Search results for "Volume element"
showing 10 items of 12 documents
Variational Aspects of the Physically-Based Approach to 3D Non-Local Continuum Mechanics
2010
This paper deals with the generalization to three-dimensional elasticity of the physically-based approach to non-local mechanics, recently proposed by the authors in one-dimensional case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range central forces exerted by non-adjacent elements. Specifically, the long-range forces are modeled as central body forces depending on the relative displacements between the centroids of the volume elements, measured along the line connecting the centroids. Furthermore, the long-range forces are assumed to be proportional to a proper, material-dependent, distance-decay…
The finite element method for the mechanically based model of non-local continuum
2011
SUMMARY In this paper the finite element method (FEM) for the mechanically based non-local elastic continuum model is proposed. In such a model each volume element of the domain is considered mutually interacting with the others, beside classical interactions involved by the Cauchy stress field, by means of central body forces that are monotonically decreasing with their inter-distance and proportional to the product of the interacting volume elements. The constitutive relations of the long-range interactions involve the product of the relative displacement of the centroids of volume elements by a proper, distance-decaying function, which accounts for the decrement of the long-range interac…
Long-range cohesive interactions of non-local continuum faced by fractional calculus
2008
Abstract A non-local continuum model including long-range forces between non-adjacent volume elements has been studied in this paper. The proposed continuum model has been obtained as limit case of two fully equivalent mechanical models: (i) A volume element model including contact forces between adjacent volumes as well as long-range interactions, distance decaying, between non-adjacent elements. (ii) A discrete point-spring model with local springs between adjacent points and non-local springs with distance-decaying stiffness connecting non-adjacent points. Under the assumption of fractional distance-decaying interactions between non-adjacent elements a fractional differential equation in…
Material Internal Frictional Dissipation Modelling
2009
This presentation is concerned with a first introductory study devoted to internal frictional dissipation modelling of cracked materials. The problem is set as periodic Representative Volume Element (RVE) with oriented cracks diffused in the bulk material. As first stage, useful for moderate loading levels, cracks are considered fixed and stable at certain position and are modelled as perfect frictional mechanical interface with unilateral contact features. Analyses on cyclic material response are discussed for 2D problems. A second type of analyses is performed considering a further cohesion strength and a crack propagation criteria, which are typical of interface damage mechanical approac…
Formulation and validation of a reduced order model of 2D materials exhibiting a two-phase microstructure as applied to graphene oxide
2018
Abstract Novel 2D materials, e.g., graphene oxide (GO), are attractive building blocks in the design of advanced materials due to their reactive chemistry, which can enhance interfacial interactions while providing good in-plane mechanical properties. Recent studies have hypothesized that the randomly distributed two-phase microstructure of GO, which arises due to its oxidized chemistry, leads to differences in nano- vs meso‑scale mechanical responses. However, this effect has not been carefully studied using molecular dynamics due to computational limitations. Herein, a continuum mechanics model, formulated based on density functional based tight binding (DFTB) constitutive results for GO …
Micro-cracking of brittle polycrystalline materials with initial damage
2016
In this paper, the effect of pre-existing damage on brittle micro-cracking of polycrystalline materials is explored. The behaviour of single and multiple cracks randomly distributed within a grain scale polycrystalline aggregate is investigated using a recently developed grain boundary 3D computational framework. Each grain is modelled as a single crystal anisotropic domain. Opening, sliding and/or contact at grain boundaries are modelled using nonlinear cohesive-frictional laws. The polycrystalline micro-morphologies are generated using Voronoi tessellation algorithms in combination with a regularisation scheme to avoid the presence of unnecessary small geometrical entities (edges and face…
A computationally effective 3D Boundary Element Method for polycrystalline micromechanics
2015
An effective computational framework for homogenization and microcracking analysis of polycrystalline RVEs is presented. The method is based on a recently developed grain-boundary formulation for polycrystalline materials and several enhancements over the original technique are introduced to reduce the computational effort needed to model three-dimensional polycrystalline aggregates, which is highly desirable, especially in a multiscale perspective. First, a regularization scheme is used to remove pathological entities, usually responsible for unduly large mesh refinements, from Voronoi polycrystalline morphologies. Second, an improved meshing strategy is used, with an aim towards meshing r…
Multiscale modeling of polycrystalline materials: A boundary element approach to material degradation and fracture
2015
Abstract In this work, a two-scale approach to degradation and failure in polycrystalline materials is proposed. The formulation involves the engineering component level (macro-scale) and the material grain level (micro-scale). The macro-continuum is modeled using a three-dimensional boundary element formulation in which the presence of damage is formulated through an initial stress approach to account for the local softening in the neighborhood of points experiencing degradation at the micro-scale. The microscopic degradation is explicitly modeled by associating Representative Volume Elements (RVEs) to relevant points of the macro continuum, for representing the polycrystalline microstruct…
On the vibrations of a mechanically based non-local beam model
2012
The vibration problem of a Timoshenko non-local beam is addressed. The beam model involves assuming that the equilibrium of each volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are taken as depending on the product of the interacting volume elements and on their relative displacement through a material-dependent distance-decaying function. To derive the motion equations and the related mechanical boundary conditions, the Hamilton's principle is applied The vibration problem of a Timoshenko non-local beam …
A mechanically based approach to non-local beam theories
2011
A mechanically based non-local beam theory is proposed. The key idea is that the equilibrium of each beam volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are modeled as depending on the product of the interacting volume elements, their relative displacement and a material-dependent distance-decaying function. To derive the beam equilibrium equations and the pertinent mechanical boundary conditions, the total elastic potential energy functional is used based on the Timoshenko beam theory. In this manner, t…