Visualizing Gradients of Stress Tensor Fields

2017 ◽  
pp. 65-81 ◽  
Author(s):  
Valentin Zobel ◽  
Markus Stommel ◽  
Gerik Scheuermann
Keyword(s):  
Stress Tensor ◽  
Tensor Fields

Equilibrated divergence measure stress tensor fields for heavy masonry bodies

2009 ◽  
Vol 28 (2) ◽  
pp. 223-232 ◽  
Author(s):  
Massimiliano Lucchesi ◽  
Miroslav Šilhavý ◽  
Nicola Zani
Keyword(s):  
Stress Tensor ◽  
Divergence Measure ◽  
Tensor Fields

Automatic Calibration of a Geomechanical Model from Sparse Data for Estimating Stress in Deep Geological Formations

2021 ◽  
Author(s):  
O. Andersen ◽  
M. Kelley ◽  
V. Smith ◽  
S. Raziperchikolaee
Keyword(s):  
Stress Field ◽  
Stress Tensor ◽  
Co2 Storage ◽  
Measurement Data ◽  
Automatic Calibration ◽  
Storage Site ◽  
Tensor Fields ◽  
Geomechanical Model ◽  
Fully Automatic

Summary In this study, we demonstrate geomechanical modeling with fully automatic parameter calibration to estimate the full geomechanical stress fields of a prospective US CO2 storage site, based on sparse measurement data. The goal is to compute full stress tensor field estimates (principal stresses and orientations) that are maximally compatible with observations within the constraints of the model assumptions, thereby extending point-wise, incomplete partial stress measurement to a simulated full formation stress field, as well as a rough assessment of the associated error. We use the Perch site, located in Otsego Country, Michigan, as our case study. Input data consists of partial stress tensor information inferred from in-situ borehole tests, geophysical well logs and processing of seismic data. A static earth model of the site was developed, and geomechanical simulation functionality of the open-source MATLAB Reservoir Simulation Toolbox (MRST) used to model the stress field. Adjoint-based nonlinear optimization was used to adjust boundary conditions and material properties to calibrate simulated results to observations. Results were interpreted through a Bayesian framework. The focus of this article is to demonstrate how the fully automatic calibration procedure works and discuss the results obtained but does not attempt a detailed analysis of the stress field in the context of the proposed CO2 storage initiatives. Our work is part of a larger effort to non-invasively determine in-situ stresses in deep formations considered for CO2 storage. Guided by previously published research on geomechanical model calibration, our work presents a novel calibration approach supporting a potentially large number of linear or nonlinear calibration parameters, in order to produce results optimally agreeing with available measurements and thus extend partial point-wise estimates to full tensor fields compatible with the physics of the site.

Full Potential Electronic Structure Calculations and the Concept of Stress Fields and Energy Densities for Total Energy Calculations

1991 ◽  
Vol 253 ◽  
Author(s):  
P. Ziesche
Keyword(s):  
Energy Density ◽  
Stress Field ◽  
Stress Tensor ◽  
Particle Density ◽  
Local Stress ◽  
Full Potential ◽  
Many Body ◽  
Tensor Fields ◽  
Defect Energies ◽  
Total Energies

ABSTRACTWith the availability of reliable full atomic cell orbitals the possibility arises to calculate pressure or stress, restoring or relaxation driving Hellmann -Feynman forces, and total energies (especially of defects) alternatively and directly via stress tensor fields and energy densities, two local quantities. Although quantum mechanical stress field and energy density can not be defined uniquely, there is a recent interest in these quantities, because integrals with physical meaning are gauge invariant.The mentioned fields can be defined (i) for the full many-body description with the exact one-particle density matrix and pair distribution function as well as (ii) for the Kohn-Sham one-particle description with LDA or beyond (gradient expansion approximation). If the local stress field for a special system once is constructed, then the global stress tensor and /or forces on nuclei can be calculated via the stress theorem and the force theorem by means of unit cell surface integrals. The energy density can be derived from the terms of the stress field by taking the trace and can be used to calculate defect energies without bothering about the thermodynamic limit.

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