COLLECTIONS

Documents published in Scipedia

• Rayleigh wave correction for the BEM analysis of two-dimensional elastodynamic problems in a half-space

  I. Arias, J. Achenbach

  Int. J. Numer. Meth. Engng. (2004). Vol. 60 (13), pp. 2131-2146

  
  

  Abstract

  A simple, elegant approach is proposed to correct the error introduced by the truncation of the infinite boundary in the BEM modelling of two-dimensional wave propagation problems in elastic half-spaces. The proposed method exploits the knowledge of the far-field asymptotic behaviour of the solution to adequately correct the BEM displacement system matrix for the truncated problem to account for the contribution of the omitted part of the boundary. The reciprocal theorem of elastodynamics is used for a convenient computation of this contribution involving the same boundary integrals that form the original BEM system. The method is formulated for a two-dimensional homogeneous, isotropic, linearly elastic half-space and its implementation in a frequency domain boundary element scheme is discussed in some detail. The formulation is then validated for a free Rayleigh pulse travelling on a half-space and successfully tested for a benchmark problem with a known approximation to the analytical solution. This is the pre-peer reviewed version of the following article: Arias, I.; Achenbach, J. Rayleigh wave correction for the BEM analysis of two-dimensional elastodynamic problems in a half-space.

  Abstract
  A simple, elegant approach is proposed to correct the error introduced by the truncation of the infinite boundary in the BEM modelling of two-dimensional wave propagation [...]

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• Use of reciprocity considerations for the two-dimensional BEM analysis of wave propagation in an elastic half-space with applications to acoustic emission

  I. Arias, J. Achenbach

  Wave Motion (2004). Vol. 39 (4), pp. 281-294

  
  

  Abstract

  A simple numerical treatment of the infinite boundary in the BEM analysis of two-dimensional wave propagation problems in elastic half-spaces is proposed to avoid the spurious reflections of non-decaying Rayleigh waves introduced by the truncation of the boundary. The proposed method exploits the knowledge of the far-field asymptotic behavior of the solution to adequately correct the BEM displacement system matrix for the truncated problem to account for the contribution of the omitted part of the boundary. The reciprocal theorem of elastodynamics is used for a convenient computation of this contribution exclusively in terms of the boundary integrals of the original BEM system. The method is applied to the study of the acoustic emission from nucleating and propagating surface-breaking and buried cracks in a two-dimensional elastic half-space. It is shown to be particularly advantageous since it allows for an accurate calculation of the generated signal even when the observation point is located far from the acoustic emission source.

  Abstract
  A simple numerical treatment of the infinite boundary in the BEM analysis of two-dimensional wave propagation problems in elastic half-spaces is proposed to avoid the spurious [...]

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• A model for the ultrasonic detection of surface-breaking cracks by the scanning laser source technique

  I. Arias, J. Achenbach

  Wave Motion (2004). Vol. 39 (1), pp. 61-75

  
  

  Abstract

      A model for the scanning laser source (SLS) technique is presented. The SLS is a novel laser-based inspection method for the ultrasonic detection of small surface-breaking cracks. The generated ultrasonic signal is monitored as a line-focused laser is scanned over the defect. Characteristic changes in the amplitude and the frequency content are observed. The modeling approach is based on the decomposition of the field generated by the laser in a cracked two-dimensional half-space, by virtue of linear superposition, into the incident and the scattered fields. The incident field is that generated by laser illumination of a defect-free half-space. A thermoelastic model has been used which takes account of the effect of thermal diffusion, as well as the finite width and duration of the laser source. The scattered field incorporates the interactions of the incident field with the surface-breaking crack. It has been analyzed numerically by a direct frequency domain boundary element method. A comparison with an experiment for a large defect shows that the model captures the observed phenomena. A simulation for a small crack illustrates the ability of the SLS technique to detect defects smaller than the wavelength of the generated Rayleigh wave.  

  Abstract
      A model for the scanning laser source (SLS) technique is presented. The SLS is a novel laser-based inspection method for the ultrasonic detection [...]

