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Applications of polyhedral finite elements in solid mechanics

Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics

Bishop, Joseph E.

The finite element method has revolutionized structural analysis since its inception over 50 years ago, by enabling the computer analysis of geometrically complex structures. The main requirement of the finite element method is that an appropriate partition, or mesh, of the structure be created first. The elements of the partition typically have standard shapes, such as the hexahedron, pentahedron, and tetrahedron. While this small library of standard element shapes is sufficient for many applications, there is a growing need for more general polyhedral shapes, ones that can have an arbitrary number of vertices, edges, and faces, and ones that can be non-convex. In this chapter, we discuss current and possible future applications of polyhedral finite elements in solid mechanics. These applications include rapid engineering analysis through novel meshing and discretization techniques, and fracture and fragmentation modeling. Several finite element formulations of general polyhedra have been developed. In this chapter we use a polyhedral formulation based on the use of harmonic shape functions. Harmonic shape functions are one example of several possible generalized barycentric coordinates, as discussed in Chapter 1.

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TYPE Book YEAR 2017
OSTIScopusOSTIScopus

Investigation of the influence of geomechanical and hydrogeological properties on surface uplift at In Salah

Journal of Petroleum Science and Engineering

Newell, Pania N.; Yoon, Hongkyu Y.; Martinez, Mario J.; Bishop, Joseph E.; Bryant, S.L.

Coupled reservoir and geomechanical simulations are significantly important to understand the long-term behavior of geologic carbon storage (GCS) systems. In this study, we performed coupled fluid flow and geomechanical modeling of CO2 storage using available field data to (1) validate our existing numerical model and (2) perform parameter estimation via inverse modeling to identify the impact of key geomechanical (Young's modulus and Biot's coefficient) and hydrogeological (permeability and anisotropy ratio) properties on surface uplift and the pore pressure buildup at In Salah in Algeria. Two sets of surface uplift data featuring low and high uplifts above two injection wells and the maximum change in the pore pressure due to CO2 injection were used to constrain the inverse model. Forward simulation results with representative parameter values from the literature match both low and high surface uplifts reasonably well and predicted the maximum change in the pore pressure. In particular, forward modeling results with estimated Biot's coefficients for reservoir and caprock layers, match the observed uplift well, highlighting the significance of Biot's coefficient in coupled reservoir and geomechanical models. Parameter estimation with 12 parameter sets for both low and high uplift data demonstrates that multiple sets of parameters can match the observed data equally well and the inclusion of the pore pressure data is critically important to constrain the parameter solution during inverse modeling. For a majority of cases, estimation results for both low and high uplift data show the vertical intrinsic permeability and Young's modulus of the reservoir remained close to 13 mD (1.3×10−14 m2) and 10 GPa, respectively, suggesting that these parameters may represent the actual effective properties. Additionally, higher correlations between reservoir permeability and caprock's Biot's coefficient with high surface uplift data were observed consistently under the pore pressure constraint, suggesting the inclusion of the pore pressure constraint is required to estimate the proper values of coupled flow and geomechanical properties associated with different surface uplift data. Overall, this study suggests that given limited data, including Biot's coefficient, in addition to permeability and Young's modulus can enhance parameter estimation of the geomechanical response during GCS.

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TYPE Journal Article YEAR 2017
DOIOSTIScopus

Direct Numerical Simulations in Solid Mechanics for Quantifying the Macroscale Effects of Microstructure and Material Model-Form Error

JOM

Bishop, Joseph E.; Emery, John M.; Battaile, Corbett C.; Littlewood, David J.; Baines, Andrew J.

Two fundamental approximations in macroscale solid-mechanics modeling are (1) the assumption of scale separation in homogenization theory and (2) the use of a macroscopic plasticity material model that represents, in a mean sense, the multitude of inelastic processes occurring at the microscale. With the goal of quantifying the errors induced by these approximations on engineering quantities of interest, we perform a set of direct numerical simulations (DNS) in which polycrystalline microstructures are embedded throughout a macroscale structure. The largest simulations model over 50,000 grains. The microstructure is idealized using a randomly close-packed Voronoi tessellation in which each polyhedral Voronoi cell represents a grain. An face centered cubic crystal-plasticity model is used to model the mechanical response of each grain. The overall grain structure is equiaxed, and each grain is randomly oriented with no overall texture. The detailed results from the DNS simulations are compared to results obtained from conventional macroscale simulations that use homogeneous isotropic plasticity models. The macroscale plasticity models are calibrated using a representative volume element of the idealized microstructure. Ultimately, we envision that DNS modeling will be used to gain new insights into the mechanics of material deformation and failure.

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TYPE Journal Article YEAR 2016
DOIOSTIScopus
Results 101–125 of 244
Results 101–125 of 244