strains, the constitutive parameters of which depend in a different way on the crack depth and we state how precisely they do. This should pave the way to a rational development of a phase-field gradient model for thin structures
A variational model for plastic reorientation in fibrous material: numerical experiments on phase segregation
Full text linkWe propose a continuum model of fibrous material that may undergo an internal reorganization, which turns out in a plastic change of the orientation of the fibers when the remodeling torque achieves a threshold. We have recently found that the reorientation may induce a complex scenario in the response of such materials. In a traction test, we show that the most general transversely isotropic material may evolve in three different ways; in particular, the fibers asymptotically tend (regularly or with jumps): (A) to a given angle; (B) to align perpendicularly to the load direction; (C) to align with the load direction if their initial orientation is less than a given value otherwise perpendicularly. We focus on the latter material response (C) which has all the ingredients to manifest a phase transition phenomenon. Finally, we provide a numerical investigation to demonstrate phase segregation
A variational model for finger-driven cell diffusion in the extracellular matrix
No full textWe present a simple chemo-mechanical variational model for a fibrous material that describes (i) the emergence of the anisotropy due to microscopic buckling instabilities (ii) a diffusion in the substrate of the cell phase driven by the new created macroscopic bands characterized by intense compressive deformation. The model is applicable for simulating the spreading of cells within tissues and their interaction with tissue remodeling during mesenchymal migration
A phase-field model for fracture in beams from asymptotic results in 2D elasticity
Full text linkWe propose a derivation of a damage model in slender structures, focusing on the particular case of a rod. The peculiarity of the model is that it takes into account the changes in rigidity of the body, distinguishing between bending, traction and the possible mixed interactions between the two. The approach is based on a matched asymptotic expansion, taking the recent work of Baldelli et al [1] as starting point. Choosing the slenderness of the rod as small parameter for the asymptotic expansion, we determine the first order at which a correction occurs with respect to the Saint-Venant solution of the elastic problem, due to the presence of a crack. The results highlight that the presence of a defect affects in different ways the bending and traction rigidities of the rod, and that a coupling between the two deformation modes might occur, depending on the geometry of the crack. Moreover, the derivation allows to explicitly calculate the coefficients of this correction, for any given depth of the crack, by means of a simple numerical procedure. Application to the classic three-point bending problem is considered in order to highlight the predictive capabilities of the model. These results suggest ways in which state of the art phasefield models (e.g. [2]) for damage could be refined. This work goes in the direction of developing phase-field models suitable for application to slender structures, where the use of reduced dimensional models has proved promising [3]
Pressurized CNTs under tension: A finite-deformation lattice model
No full textWe propose a finite-deformation lattice model for carbon nanotubes (CNTs), in which an energetic cost is assigned to changes in bond lengths, bond angles, and dihedral angles, while atomic interactions are governed by a Reactive Empirical Bond-Order potential. For the first time, we consider the effect of severe traction and pressure applied simultaneously, with the ultimate goal of understanding how material properties are affected by such loads. In particular, the radial stiffness and the axial stiffness have been investigated: on making use of the second generation Brenner potential, we have found that peculiar transitions softening-hardening-softening occur in both the radial and axial stiffness, a behavior that could be compared with the ones observed in experiments or predicted by ab initio methods. The constitutive response described here can be exploited in the design of CNT-based hydrogen storage systems, and it opens a new possibility for tuning material properties, in order to make CNTs softer or harder in a controlled way
Design of auxetic plates with only one degree of freedom
No full textA continuum elastic plate has infinite degrees of freedom: according to the applied loads, it assumes the shape that the minimization of the total energy prescribes, in dependence of the material it is made of. The possibility to control the shape of a morphing structure is receiving an increasing attention in several fields; in this connection, if a classical elastic plate is considered, it is not possible, in general, to tune the elastic properties of the material in order to select, between the infinite deformation modes the plate may have, the one desired. We present a prototypical case that tries to satisfy this desideratum, opening the way to the systematic design of microstructure's geometries to fully control a system's shape independently of the applied loads. A novel yet simple architecture for thin plates having only one degree of freedom is proposed. The plate is realized as a tessellation composed by rigid equal hexagonal tiles hinged to each other along the sides, and it can deform in just one way, that is, into a predetermined synclastic surface, whatever loads are applied to it. Such tessellated plate also has a remarkable auxetic behavior in bending, with the ratio between transverse and longitudinal curvatures in uniaxial bending reaching values larger than one. Modeling assumptions and analysis results, at both the discrete and the continuum level, are verified by tests carried out onto additively manufactured bi-material specimens, showing that it is possible to design the deformed configuration by controlling the hexagons’ geometry. The proposed architecture for realizing auxetic plates with only one degree of freedom is highly scalable and easily manufacturable, and it can find applications for auxetic scaffolds, prosthetic stress shields, energy harvesters, and wearable devices
Competition between epithelial tissue elasticity and surface tension in cancer morphogenesis
No full textWe derive a continuum mechanical model to capture the morphological changes occurring at the pretumoral stage of epithelial tissues. The proposed model aims to investigate the competition between the bulk elasticity of the epithelium and the surface tensions of the apical and basal sides. According to this model, when the apico-basal tension imbalance reaches a critical value, a subcritical bifurcation is triggered and the epithelium attains its physiological folded shape. Based on data available in the literature, our model predicts that pretumoral cells are softer than healthy cells
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