Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


ucin1313753940.pdf (6.65 MB)

ETD Abstract Container

Abstract Header

Bridging Scale Simulation of Lattice Fracture and Dynamics using Enriched Space-Time Finite Element Method

Chirputkar, Shardool U.
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1313753940

Abstract Details

2011, PhD, University of Cincinnati, Engineering and Applied Science: Mechanical Engineering.
Multiscale methods based on coupled atomistic-continuum representations have received significant attention in recent years due to their unique approach in balancing accuracy with efficiency for a wide spectrum of problems in solid mechanics. Examples include dislocation-originated plasticity, fracture, shear band localization and many others. Motivated by these advances, a concurrent simulation approach employing the space-time finite element method and molecular dynamics (MD) is developed in this dissertation with a focus on lattice dynamics and fracture. A space-time version of MD is initially proposed based on the time discontinuous Galerkin space-time finite element method. In the multiscale simulations, MD is coupled with coarse scale space-time finite element simulation based on a coarse grained material model. For the numerical approximation, standard space-time shape functions are augmented with enrichment function(s) based on the problem physics by exploiting the partition of unity concept. With the appropriate enrichment function(s), fine scale physics such as phonons and fractures can be represented in the coarse scale simulation in spatial and temporal scales. The two simulations can employ different time steps; the unconditional stability of the method makes selection of a large time step possible. Coupling between the simulations is achieved with the introduction of a projection operator and bridging scale treatment. The proposed approach is first employed to solve lattice dynamics with a focus on wave propagation. It is shown that a reflectionless interface at the atomistic-continuum simulation interface is achieved. The enriched continuum simulation retains all the atomistic level details and is able to transmit this information to another distinct atomistic region within the domain resulting in an energy conserving simulation method. The method is applied to systems with both linear and nonlinear potentials. An important feature of this approach is its non-dissipative nature resulting in accurate prediction of displacements and energy. For the dynamic lattice fracture problem, hexagonal lattices with armchair and zigzag configurations are considered. Atomistic region is prescribed in the neighborhood of a crack tip. Debonding at the atomistic scale is used for crack initiation and propagation. With the evolving crack front, the atomistic region is dynamically adjusted to minimize the computational expense. Enrichment function employing discontinuous representations are established for elements that are completely breached by the crack. If the crack configuration in an element leads to material instability/ill-conditioning of the space-time stiffness matrix, remeshing schemes are proposed. The robustness of the method is extensively demonstrated for mode I, II and mixed mode I/II cracks. It has been demonstrated that the proposed scheme can handle a wide variety of crack dynamics such as propagation of single/multiple cracks, crack branching/ merging. Based on the extensive work performed, it is concluded that the proposed framework is both accurate and efficient. In particular, the ability to establish multiscale approximations in both the spatial and temporal domain is an important feature that can be fully explored for a host of challenging multiscale engineering problems.
Dong Qian, PhD (Committee Chair)
Thomas Eason, PhD (Committee Member)
Donald French, PhD (Committee Member)
Yijun Liu, PhD (Committee Member)
David Thompson, PhD (Committee Member)
165 p.
Mechanics
Multiscale simulations; Lattice Fracture; Space-time finite element method; XFEM; Enriched finite element method

Recommended Citations

Citations

  • Chirputkar, S. U. (2011). Bridging Scale Simulation of Lattice Fracture and Dynamics using Enriched Space-Time Finite Element Method [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1313753940

    APA Style (7th edition)

  • Chirputkar, Shardool. Bridging Scale Simulation of Lattice Fracture and Dynamics using Enriched Space-Time Finite Element Method. 2011. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1313753940.

    MLA Style (8th edition)

  • Chirputkar, Shardool. "Bridging Scale Simulation of Lattice Fracture and Dynamics using Enriched Space-Time Finite Element Method." Doctoral dissertation, University of Cincinnati, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1313753940

    Chicago Manual of Style (17th edition)

ucin1313753940
572
© 2011, some rights reserved.Creative Commons License Bridging Scale Simulation of Lattice Fracture and Dynamics using Enriched Space-Time Finite Element Method by Shardool U. Chirputkar is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Cincinnati and OhioLINK.