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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
OSTIScopus

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

Journal of Petroleum Science and Engineering

Newell, Pania; Yoon, Hongkyu; 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

Simulating fragmentation and fluid-induced fracture in disordered media using random finite-element meshes

International Journal for Multiscale Computational Engineering

Bishop, Joseph E.; Martinez, Mario J.; Newell, Pania

Fracture and fragmentation are extremely nonlinear multiscale processes in which microscale damage mechanisms emerge at the macroscale as new fracture surfaces. Numerous numerical methods have been developed for simulating fracture initiation, propagation, and coalescence. Here, we present a computational approach for modeling pervasive fracture in quasi-brittle materials based on random close-packed Voronoi tessellations. Each Voronoi cell is formulated as a polyhedral finite element containing an arbitrary number of vertices and faces. Fracture surfaces are allowed to nucleate only at the intercell faces. Cohesive softening tractions are applied to new fracture surfaces in order to model the energy dissipated during fracture growth. The randomly seeded Voronoi cells provide a regularized discrete random network for representing fracture surfaces. The potential crack paths within the random network are viewed as instances of realizable crack paths within the continuum material. Mesh convergence of fracture simulations is viewed in a weak, or distributional, sense. The explicit facet representation of fractures within this approach is advantageous for modeling contact on new fracture surfaces and fluid flow within the evolving fracture network. Applications of interest include fracture and fragmentation in quasi-brittle materials and geomechanical applications such as hydraulic fracturing, engineered geothermal systems, compressed-air energy storage, and carbon sequestration.

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TYPE Journal Article YEAR 2016
DOIOSTIScopus

Quantifying the Impact of Material-Model Error on Macroscale Quantities-of-Interest Using Multiscale a Posteriori Error-Estimation Techniques

MRS Advances

Brown, Judith A.; Bishop, Joseph E.

An a posteriori error-estimation framework is introduced to quantify and reduce modeling errors resulting from approximating complex mesoscale material behavior with a simpler macroscale model. Such errors may be prevalent when modeling welds and additively manufactured structures, where spatial variations and material textures may be present in the microstructure. We consider a case where a <100> fiber texture develops in the longitudinal scanning direction of a weld. Transversely isotropic elastic properties are obtained through homogenization of a microstructural model with this texture and are considered the reference weld properties within the error-estimation framework. Conversely, isotropic elastic properties are considered approximate weld properties since they contain no representation of texture. Errors introduced by using isotropic material properties to represent a weld are assessed through a quantified error bound in the elastic regime. An adaptive error reduction scheme is used to determine the optimal spatial variation of the isotropic weld properties to reduce the error bound.

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TYPE Journal Article YEAR 2016
DOIOSTIScopus

Brittle fracture phase-field modeling of a short-rod specimen

Escobar, Ivana; Tupek, Michael R.; Bishop, Joseph E.

Predictive simulation capabilities for modeling fracture evolution provide further insight into quantities of interest in comparison to experimental testing. Based on the variational approach to fracture, the advent of phase-field modeling achieves the goal to robustly model fracture for brittle materials and captures complex crack topologies in three dimensions.

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TYPE SAND Report YEAR 2015
DOIOSTI
Results 101–150 of 245
Results 101–150 of 245