The nanomechanics of shale [electronic resource] : an experimental and computational approach to constitutive model development
Keywords: Civil and Environmental Engineering.

Shale formations contain large oil and gas resources that have recently been exploited by hydraulic fracturing, and serve also as a typical caprock for CO2 storage reservoirs. Developing our understanding of, and predictive modeling capability for, the mechanical behavior of shale is therefore an important aspect of addressing pressing energy related social and sustainability issues, such as energy resilience, environmental safety, and climate change mitigation. The deformation and fracture properties of shale depend on the mechanical properties of its basic constituents, including nano- to micrometer sized organic, clay, and hard-mineral particles, as well as nanoscale porosity. A great deal of understanding of the overall mechanical properties of shales can be gained by studying the deformation and fracture properties of these constituents and how they behave as a composite material at nano- to micrometer length scales, informing the development of constitutive theory consistent with the nanomechanical origins of the shale's exhibited macromechanical behavior. This work describes a combined experimental and computational approach to the development of constitutive theory for shale. The experimental part of this work consisted of nanoindentation testing spanning nano- to micro-length scales coupled with FIB-SEM imaging and EDX spectroscopy. The FIB-SEM imaging and EDX spectroscopy were utilized to characterize the shale at the scale of the nanoindentation testing in both pre- and post-indented regions. The experiments reveal the mechanical properties of the relatively homogeneous constituent materials as well as those of the heterogeneous composite material, and provide insight into the shale's nanomechanical nature. Qualitative and quantitative interpretations of these measurements have motivated the development of material-appropriate constitutive modeling for organic and clay rich shales. A novel finite deformation elastoplastic constitutive framework for geomaterials is presented that makes use of Eshelby's stress tensor to reckon thermodynamic principles with the large inelastic volume strains that these materials are observed to exhibit. This constitutive framework is further extended to couple critical-state plasticity and continuum ductile-damage (CS-DD) theory in order to account for the extensive microfracture and changes in porosity observed through FIB-SEM imaging of post-indented regions. An important outcome of this work is to show that traditional finite deformation elastoplasticity models typically used for geomaterials are not consistent with the second law of thermodynamics, and may actually violate the second law under certain loading conditions. A novel stress measure for the spatial representation of hyperelastic constitutive laws is introduced as an alternative to traditional Kirchhoff stress formulations that are shown to satisfy the second law but give rise to spurious stresses under inelastic volumetric deformation. The thermodynamically consistent CS-DD framework is developed in the form of novel Modified Cam-Clay/Damage and Drucker-Prager/Damage material models incorporating continuum damage mechanics, and is implemented in 2D and 3D finite element simulations of laboratory and in-situ measurements.