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• Thermoelastic generation of ultrasound by line-focused laser irradiation

  I. Arias, J. Achenbach

  Int. J. Solids and Structures (2003). Vol. 40 (25), pp. 6917-6935

  
  

  Abstract

  A two-dimensional theoretical model for the field generated in the thermoelastic regime by line-focused laser illumination of a homogeneous, isotropic, linearly elastic half-space is presented. The model accounts for the effects of thermal diffusion and optical penetration, as well as the finite width and duration of the laser source. The model is obtained by solving the thermoelastic problem in plane strain, rather than by integrating available solutions for the point-source, leading to a lower computational effort. The well-known dipole model follows from appropriate limits. However, it is shown that, by simple elasticity arguments, the strength of the dipole can be related a-priori to the heat input and certain material properties. The strength is found to be smaller than that of the dipoles equivalent to a buried source due to the effect of the free surface. This fact has been overlooked by some previous researchers. Excellent quantitative agreement with experimental observations provides validation for the model. Some representative results are presented to illustrate the generated field and provide insight into the relevance of the different mechanisms taken into account in the model.

  Abstract
  A two-dimensional theoretical model for the field generated in the thermoelastic regime by line-focused laser illumination of a homogeneous, isotropic, linearly elastic half-space [...]

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• Phase field modeling of brittle fracture in an Euler–Bernoulli beam accounting for transverse part-through cracks

  W. Lai, J. Gao, Y. Li, M. Arroyo, Y. Shen

  Comput. Methods Appl. Mech. Engrg., (2020). Vol. 361, pp. 112787

  
  

  Abstract

  We present a phase field model to simulate brittle fracture in an initially straight Euler–Bernoulli beam, with generalization to curved beams. We start from formulating the problem with the principle of minimum potential energy in a 3D solid, with the displacement field and the phase field as primary arguments. We then select, for each cross section, representative fields that characterize the said cross section, including the beam deflection and rotation, and two independent ansatz variables within the cross section to represent the phase field. The problem then reduces to a minimization with only one-dimensional field variables. A feature of the proposed method is, without discretizing the phase field within the cross section, it can represent its variation within the cross section, allowing to simulate cracks partially going through the thickness due to bending as well as axial loads.

  Abstract
  We present a phase field model to simulate brittle fracture in an initially straight Euler–Bernoulli beam, with generalization to curved beams. We start from formulating [...]

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• Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations

  A. Torres-Sánchez, D. Santos-Oliván, M. Arroyo

  Journal of Computational Physics (2020). Vol. 405, pp. 109168

  
  

  Abstract

  We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, e.g. as in finite element or NURBS surface representations. Our goal is to use this method to solve numerically tensor-valued partial differential equations (PDEs) on surfaces. Previous methods use scalar potentials to numerically describe vector fields on surfaces, at the expense of requiring higher-order derivatives of the approximated fields and limited to simply connected surfaces, or represent tangential tensor fields as tensor fields in 3D subjected to constraints, thus increasing the essential number of degrees of freedom. In contrast, the LMP method uses an optimal number of degrees of freedom to represent a tensor, is general with regards to the topology of the surface, and does not increase the order of the PDEs governing the tensor fields. The main idea is to construct maps between the element parametrizations and a local Monge parametrization around each node. We test the LMP method by approximating in a least-squares sense different vector and tensor fields on simply connected and genus-1 surfaces. Furthermore, we apply the LMP method to two physical models on surfaces, involving a tension-driven flow (vector-valued PDE) and nematic ordering (tensor-valued PDE), on different topologies. The LMP method thus solves the long-standing problem of the interpolation of tensors on general surfaces with an optimal number of degrees of freedom.

  Abstract
  We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, [...]

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• Surface tension controls the hydraulic fracture of adhesive interfaces bridged by molecular bonds

  D. Kaurin, M. Arroyo

  Physical review letters (2019). Vol. 123 (22), pp. 1-6 (Preprint)

  
  

  Abstract

  Biological function requires cell-cell adhesions to tune their cohesiveness; for instance, during the opening of new fluid-filled cavities under hydraulic pressure. To understand the physical mechanisms supporting this adaptability, we develop a stochastic model for the hydraulic fracture of adhesive interfaces bridged by molecular bonds. We find that surface tension strongly enhances the stability of these interfaces by controlling flaw sensitivity, lifetime, and optimal architecture in terms of bond clustering. We also show that bond mobility embrittles adhesions and changes the mechanism of decohesion. Our study provides a mechanistic background to understand the biological regulation of cell-cell cohesion and fracture.

  Abstract
  Biological function requires cell-cell adhesions to tune their cohesiveness; for instance, during the opening of new fluid-filled cavities under hydraulic pressure. To understand [...]

