Modelling of elastic continua using a grillage of structural elements based on discrete element concepts

Griffiths, D. V.; Mustoe, G.G.W.

doi:10.1002/nme.99

Cited by 154 publications

(101 citation statements)

References 4 publications

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“…By adjusting α1 and α2, macroscopic modeling of both elastic constants (E and Poisson ratio, ν) is possible. By equating strain energy densities of an elastic continuum (in plane stress) and a regular triangular lattice, the spring coefficients are related to the elastic constants as follows [16]:…”

Section: Lattice Model Formulationmentioning

confidence: 99%

“…Whereas strain conditions obtained by Eq. (2) for regular lattices have been validated, the local stress conditions have not been discussed [16]. The following section introduces existing procedures to determine local stress conditions from the lattice structure, and a new approach to accurately represent the Poisson effect.…”

Section: Lattice Model Formulationmentioning

confidence: 99%

“…Lattice models are typically based on a set of nodes and their interconnection via primitive, one-dimensional (1-D) elements. Such models, which include some types of particle models, can be viewed as mechanical analogues of the equations of continuum mechanics [1], [16], [21], [31]. The nodes can be arranged in regular or irregular patterns.…”

Section: Introductionmentioning

confidence: 99%

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Simulating the Poisson effect in lattice models of elastic continua

Asahina

Ito

Houseworth

et al. 2015

Computers and Geotechnics

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Lattice models provide discontinuous approximations of the displacement field over the computational domain, which facilitates the modeling of fracture and other discontinuous phenomena. By discretizing the domain with two-node elements, however, ordinary lattice models cannot simulate the Poisson effect in a local (intra-element) sense, which is problematic for some types of analyses.Furthermore, such methods are limited in the range of Poisson ratio values that can be simulated. We present a new approach to remedy such known, yet underappreciated, shortcomings of lattice models. In this approach, the Poisson effect is modeled through the introduction of fictitious stresses into a regular lattice. Capabilities of the new approach are demonstrated through compressive test simulations of homogeneous and heterogeneous materials. The simulation results are compared with theory and those of continuum finite element models. The comparisons show good agreement for arbitrary Poisson ratios (including ν ⩾ 1/3) with respect to nodal displacement, intra-element stress, and nodal stress. This form of discrete method, supplemented by the proposed fictitious measures of stress, retains the simplicity of collections of two-node elements.

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Section: Lattice Model Formulationmentioning

confidence: 99%

Section: Lattice Model Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simulating the Poisson effect in lattice models of elastic continua

Asahina

Ito

Houseworth

et al. 2015

Computers and Geotechnics

View full text Add to dashboard Cite

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“…where E and γ are model parameters controlling both the Young's modulus and Poisson's ratio of the material [11]. For a regular lattice and plane stress, Poisson's ratio ν is…”

Section: Modelling Approachmentioning

confidence: 99%

Influence of aggregate size and volume fraction on shrinkage induced micro-cracking of concrete and mortar

Grassl

Wong

Buenfeld

2010

Cement and Concrete Research

170

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In this paper, the influence of aggregate size and volume fraction on shrinkage induced micro-cracking and permeability of concrete and mortar was investigated. Nonlinear finite element analyses of model concrete and mortar specimens with regular and random aggregate arrangements were performed. The aggregate diameter was varied between 2 and 16 mm. Furthermore, a range of volume fractions between 0.1 and 0.5 was studied. The nonlinear analyses were based on a 2D lattice approach in which aggregates were simplified as monosized cylindrical inclusions. The analysis results were interpreted by means of crack length, crack width and change of permeability. The results show that increasing aggregate diameter (at equal volume fraction) and decreasing volume fraction (at equal aggregate diameter), increases crack width and consequently greatly increases permeability.

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“…To reduce this burden, alternatives that can improve on the capabilities of local continuum models have also been proposed, such as lattice models for modelling damage in concrete (see, e.g. [29][30][31][32]. The peridynamic method offers new promise in connecting existing material models developed in the classical continuum mechanics literature with nonlocal continuum models that can approximate the dispersion of short elastic waves, for example.…”

mentioning

confidence: 99%

Influence of van der Waals forces on increasing the strength and toughness in dynamic fracture of nanofibre networks: a peridynamic approach

Bobaru

2007

Modelling Simul. Mater. Sci. Eng.

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The peridynamic method is used here to analyse the effect of van der Waals forces on the mechanical behaviour and strength and toughness properties of three-dimensional nanofibre networks under imposed stretch deformation. The peridynamic formulation allows for a natural inclusion of long-range forces (such as van der Waals forces) by considering all interactions as 'long-range'. We use van der Waals interactions only between different fibres and do not need to model individual atoms. Fracture is introduced at the microstructural (peridynamic bond) level for the microelastic type bonds, while van der Waals bonds can reform at any time. We conduct statistical studies to determine a certain volume element for which the network of randomly oriented fibres becomes quasi-isotropic and insensitive to statistical variations. This qualitative study shows that the presence of van der Waals interactions and of heterogeneities (sacrificial bonds) in the strength of the bonds at the crosslinks between fibres can help in increasing the strength and toughness of the nanofibre network. Two main mechanisms appear to control the deformation of nanofibre networks: fibre reorientation (caused by deformation and breakage) and fibre accretion (due to van der Waals interaction). Similarities to the observed toughness of polymer adhesive in the abalone shell composition are explained.

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Modelling of elastic continua using a grillage of structural elements based on discrete element concepts

Cited by 154 publications

References 4 publications

Simulating the Poisson effect in lattice models of elastic continua

Simulating the Poisson effect in lattice models of elastic continua

Influence of aggregate size and volume fraction on shrinkage induced micro-cracking of concrete and mortar

Influence of van der Waals forces on increasing the strength and toughness in dynamic fracture of nanofibre networks: a peridynamic approach

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