Parametric finite-volume micromechanics of periodic materials with elastoplastic phases

The recently incorporated parametric mapping capability into the finite-volume direct averaging micromechanics (FVDAM) theory has produced a paradigm shift in the theory’s development. The use of quadrilateral subvolumes made possible by the mapping facilitates efficient modeling of microstructures with arbitrarily shaped heterogeneities, and eliminates artificial stress concentrations produced by the rectangular subvolumes employed in the standard version. Herein, the parametric FVDAM theory is extended to the inelastic domain by implementing additional formulation required to accommodate plastic and thermal loading. Two different approaches of implementing plasticity have been investigated. The first approach is based on the treatment employed in previous versions of the theory wherein plastic strain fields are represented by a series expansion in Legendre polynomials. The second approach is based on direct surface-averaging of plastic strains calculated at a number of collocation points along the quadrilateral subvolumes’ surfaces, and offers substantial simplification in the parametric finite-volume theory’s elastic–plastic framework. Moreover, substantial reductions in execution times without loss of accuracy are realized due to the elimination of redundant plastic strain calculations in the subvolumes’ interiors employed in the evaluation of the Legendre polynomial coefficients. Numerical studies demonstrate the advantages of the parametric FVDAM theory relative to the standard version, together with new results that highlight its modeling capabilities vis-a-vis an emerging class of periodic lamellar materials with wavy microstructures and the thus-far undocumented architectural effects amplified by plasticity.     

Scale transition of a higher order plasticity model – A consistent homogenization theory from meso to macro

Standard plasticity models cannot capture the microstructural size effect associated with grain sizes, as well as structural size effects induced by external boundaries and overall gradients. Many higher-order plasticity models introduce a length scale parameter to resolve the latter limitation – microstructural influences are not explicitly account for. This paper adopts two distinct length scales in the formulation, i.e. an intrinsic length scale (l) governing micro-processes such as dislocation pile-up at internal boundaries, as well as the characteristic grain size (L), and aims to unravel the interaction between these two length scales and the characteristic specimen size (H) at the macro level. At the meso-scale, we adopt the strain gradient plasticity model developed in Gurtin (2004) [Gurtin, M.E., 2004. A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin. J. Mech. Phys. Solids 52, 2545–2568] which accounts for the direct influence of grain boundaries. Through a novel homogenization theory, the plasticity model is translated consistently from meso to macro. The two length scale parameters (l and L) manifest themselves naturally at the macro scale, hence capturing both types of size effects in an average sense. The resulting (macro) higher-order model is thermodynamically consistent to the meso model, and has the same structure as a micromorphic continuum. Finally, we consider a bending example for the two limiting cases – microhard and microfree conditions at grain boundaries – and illustrate the excellent match between the meso and homogenized solutions.     

Analysis of micro-structural effects on phononic waves in layered elastic media with periodic nonsmooth coordinates

Propagation of elastic phononic waves in layered composite materials is analyzed by introducing nonsmooth periodic coordinates associated with structural specifics of the materials. Spatial scales of the original (smooth) coordinates are estimated by the wave lengths. In terms of the new coordinates, the homogenization procedure occurs naturally from the continuity conditions imposed on elastic displacements and forces at layer interfaces. As a result, higher-order asymptotic approximations describing spatiotemporal ‘macro’- and ‘micro’-effects of wave propagation are obtained in closed form. Such solutions provide visualizations for the wave shapes illustrating their structure induced local details. In particular, beat-wise mode shapes and effective anisotropy of acoustic wave propagation are revealed. The subharmonic beating in wave modes occur when wave lengths orthogonal to layers is about to ‘resonate’ with layer’ thickness. If the wave speed has a non-zero projection along the layers, then phase shifts between the beats are observed in different cross sections perpendicular to the layers.     

Shear-horizontal waves in periodic layered nanostructure with both nonlocal and interface effects

The propagation of shear-horizontal(SH) waves in the periodic layered nanocomposite is investigated by using both the nonlocal integral model and the nonlocal differential model with the interface effect. Based on the transfer matrix method and the Bloch theory, the band structures for SH waves with both vertical and oblique incidences to the structure are obtained. It is found that by choosing appropriate interface parameters, the dispersion curves predicted by the nonlocal differential model w...