Homogenization techniques for thermoviscoelastic solids containing cracks

Multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks

“…For the cases where the previous assumptions are valid, one can show that the relations connecting the global and local scales are given by the following (mean field) homogenization principles [1,3,5], for infinitesimal deformations:…”

A model for predicting the evolution of multiple cracks on multiple length scales in viscoelastic composites

“…If this is not the case, then higher order moments will necessarily have to be included at the macroscale [10]. Now note that, so long as any tractions on the crack faces are self equilibrating, Equation (2) may be used to show that [11][12][13] (12) where n → μ is the unit outer normal vector on the local boundary, ∂V μ . Note that the boundary averaged stress given in Equation (12) actually is physically more palatable than the volume averaged stress given in Equation (7), as it is commensurate with the original definition of stress, as defined by Cauchy [26] to act on a surface.…”

“…However, when cracks grow and evolve with time, it becomes a very important aspect of the homogenization process, as will now be shown by considering the homogenization process for the strain tensor. It can be shown by careful employment of the divergence theorem that (13) where (14) is the mean strain at the local scale (15) is the boundary averaged strain on the initial (external) boundary of the local volume, ∂V μ E , and (16) is the boundary averaged strain on the newly created (internal) boundary due to cracking, ∂V μ I , and is called a damage parameter [4,14]. Since kinematic Equation (15) is consistent with kinetic Equation (12), it is reasonable to construct constitutive equations at the macroscale in terms of these two variables, rather than in terms of volume averages.…”

Method for Performing Accelerated Characterization of Viscoelastic Constitutive Behavior of Asphaltic Concrete

“…In this work, we consider only loadings that produce no damage, so that the loads must necessarily be small. In the case where damage is induced during the experiment, another approach is required (Allen and Yoon 1998).…”