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Advanced Smoothed Finite Element Modeling for Fracture Mechanics Analyses

Bhowmick, Sauradeep
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1623240613376967

Abstract Details

2021, PhD, University of Cincinnati, Engineering and Applied Science: Engineering Mechanics.
Computational fracture mechanics has been an active area of research in the engineering community for decades. The classical objective of fracture mechanics is to determine the damage caused by defects originating from regions of stress intensification. Their response under different loading conditions in different media is of grave importance in structural analysis. In the traditional framework of widely used numerical techniques like the finite element method (FEM), meshfree methods, boundary element method (BEM) several tools have been proposed to solve such problems. However, due to inherent issues associated with the numerical techniques and the computational complexities relating to the study of crack propagation, we are yet to arrive at a standard. Addressing that, this dissertation proposes a robust, e?icient numerical technique to solve fracture mechanics problems in the framework of the smoothed finite element method (S-FEM). The main contributions are: 1.The singular edge-based smoothed finite element method (sES-FEM) using a special layer of five-node singular elements (sT5) connected to the singular point, is proposed to model stress singularity in solids. The aim is develop an analytical means for integration to obtain the smoothed strains. The sT5 element has an additional node at each of the two edges connected to the crack tip, and the displacements are enriched with necessary terms to simulate the singularity. Our analytical integration techniques reduce the dependency on the order of numerical integration during the computation of the smoothed strain matrix. 2.A novel smoothed finite-element and phase-field method (S-FEM+PFM) for simulating fracture paths in brittle materials is proposed. Our S-FEM+PFM is formulated and implemented in the commercial software ABAQUS, using user defined subroutines. The formulation, within the framework of the (CS-FEM), is further extended to formulate a smoothed phase field model (S-PFM). Because gradient smoothing is used for derivatives of all the shape functions involved, no iso-parametric mapping and hence no Jacobian matrix are involved. This allows the use of heavily distorted elements in the models. In addition, we newly formulated a cell based smoothed triangular wedge (W6) element (CS-FEM-W6),which facilitates further in meshing complicated geometries. 3.The smoothed phase-field technique to model fracture in elastic brittle solids is implemented in the framework of the edge and face based smoothed finite element method (ES/FS-FEM) for 2D and 3D problems. This enables the use of 3-noded triangular (T3) elements for two-dimensional (2D) problems, and 4-noded tetrahedral elements for three-dimensional (3D) problems. Because bothT3 and T4 element can be automatically generated for complicated domains, the present approaches are e?icient techniques to model complex crack topologies. 4.The SPFM is extended to study crack propagation under dynamic brittle fracture. With the impact of the inertial forces considered, dynamic fracture involves several complications due to instabilities associated with higher kinetic energy. The method is very robust and can reproduce experimentally observed crack branching phenomenon. It is also extended to solve for fracture in elasto-plastic solids.
Gui-Rong Liu, Ph.D. (Committee Chair)
Yao Fu (Committee Member)
Woo Kyun Kim, Ph.D. (Committee Member)
229 p.
Mechanical Engineering
Smoothed Finite Element; Gradient Smoothing; Meshfree; Phase Field Fracture; Fracture Mechanics; ABAQUS

Recommended Citations

Citations

  • Bhowmick, S. (2021). Advanced Smoothed Finite Element Modeling for Fracture Mechanics Analyses [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1623240613376967

    APA Style (7th edition)

  • Bhowmick, Sauradeep. Advanced Smoothed Finite Element Modeling for Fracture Mechanics Analyses. 2021. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1623240613376967.

    MLA Style (8th edition)

  • Bhowmick, Sauradeep. "Advanced Smoothed Finite Element Modeling for Fracture Mechanics Analyses." Doctoral dissertation, University of Cincinnati, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1623240613376967

    Chicago Manual of Style (17th edition)

ucin1623240613376967
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