Computational analysis of nonlinear creep of polyphase aggregates: Influence of phase morphology

Abstract

The constitutive laws of polyphase aggregates dominantly depend on the operative deformation mechanisms, phase morphology and modes, and environmental conditions. Each of these factors has the potential to dramatically affect bulk mechanical properties as well as the local stress and strain rate distributions. To focus on the effects of phase morphology, we have developed a rigorous multiscale approach based on asymptotic expansion homogenization. The proposed methodology has two fundamental goals: (1) accurately predict bulk behavior in aggregates by explicitly taking into account phase morphology and (2) calculate detailed distributions of strain rates, stresses, and viscosities in heterogeneous materials. The methodology is able to consider general nonlinear phase constitutive laws that relate strain rates to stresses, temperature, and other factors such as water fugacity and grain size. We demonstrate the approach by analyzing power law creep of computer-generated and natural polyphase systems and benchmarking the results against analytical solutions. As an outcome of this analysis, we find that the approximation of an aggregate as a power law material is reasonable for isotropic, homogeneous phase distributions but breaks down significantly with high degrees of phase organization. We also present distributions in strain rate, stress, and viscosity for different applied loading conditions. Results exhibit areas of high internal stresses and substantial localization. We describe and provide a freely available software package supporting these calculations.

Strain localization in polycrystalline material with second phase particles: Numerical modeling with application to ice mixtures

“…Thus, such aggregates can be represented by composite/modified power law flow laws. Similar results were obtained in previous numerical studies [e.g., Takeda and Griera , ; Cook et al ., ]. Our result is also in agreement with the experimental study of Cyprych et al .…”

“…A good example of such behavior is a model of Cook et al . [], who analyzed a simplified two‐phase steady‐state microstructure of plagioclase matrix with a weak, anastomosing biotite foliation at high T and strain rates of 10 −4 to 10 −6 s −1 . They found strain rates in isolated biotite grains comparable to strain rates in the matrix, even though mica is softer than plagioclase at strain rates of 10 −6 s −1 .…”

Ferropericlase Control of Lower Mantle Rheology: Impact of Phase Morphology

“…For this reason, past numerical studies of such systems have attempted to develop a parameterization of the impact of weak phase topology on the effective rheology for specific inclusion shapes such as layers, squares, or ellipses (e.g., Dabrowski et al, ; Fletcher, ; Handy, , ; Takeda, ; Takeda & Griera, ; Treagus, ; Tullis et al, ). More recently, both Cook et al () and Gerbi et al () also considered the effect of more complex morphologies on the effective rheology of power law materials.…”

Sheath fold development in monoclinic shear zones

“…High R yz values can be difficult to measure in nature (Skjernaa, ), and, for the same reason, very small or large k ‐values might be systematically over‐ or underestimated. The observed deviations between the field and numerical data can also result from the simplified geometry and rheological behaviour used in our model, whereas rocks in shear zones are often heterogeneous, anisotropic and nonlinear (Cook, Vel, Gerbi & Johnson, ; Dabrowski & Schmid, ; Schmalholz & Schmid, ). In our analysis, we have focused on sheath folds developing around slip surfaces, but we acknowledge that various other mechanisms may lead to sheath fold formation.…”

“…The observed deviations between the field and numerical data can also result from the simplified geometry and rheological 10 -1 10 0 10 1 10 2 10 I G U R E 4 (a) Simulation results and field measurements (after Alsop & Holdsworth, 2006) showing the relation between the aspect ratio of the outermost closed contour (R yz ) and the k-value. (b) Numerical data showing R yz as a function of the ratio between the principal strain in the Y-direction and the smaller of the principal strains measured in the X-Z plane (see text for details) behaviour used in our model, whereas rocks in shear zones are often heterogeneous, anisotropic and nonlinear (Cook, Vel, Gerbi & Johnson, 2014;Dabrowski & Schmid, 2011;Schmalholz & Schmid, 2012).…”