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• Out-of-equilibrium mechanochemistry and self-organization of fluid membranes interacting with curved proteins

  C. Tozzi, N. Walani, M. Arroyo

  New journal of physics (2019). Vol. 21, pp. 1-23

  
  

  Abstract

  The function of biological membranes is controlled by the interaction of the fluid lipid bilayer with various proteins, some of which induce or react to curvature. These proteins can preferentially bind or diffuse towards curved regions of the membrane, induce or stabilize membrane curvature and sequester membrane area into protein-rich curved domains. The resulting tight interplay between mechanics and chemistry is thought to control organelle morphogenesis and dynamics, including traffic, membrane mechanotransduction, or membrane area regulation and tension buffering. Despite all these processes are fundamentally dynamical, previous work has largely focused on equilibrium and a self-consistent theoretical treatment of the dynamics of curvature sensing and generation has been lacking. Here, we develop a general theoretical and computational framework based on a nonlinear Onsager’s formalism of irreversible thermodynamics for the dynamics of curved proteins and membranes. We develop variants of the model, one of which accounts for membrane curving by asymmetric crowding of bulky off-membrane protein domains. As illustrated by a selection of test cases, the resulting governing equations and numerical simulations provide a foundation to understand the dynamics of curvature sensing, curvature generation, and more generally membrane curvature mechano-chemistry.

  Abstract
  The function of biological membranes is controlled by the interaction of the fluid lipid bilayer with various proteins, some of which induce or react to curvature. These proteins [...]

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• Modelling fluid deformable surfaces with an emphasis on biological interfaces

  A. Torres-Sánchez, D. Millán, M. Arroyo

  Journal of fluid mechanics (2019). Vol. 872, pp. 218-271 (Preprint)

  
  

  Abstract

  Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers, the actomyosin cortex or epithelial cell sheets. These interfaces exhibit a complex interplay between elasticity, low Reynolds number interfacial hydrodynamics, chemistry and geometry, and govern important biological processes such as cellular traffic, division, migration or tissue morphogenesis. To address the modelling challenges posed by this class of problems, in which interfacial phenomena tightly interact with the shape and dynamics of the surface, we develop a general continuum mechanics and computational framework for fluid deformable surfaces. The dual solid–fluid nature of fluid deformable surfaces challenges classical Lagrangian or Eulerian descriptions of deforming bodies. Here, we extend the notion of arbitrarily Lagrangian–Eulerian (ALE) formulations, well-established for bulk media, to deforming surfaces. To systematically develop models for fluid deformable surfaces, which consistently treat all couplings between fields and geometry, we follow a nonlinear Onsager formalism according to which the dynamics minimizes a Rayleighian functional where dissipation, power input and energy release rate compete. Finally, we propose new computational methods, which build on Onsager’s formalism and our ALE formulation, to deal with the resulting stiff system of higher-order partial differential equations. We apply our theoretical and computational methodology to classical models for lipid bilayers and the cell cortex. The methods developed here allow us to formulate/simulate these models in their full three-dimensional generality, accounting for finite curvatures and finite shape changes. This article has been published in a revised form in Journal of fluid mechanics,

  Abstract
  Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers, the actomyosin cortex or epithelial cell sheets. These interfaces exhibit a [...]

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• The plasma membrane as a mechanochemical transducer

  A. Roux, X. Quiroga, N. Walani, M. Arroyo, P. Roca

  Philosophical transaction of the Royal Society B. Diological sciences (2019). Vol. 374, pp. 1-15

  
  

  Abstract

  Cells are constantly submitted to external mechanical stresses, which they must withstand and respond to. By forming a physical boundary between cells and their environment that is also a biochemical platform, the plasma membrane (PM) is a key interface mediating both cellular response to mechanical stimuli, and subsequent biochemical responses. Here, we review the role of the PM as a mechanosensing structure. We first analyse how the PM responds to mechanical stresses, and then discuss how this mechanical response triggers downstream biochemical responses. The molecular players involved in PM mechanochemical transduction include sensors of membrane unfolding, membrane tension, membrane curvature or membrane domain rearrangement. These sensors trigger signalling cascades fundamental both in healthy scenarios and in diseases such as cancer, which cells harness to maintain integrity, keep or restore homeostasis and adapt to their external environment. This article is part of a discussion meeting issue ‘Forces in cancer: interdisciplinary approaches in tumour mechanobiology’.

  Abstract
  Cells are constantly submitted to external mechanical stresses, which they must withstand and respond to. By forming a physical boundary between cells and their environment [...]

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