A Generalized Continuum Formulation for Composite Microcracked Materials and Wave Propagation in a Bar

Abstract

A multifield continuum is adopted to grossly describe the dynamical behavior of composite microcracked solids. The constitutive relations for the internal and external (inertial) actions are obtained using a multiscale modeling based on the hypotheses of the classical molecular theory of elasticity and the ensuing overall elastodynamic properties allow us to take properly into account the microscopic features of these materials. Referring to a one-dimensional microcracked bar, the ability of such a continuum to reveal the presence of internal heterogeneities is investigated by analyzing the relevant dispersive wave propagation properties. Scattering of traveling waves is shown to be associated with the microcrack density in the bar.

A multiphysics and multiscale approach for modeling microcracked thermo-elastic materials

“…We compare the results with a bar without microcracks, whose governing equation reduces to the classical wave equation .€ u À Cu 00 ¼ 0, that we numerically solve for different ratios a u =a d and with the initial and boundary conditions (19) 1À4 . As already shown in [79,70], due to the dispersion properties in wave propagation, related to the presence of the term d -that is neither a time nor a space second derivative -the shape of the resulting wave is altered by the presence of the microcracks. This is a consequence of partial reflections of waves occurring in encountering the microcracks (scattering).…”

“…Note that, the higher a d , the higher the microcrack density (for a detailed justification of this statement, see [79,70]). We compare the results with a bar without microcracks, whose governing equation reduces to the classical wave equation .€ u À Cu 00 ¼ 0, that we numerically solve for different ratios a u =a d and with the initial and boundary conditions (19) 1À4 .…”

“…To fix ideas, we focus on porous metal-ceramic composites (MCC, CMC) such as tungsten or titanium/molybdenum carbides (WC/Co, TiC/Mo 2 C), alumina/zirconia materials (Al 2 O 3 / ZrO 2 ). The continuum with a just mechanical structure has been proposed in [72,42,79,78] and applied for particle/fiber reinforced polymer/ceramic matrix and masonry. Here we extend the microstructure to the thermomechanical framework, stemming from the ideas exposed in [24], where a simple and paradigmatic example of continua with (micro-)structure is exposed within the beams theory framework.…”

Dynamical properties of a composite microcracked bar based on a generalized continuum formulation

“…Within this latter class of implicit non-local models, moreover, a multiscale approach that can be classified among continua with affine microstructure [8] or continua with configurational forces [10], has been pursued, as presented and described in [28][29][30][31][32][33]. The method consists in the description of the mechanical behavior of a continuum model, i.e., the macromodel, and of a complex lattice model, representing the micromodel.…”

Mathematical analysis of a solution method for finite-strain holonomic plasticity of Cosserat materials

“…In recent years, the scientific interest towards sophisticated and heterogeneous materials featuring multiple internal length scales has grown significantly, mainly due to the possibility of playing with the internal microstructure of these materials to model and engineer structures that exhibit properties not found in conventional materials (refer, e.g., to [1,2] and references therein). Such materials include cellular solids, fibrous and particle composites, biological materials, robots, and also building-scale systems made of masonry structures [3,4,5,6,7,8]. The mechanical modeling of these materials and structures calls for the introduction of degrees of freedom that are not accounted for in classical continuum mechanics, typically rotation of points (or micro-rotations) and couple stresses [9,10,11].…”