Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Peridynamics (4)
- Dynamic fracture (3)
- Brittle fracture (2)
- Crack branching (2)
- Adaptive refinement (1)
-
- BEF (1)
- Beam on Elastic Foundation (1)
- Buildings (1)
- Continuum mechanics (1)
- Convergence (1)
- Earthquakes (1)
- Fiber networks (1)
- Free Vibration (1)
- HPM (1)
- Homotopy Perturbation Method (1)
- Linear (1)
- Meshfree methods (1)
- Multiscale modeling (1)
- Nanofibers (1)
- Non-local methods (1)
- Nonlinear systems (1)
- Nonlocal methods (1)
- Nonlocal models (1)
- Nonstationary excitations (1)
- Sacrificial bonds (1)
- Stochastic control (1)
- Vehicle dynamics (1)
- File Type
Articles 1 - 6 of 6
Full-Text Articles in Applied Mechanics
The Meaning, Selection, And Use Of The Peridynamic Horizon And Its Relation To Crack Branching In Brittle Materials, Florin Bobaru, Wenke Hu
The Meaning, Selection, And Use Of The Peridynamic Horizon And Its Relation To Crack Branching In Brittle Materials, Florin Bobaru, Wenke Hu
Florin Bobaru Ph.D.
This note discusses the peridynamic horizon (the nonlocal region around a material point), its role, and practical use in modeling. The objective is to eliminate some misunderstandings and misconceptions regarding the peridynamic horizon. An example of crack branching in a nominally brittle material (homalite) is addressed and we show that crack branching takes place without wave interaction. We explain under what conditions the crack propagation speed depends on the horizon size and the role of incident stress waves on this speed.
Convergence, Adaptive Refinement, And Scaling In 1d Peridynamics, Florin Bobaru Ph.D., Mijia Yabg Ph.D., Leonardo F. Alves M.S., Stewart A. Silling Ph.D., Ebrahim Askari Ph.D., Jifeng Xu Ph.D.
Convergence, Adaptive Refinement, And Scaling In 1d Peridynamics, Florin Bobaru Ph.D., Mijia Yabg Ph.D., Leonardo F. Alves M.S., Stewart A. Silling Ph.D., Ebrahim Askari Ph.D., Jifeng Xu Ph.D.
Florin Bobaru Ph.D.
We introduce here adaptive refinement algorithms for the non-local method peridynamics, which was proposed (in J. Mech. Phys. Solids 2000; 48:175–209) as a reformulation of classical elasticity for discontinuities and long-range forces. We use scaling of the micromodulus and horizon and discuss the particular features of adaptivity in peridynamics for which multiscale modeling and grid refinement are closely connected. We discuss three types of numerical convergence for peridynamics and obtain uniform convergence to the classical solutions of static and dynamic elasticity problems in 1D in the limit of the horizon going to zero. Continuous micromoduli lead to optimal rates of …
Influence Of Van Der Waals Forces On Increasing The Strength And Toughness In Dynamic Fracture Of Nanofibre Networks: A Peridynamic Approach, Florin Bobaru Ph.D.
Influence Of Van Der Waals Forces On Increasing The Strength And Toughness In Dynamic Fracture Of Nanofibre Networks: A Peridynamic Approach, Florin Bobaru Ph.D.
Florin Bobaru Ph.D.
The peridynamic method is used here to analyse the effect of van der Waals forces on the mechanical behaviour and strength and toughness properties of three-dimensional nanofibre networks under imposed stretch deformation. The peridynamic formulation allows for a natural inclusion of long-range forces (such as van der Waals forces) by considering all interactions as ‘long-range’. We use van der Waals interactions only between different fibres and do not need to model individual atoms. Fracture is introduced at the microstructural (peridynamic bond) level for the microelastic type bonds, while van der Waals bonds can reform at any time. We conduct statistical …
Studies Of Dynamic Crack Propagation And Crack Branching With Peridynamics, Youn Doh Ha Ph.D., Florin Bobaru Ph.D.
Studies Of Dynamic Crack Propagation And Crack Branching With Peridynamics, Youn Doh Ha Ph.D., Florin Bobaru Ph.D.
Florin Bobaru Ph.D.
In this paper we discuss the peridynamic analysis of dynamic crack branching in brittle materials and show results of convergence studies under uniform grid refinement (m-convergence) and under decreasing the peridynamic horizon (δ-convergence). Comparisons with experimentally obtained values are made for the crack-tip propagation speed with three different peridynamic horizons.We also analyze the influence of the particular shape of themicro-modulus function and of different materials (Duran 50 glass and soda-lime glass) on the crack propagation behavior. We show that the peridynamic solution for this problem captures all the main features, observed experimentally, of dynamic crack propagation and branching, as well …
Stochastic Optimal Control In Nonlinear Systems, Celestin Nkundineza
Stochastic Optimal Control In Nonlinear Systems, Celestin Nkundineza
Celestin Nkundineza
Stochastic control is an important area of research in engineering systems that undergo disturbances. Controlling individual states in such systems is critical. The present investigation is concerned with the application of the stochastic optimal control strategy developed by To (2010) and its implementation as well as providing computed results of linear and nonlinear systems under stationary and nonstationary random excitations. In the strategy the feedback matrix is designed based on the achievement of the objectives for individual states in the system through the application of the Lyapunov equation for the system. Each diagonal element in the gain or associated gain …
The Homotopy Perturbation Method For Free Vibration Analysis Of Beam On Elastic Foundation, Baki Ozturk, Safa Bozkurt Coskun
The Homotopy Perturbation Method For Free Vibration Analysis Of Beam On Elastic Foundation, Baki Ozturk, Safa Bozkurt Coskun
Safa Bozkurt Coskun
In this study, the homotopy perturbation method (HPM) is applied to free vibration analysis of beam on elastic foundation. This numerical method is applied on three different axially loaded cases, namely: 1) one end fixed, the other end simply supported; 2) both ends fixed and 3) both ends simply supported cases. Analytical solutions and frequency factors are evaluated for different ratios of axial load N acting on the beam to Euler buckling load, Nr. The application of HPM for the particular problem in this study gives results which are in excellent agreement with both analytical solutions and the variational iteration …