196 research outputs found
Fractal pattern formation at elastic-plastic transition in heterogeneous materials
Fractal patterns are observed in computational mechanics of elastic-plastic
transitions in two models of linear elastic/perfectly-plastic random
heterogeneous materials: (1) a composite made of locally isotropic grains with
weak random fluctuations in elastic moduli and/or yield limits; and (2) a
polycrystal made of randomly oriented anisotropic grains. In each case, the
spatial assignment of material randomness is a non-fractal, strict-white-noise
field on a 256 x 256 square lattice of homogeneous, square-shaped grains; the
flow rule in each grain follows associated plasticity. These lattices are
subjected to simple shear loading increasing through either one of three
macroscopically uniform boundary conditions (kinematic, mixed-orthogonal or
traction), admitted by the Hill-Mandel condition. Upon following the evolution
of a set of grains that become plastic, we find that it has a fractal dimension
increasing from 0 towards 2 as the material transitions from elastic to
perfectly-plastic. While the grains possess sharp elastic-plastic stress-strain
curves, the overall stress-strain responses are smooth and asymptote toward
perfectly-plastic flows; these responses and the fractal dimension-strain
curves are almost identical for three different loadings. The randomness in
elastic moduli alone is sufficient to generate fractal patterns at the
transition, but has a weaker effect than the randomness in yield limits. In the
model with isotropic grains, as the random fluctuations vanish (i.e. the
composite becomes a homogeneous body), a sharp elastic-plastic transition is
recovered.Comment: paper is in pres
Electric-field-induced displacement of a charged spherical colloid embedded in an elastic Brinkman medium
When an electric field is applied to an electrolyte-saturated polymer gel
embedded with charged colloidal particles, the force that must be exerted by
the hydrogel on each particle reflects a delicate balance of electrical,
hydrodynamic and elastic stresses. This paper examines the displacement of a
single charged spherical inclusion embedded in an uncharged hydrogel. We
present numerically exact solutions of coupled electrokinetic transport and
elastic-deformation equations, where the gel is treated as an incompressible,
elastic Brinkman medium. This model problem demonstrates how the displacement
depends on the particle size and charge, the electrolyte ionic strength, and
Young's modulus of the polymer skeleton. The numerics are verified, in part,
with an analytical (boundary-layer) theory valid when the Debye length is much
smaller than the particle radius. Further, we identify a close connection
between the displacement when a colloid is immobilized in a gel and its
velocity when dispersed in a Newtonian electrolyte. Finally, we describe an
experiment where nanometer-scale displacements might be accurately measured
using back-focal-plane interferometry. The purpose of such an experiment is to
probe physicochemical and rheological characteristics of hydrogel composites,
possibly during gelation
Transcranial magnetic stimulation: Improved coil design for deep brain investigation
This paper reports on a design for a coil for transcranial magnetic stimulation. The design shows potential for improving the penetration depth of the magnetic field, allowing stimulation of subcortical structures within the brain. The magnetic and induced electric fields in the human head have been calculated with finite element electromagnetic modeling software and compared with empirical measurements. Results show that the coil design used gives improved penetration depth, but also indicates the likelihood of stimulation of additional tissue resulting from the spatial distribution of the magnetic field
A Stochastic Multi-scale Approach for Numerical Modeling of Complex Materials - Application to Uniaxial Cyclic Response of Concrete
In complex materials, numerous intertwined phenomena underlie the overall
response at macroscale. These phenomena can pertain to different engineering
fields (mechanical , chemical, electrical), occur at different scales, can
appear as uncertain, and are nonlinear. Interacting with complex materials thus
calls for developing nonlinear computational approaches where multi-scale
techniques that grasp key phenomena at the relevant scale need to be mingled
with stochastic methods accounting for uncertainties. In this chapter, we
develop such a computational approach for modeling the mechanical response of a
representative volume of concrete in uniaxial cyclic loading. A mesoscale is
defined such that it represents an equivalent heterogeneous medium: nonlinear
local response is modeled in the framework of Thermodynamics with Internal
Variables; spatial variability of the local response is represented by
correlated random vector fields generated with the Spectral Representation
Method. Macroscale response is recovered through standard ho-mogenization
procedure from Micromechanics and shows salient features of the uniaxial cyclic
