COLLECTIONS

Documents published in Scipedia

• Geometric derivation of the microscopic stress: a covariant central force decomposition

  A. Torres-Sánchez, J. Vanegas, M. Arroyo

  Journal of the Mechanics and Physics of Solids (2016). Vol. 93, pp. 224-239 (preprint)

  
  

  Abstract

  We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle-Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving-Kirkwood-Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.

  Abstract
  We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation [...]

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• Shape transformations of lipid bilayers following rapid cholesterol uptake

  M. Rahimi, D. Regan, M. Arroyo, A. Subramaniam, H. Stone, M. Staykova

  Biophysical journal (2016). Vol. 111 (12), pp. 2651-2657 (Preprint)

  
  

  Abstract

  High cholesterol levels in the blood increase the risk of atherosclerosis. A common explanation is that the cholesterol increase in the plasma membrane perturbs the shape and functions of cells by disrupting the cell signaling pathways and the formation of membrane rafts. In this work, we show that after enhanced transient uptake of cholesterol, mono-component lipid bilayers change their shape similarly to cell membranes in vivo. The bilayers either expel lipid protrusions or spread laterally as a result of the ensuing changes in their lipid density, the mechanical constraints imposed on them, and the properties of cyclodextrin used as a cholesterol donor. In light of the increasingly recognized link between membrane tension and cell behavior, we propose that the physical adaptation of the plasma membrane to cholesterol uptake may play a substantial role in the biological response.

  Abstract
  High cholesterol levels in the blood increase the risk of atherosclerosis. A common explanation is that the cholesterol increase in the plasma membrane perturbs the shape [...]

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• Hydraulic fracture and toughening of a brittle layer bonded to a hydrogel

  A. Lucantonio, G. Noselli, X. Trepat, A. DeSimone, M. Arroyo

  Physical review letters (2015). Vol. 115 (18), pp. 188105-1/188105-5

  
  

  Abstract

  Brittle materials propagate opening cracks under tension. When stress increases beyond a critical magnitude, then quasistatic crack propagation becomes unstable. In the presence of several precracks, a brittle material always propagates only the weakest crack, leading to catastrophic failure. Here, we show that all these features of brittle fracture are fundamentally modified when the material susceptible to cracking is bonded to a hydrogel, a common situation in biological tissues. In the presence of the hydrogel, the brittle material can fracture in compression and can hydraulically resist cracking in tension. Furthermore, the poroelastic coupling regularizes the crack dynamics and enhances material toughness by promoting multiple cracking.

  Abstract
  Brittle materials propagate opening cracks under tension. When stress increases beyond a critical magnitude, then quasistatic crack propagation becomes unstable. In the presence [...]

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• Fracture toughening and toughness asymmetry induced by flexoelectricity

  A. Abdollahi, C. Peco, M. Arroyo, G. Catalan, I. Arias

  Physical review B: condensed matter and material physics (2015). Vol. 92 (9), pp. 1-7 (Preprint)

  
  

  Abstract

  Cracks generate the largest strain gradients that any material can withstand. Flexoelectricity (coupling between strain gradient and polarization) must therefore play an important role in fracture physics. Here we use a self-consistent continuum model to evidence two consequences of flexoelectricity in fracture: the resistance to fracture increases as structural size decreases, and it becomes asymmetric with respect to the sign of polarization. The latter phenomenon manifests itself in a range of intermediate sizes where piezo- and flexoelectricity compete. In BaTiO3 at room temperature, this range spans from 0.1 to 50 nm, a typical thickness range for epitaxial ferroelectric thin films.

  Abstract
  Cracks generate the largest strain gradients that any material can withstand. Flexoelectricity (coupling between strain gradient and polarization) must therefore play an important [...]

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• A stabilized formulation with maximum entropy meshfree approximants for viscoplastic flow simulation in metal forming

  F. Greco, L. Filice, C. Peco, M. Arroyo

  Int. J. Numer. Meth. Engng. (2015). Vol. 8 (3), pp. 341-353 (preprint)

  
  

  Abstract

  The finite element method is the reference technique in the simulation of metal forming and provides excellent results with both Eulerian and Lagrangian implementations. The latter approach is more natural and direct but the large deformations involved in such processes require remeshing-rezoning algorithms that increase the computational times and reduce the quality of the results. Meshfree methods can better handle large deformations and have shown encouraging results. However, viscoplastic flows are nearly incompressible, which poses a challenge to meshfree methods. In this paper we propose a simple model of viscoplasticity, where both the pressure and velocity fields are discretized with maximum entropy approximants. The inf-sup condition is circumvented with a numerically consistent stabilized formulation that involves the gradient of the pressure. The performance of the method is studied in some benchmark problems including metal forming and orthogonal cutting.

  Abstract
  The finite element method is the reference technique in the simulation of metal forming and provides excellent results with both Eulerian and Lagrangian implementations. The [...]

