A multifield continuum model for the description of the response of microporous/microcracked composite materials

Abstract

The description of the mechanical behavior of composite materials is an open challenge in engineering. The focus of this work is on micro-cracked/microporous composites, made of stiff grains embedded in a cracked or porous deformable matrix. Grains interact between each other and with cracks or pores localized at the interfaces, which reduce the contact area between grains. Pores' interaction is also taken into account. We apply a two-scale modeling strategy based on a discrete to scale-dependent (non-classical) continuum equivalence procedure. The constitutive relationships of the resulting microcontinuum, identified by requiring equivalence, in terms of virtual work, between discrete and continuum non-local descriptions of the reference material, take directly into account the material internal structure, and in particular material internal lengths. Field and boundary conditions of the equivalent continuum are also derived based on work equivalence between internal and external actions. The response of the obtained one-dimensional equivalent model and of a finite element model of a bar with pores are compared, showing a very good match between each other in a wide range of pore densities.

Dynamic Characterization of Hexagonal Microstructured Materials with Voids from Discrete and Continuum Models

“…The first six frequencies for all study cases here shows a decrease trend as the void size increases. The current study can be helpful for further studies concerning wave propagation and dispersion properties in the porous media [ 8 , 9 , 16 ].…”

“…The application of homogenization approaches can be widely found in the literature to account for the effect of voids and/or cracks on the mechanical behavior of different kinds of materials, such as advanced materials [ 4 ] and ceramics [ 5 , 6 ]. Leonetti et al [ 7 ] presented an accurate prediction for a multiscale damage analysis of periodic composites [ 8 , 9 ]. The key to a successful application of homogenization techniques for microstructured materials is the selection of a suitable macroscopic continuum that is able to consider the effects of the internal lengths [ 10 , 11 ].…”

Bending characteristics of carbon nanotubes: Micropolar elasticity models and molecular dynamics simulations

“…In micropolar theory, as a subset of microcontinuum field theories, this non-standard DOF is set to be the microrotation and consequently additional strain and stress measures as well as material parameters containing information about internal structure are introduced into the field and constitutive equations [49,50,57,58]. As a result, micropolar theory has been successfully used to describe a wide range of materials with internal structures, especially those where relative rotations are predominant, such as brick masonry-like materials [59][60][61], heterogeneous structures with internal cracks/voids/inclusions [62][63][64][65], and particulate composites [66][67][68][69][70]. A subcase of micropolar theory is the couple stress theory originally developed by Toupin [71], Mindlin and Tiersten [72] and Koiter [73], in which microrotations are constrained to follow macrorotations (local rigid rotations) yielding symmetric strain measures [74,75], however, it should be noted that the original form of couple stress theory suffers from indeterminacy of the spherical part of couple stress tensor and the appearance of the normal component of couple traction vector on boundary surfaces [47,76,77].…”

Design of Mechanical Metamaterials Based on Biphasic Periodic Microstructures

“…This approach enables efficient determination of the associated dispersion curves by enforcing periodicity conditions on the boundary of the repetitive cell. It should be mentioned that other approaches to the modelling of such periodic materials, making use of multifield continua, were presented in the literature [7]. In Section 4, parametric analyses in the space of geometric parameters are carried out, showing how the bandgap amplitude varies in the biphasic model.…”