Particulate random composites homogenized as micropolar materials

Abstract

Many composite materials, widely used in different engineering fields, are characterized by random distributions of the constituents. Examples range from polycrystals to concrete and masonry-like materials. In this work we propose a statistically-based scale-dependent multiscale procedure aimed at the simulation of the mechanical behavior of a two-phase\ud particle random medium and at the estimation of the elastic moduli of the energy-equivalent homogeneous\ud micropolar continuum. The key idea of the procedure is to approach the so-called Representative Volume Element (RVE) using finite-size scaling of Statistical Volume Elements (SVEs). To this end properly defined Dirichlet, Neumann, and periodic-type non-classical boundary value problems are numerically solved on the SVEs defining hierarchies of constitutive bounds.\ud The results of the performed numerical simulations point out the importance of accounting for spatial randomness as well as the additional degrees of freedom of the continuum with rigid local structure

A micromechanics‐based inverse study for stochastic order reduction of elastic UD fiber reinforced composites analyses

“…When uncertainties are involved, or when the volume element is not several order of magnitude larger than the microscale size, the mesoscale volume element does not respect the statistical representativity and is called statistical or stochastic volume element (SVE). 16 Therefore, the homogenized response depends on the SVE realization, and on the applied boundary conditions as discussed for two-dimensional (2D) particle reinforced composites in the case of elasticity, 17,18 linear micropolar continua, [19][20][21] elastoplasticity, 17 thermoelasticity, or again finite elasticity. 17 For a given type of boundary condition, the homogenized properties of SVE realizations exhibit a distribution whose standard deviation increases when the SVE size becomes closer to the inclusion size.…”

A multiscale description of particle composites: From lattice microstructures to micropolar continua

“…For the transition from the discrete micro-level to the two-phases continuum mesolevel (i), a coarse-graining procedure based on a generalized Cauchy-Born correspondence maps and energy equivalence has been adopted [10,13,16]. For the meso/macro level transition instead (ii), a statistical homogenization procedure has been developed [33,34]. This procedure is based on the solution of Boundary Value Problems (BVPs), posed on Statistically Representative Elements (SVEs), under Boundary Conditions (BCs) derived from a generalized macrohomogeneity condition of Hill's type [35].…”

“…With the aim of investigating the gross mechanical response of this special class of random composites, we adopt a statistically-based multiscale procedure which allow us to detect the size of the RVE, that is unknown in the case of random media [44,45], and to estimate the constitutive moduli of the energy equivalent homogeneous micropolar con-tinuum [33,34]. The RVE is obtained by increasing a scale factor representing the ratio between the size of a control window (SVE) and the particle size, until the statistical convergence, defined through an ad hoc conceived criterion, is reached.…”

Identification of couple-stress moduli of vertebral trabecular bone based on the 3D internal architectures

“…Ostoja-Starzewski et al (1999), Bouyge (2000), Bouyge et al (2001Bouyge et al ( , 2002 used the couple-stress theory and strain energy based RVE method to evaluate couple-stress constants of planar, periodic, effectively isotropic or orthotropic, two-phase composites with linear elastic constituents of classical Cauchy type. Trovalusci et al (2014aTrovalusci et al ( , 2014b proposed a statistically-based scaledependent multiscale procedure aimed at the simulation of the mechanical behavior of a two-phase particle random medium and at the estimation of the elastic moduli of the energy-equivalent homogeneous micropolar continuum. In a pioneering work, Yoo and Jasiuk (2006) computed the apparent orthotropic couple-stress moduli of 3D trabecular bone using displacement and traction boundary conditions, which respectively gives upper and lower bounds of the effective couple-stress moduli.…”