Generalized continuum modeling of 2-D periodic cellular solids

By R. Kumar, David L. McDowell. 2004

220 citations recorded by the source corpus.

Subfields: Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/53ca1ab76cd276ce4b99ee11d5049619b87f268f

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In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

Dynamic compressive behaviour of cellular materials: A review of phenomenon, mechanism and modelling (2018, unknown): “generalised continuum mechanics [263-266]) are still needed for different types of cellular materials.”
A limit analysis approach based on Cosserat continuum for the evaluation of the in-plane strength of discrete media: Application to masonry (2017, unknown): “It is clear that, when these latter are considered rigid, the kinematic description of the whole medium reduces to the degrees of freedom of the nodes, and a micropolar description of the medium can be then attempted (Kumar and McDowell, 2004).”
Stiffness and strength of tridimensional periodic lattices (2012, background): “Wang and McDowell [36] calculated the in-plane stiffness and strength of a selected bidimensional cell topologies, with respect to the onset of plastic yielding.”
Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices (2012, methodology): “However, if the first order method (Chen et al, 1998; Kumar and McDowell, 2004; Spadoni and Ruzzene, 2012) is adopted, i.e. retaining the first order items of Eq.”
Homogenization of periodic hexa- and tetrachiral cellular solids (2014, methodology): “Spadoni and Ruzzene, 2012, developed a micropolar homogenization of the hexachiral beam-lattice model (see figure 2.b) based on the approach of Kumar and McDowell, 2004, that is equipped with an internal length directly associated with the characteristic size of the microstructure.”
Multiscale isogeometric topology optimization for lattice materials (2017, methodology): “Several theoretical approaches using the notion of Representative Volume Element have been proposed in the literature to calculate the mechanical properties of a lattice [6-9].”
Fatigue design of lattice materials via computational mechanics: Application to lattices with smooth transitions in cell geometry (2013, methodology): “Theoretical, numerical, and experimental approaches can be used to homogenize the properties of a lattice [2,15,16,42–52].”
Elasto-static micropolar behavior of a chiral auxetic lattice (2012, methodology): “which are identical to those obtained for a triangular lattice in Kumar and McDowell (2004) and derived without considering second or higher-order terms in the Taylor-series expansion of displacements of Eqs.”