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• Examining the mechanical equilibrium of microscopic stresses in molecular simulations

  A. Torres-Sánchez, J. Vanegas, M. Arroyo

  Physical review letters (2015). Vol. 114 (25), pp. 258102-1/258102-5 (Preprint)

  
  

  Abstract

  The microscopic stress field provides a unique connection between atomistic simulations and mechanics at the nanoscale. However, its definition remains ambiguous. Rather than a mere theoretical preoccupation, we show that this fact acutely manifests itself in local stress calculations of defective graphene, lipid bilayers, and fibrous proteins. We find that popular definitions of the microscopic stress violate the continuum statements of mechanical equilibrium, and we propose an unambiguous and physically sound definition.

  Abstract
  The microscopic stress field provides a unique connection between atomistic simulations and mechanics at the nanoscale. However, its definition remains ambiguous. Rather than [...]

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• Physical principles of membrane remodelling during cell mechanoadaptation

  A. Kosmalska, L. Casares, A. Elosegui-Artola, J. Thottacherry, R. Moreno-Vicente, V. González-Tarragó, M. Pozo, S. Mayor, M. Arroyo, D. Navajas, X. Trepat, N. Gauthier, P. Roca

  Nature communications (2015). Vol. 6 (7292), pp. 1-11

  
  

  Abstract

  Biological processes in any physiological environment involve changes in cell shape, which must be accommodated by their physical envelope-the bilayer membrane. However, the fundamental biophysical principles by which the cell membrane allows for and responds to shape changes remain unclear. Here we show that the 3D remodelling of the membrane in response to a broad diversity of physiological perturbations can be explained by a purely mechanical process. This process is passive, local, almost instantaneous, before any active remodelling and generates different types of membrane invaginations that can repeatedly store and release large fractions of the cell membrane. We further demonstrate that the shape of those invaginations is determined by the minimum elastic and adhesive energy required to store both membrane area and liquid volume at the cell-substrate interface. Once formed, cells reabsorb the invaginations through an active process with duration of the order of minutes.

  Abstract
  Biological processes in any physiological environment involve changes in cell shape, which must be accommodated by their physical envelope-the bilayer membrane. However, the [...]

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• Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy

  B. Li, C. Peco, D. Millán, I. Arias, M. Arroyo

  Int. J. Numer. Meth. Engng. (2015). Vol. 102 (3-4), pp. 711-727 (Preprint)

  
  

  Abstract

  Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations. rack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations.

  Abstract
  Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic [...]

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• Efficient implementation of Galerkin meshfree methods for large-scale problems with an emphasis on maximum entropy approximants

  C. Peco, D. Millán, A. Rosolen, M. Arroyo

  Computers and Structures (2015). Vol. 150, pp. 52-62 (Preprint)

  
  

  Abstract

  In Galerkin meshfree methods, because of a denser and unstructured connectivity, the creation and assembly of sparse matrices is expensive. Additionally, the cost of computing basis functions can be significant in problems requiring repetitive evaluations. We show that it is possible to overcome these two bottlenecks resorting to simple and effective algorithms. First, we create and fill the matrix by coarse-graining the connectivity between quadrature points and nodes. Second, we store only partial information about the basis functions, striking a balance between storage and computation. We show the performance of these strategies in relevant problems.

  Abstract
  In Galerkin meshfree methods, because of a denser and unstructured connectivity, the creation and assembly of sparse matrices is expensive. Additionally, the cost of computing [...]

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• Revisiting pyramid compression to quantify flexoelectricity: a three-dimensional simulation study

  A. Abdollahi, D. Millán, C. Peco, M. Arroyo, I. Arias

  Physical review B: condensed matter and material physics (2015). Vol. 91 (10), pp. 104103 (preprint)

  
  

  Abstract

  Flexoelectricity is a universal property of all dielectrics by which they generate a voltage in response to an inhomogeneous deformation. One of the controversial issues in this field concerns the magnitude of flexoelectric coefficients measured experimentally, which greatly exceed theoretical estimates. Furthermore, there is a broad scatter amongst experimental measurements. The truncated pyramid compression method is one of the common setups to quantify flexoelectricity, the interpretation of which relies on simplified analytical equations to estimate strain gradients. However, the deformation fields in three-dimensional pyramid configurations are highly complex, particularly around its edges. In the present work, using three-dimensional self-consistent simulations of flexoelectricity, we show that the simplified analytical estimations of strain gradients in compressed pyramids significantly overestimate flexoelectric coefficients, thus providing a possible explanation to reconcile different estimates. In fact, the interpretation of pyramid compression experiments is highly nontrivial. We systematically characterize the magnitude of this overestimation, of over one order of magnitude, as a function of the truncated pyramid configuration. These results are important to properly characterize flexoelectricity, and provide design guidelines for effective electromechanical transducers exploiting flexoelectricity.

  Abstract
  Flexoelectricity is a universal property of all dielectrics by which they generate a voltage in response to an inhomogeneous deformation. One of the controversial issues in [...]

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