response of concrete that are not explicitly modeled at mesoscale.Comment: Computational Methods for Solids and Fluids, 41, Springer
International Publishing, pp.123-160, 2016, Computational Methods in Applied
Sciences, 978-3-319-27994-
Transcranial magnetic stimulation: improved coil design for deep brain investigation
This paper reports on a design for a coil for transcranial magnetic stimulation. The design shows potential for improving the penetration depth of the magnetic field, allowing stimulation of subcortical structures within the brain. The magnetic and induced electric fields in the human head have been calculated with finite element electromagnetic modeling software and compared with empirical measurements. Results show that the coil design used gives improved penetration depth, but also indicates the likelihood of stimulation of additional tissue resulting from the spatial distribution of the magnetic field
Integrin Clustering Is Driven by Mechanical Resistance from the Glycocalyx and the Substrate
Integrins have emerged as key sensory molecules that translate chemical and physical cues from the extracellular matrix (ECM) into biochemical signals that regulate cell behavior. Integrins function by clustering into adhesion plaques, but the molecular mechanisms that drive integrin clustering in response to interaction with the ECM remain unclear. To explore how deformations in the cell-ECM interface influence integrin clustering, we developed a spatial-temporal simulation that integrates the micro-mechanics of the cell, glycocalyx, and ECM with a simple chemical model of integrin activation and ligand interaction. Due to mechanical coupling, we find that integrin-ligand interactions are highly cooperative, and this cooperativity is sufficient to drive integrin clustering even in the absence of cytoskeletal crosslinking or homotypic integrin-integrin interactions. The glycocalyx largely mediates this cooperativity and hence may be a key regulator of integrin function. Remarkably, integrin clustering in the model is naturally responsive to the chemical and physical properties of the ECM, including ligand density, matrix rigidity, and the chemical affinity of ligand for receptor. Consistent with experimental observations, we find that integrin clustering is robust on rigid substrates with high ligand density, but is impaired on substrates that are highly compliant or have low ligand density. We thus demonstrate how integrins themselves could function as sensory molecules that begin sensing matrix properties even before large multi-molecular adhesion complexes are assembled
Computational Homogenization of Architectured Materials
Architectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. The present chapter aims at providing such models, in the case of mechanical properties. As a matter of fact, one engineering challenge is to predict the effective properties of such materials; computational homogenization using finite element analysis is a powerful tool to do so. Homogenized behavior of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. Furthermore, computational homogenization is the basis for computational topology optimization which will give rise to the next generation of architectured materials. This chapter covers the computational homogenization of periodic architectured materials in elasticity and plasticity, as well as the homogenization and representativity of random architectured materials
Fractal Shear Bands at Elastic-Plastic Transitions in Random Mohr-Coulomb Materials
This paper studies fractal patterns forming at elastic-plastic transitions in soil- and rock-like materials. Taking either friction or cohesion as nonfractal vector random fields with weak noise-to-signal ratios, it is found that the evolving set of plastic grains (i.e., a shear-band system) is always a monotonically growing fractal under increasing macroscopic load in plane strain. Statistical analysis is used to assess the anisotropy of those shear bands. All the macroscopic responses display smooth transitions, but as the randomness vanishes, they turn into a sharp response of an idealized homogeneous material. Parametric study shows that increasing hardening or friction makes the transition more rapid. In addition, randomness in cohesion has a stronger effect than randomness in friction, whereas dilatation has practically no influence. Adapting the concept of scaling functions, the authors find the elastic-plastic transitions in random Mohr-Coulomb media to be similar to phase transitions in condensed-matter physics: the fully plastic state is a critical point, and with three order parameters (reduced Mohr-Coulomb stress, reduced plastic volume fraction, and reduced fractal dimension), three scaling functions are introduced to unify the responses of different materials. The critical exponents are demonstrated to be universal regardless of the randomness in various constitutive properties and their random noise levels
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