A finite element analysis of dynamic fracture initiation by ductile failure mechanisms in a 4340 steel

In some recent dropweight impact experiments [5] with pre-notched bend specimens of 4340 steel, it was observed that considerable crack tunneling occurred in the interior of the specimen prior to gross fracture initiation on the free surfaces. The final failure of the side ligaments happened because of shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. In this paper, the experiments of [5] (corresponding to 5 m/s impact speed) are analyzed using a plane strain, dynamic finite element procedure. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed. The time at which incipient failure was observed near the notch tip in this computation, and the value of the dynamic J-integral, J d, at this time, compare reasonably well with experiments. This investigation shows that J-controlled stress and deformation fields are established near the notch tip whenever J d , increases with time. Also, it is found that the evolution of micro-mechanical quantities near the notch root can be correlated with the time variation of J d .The strain rate and the adiabatic temperature rise experienced at the notch root are examined. Finally, spatial variations of stresses and deformations are analyzed in detail.

Analysis of reflection characteristics of a normal incidence plane wave on resonant sound absorbers: A finite element approach

Resonant sound absorbers are used widely as anechoic coatings in underwater applications. In this paper a finite element scheme based on the Galerkin technique is used to analyze the reflection characteristics of the resonant absorber when insonified by a normal incidence plane wave. A waveguide theory coupled with an impedance matching condition in the fluid is used to model the problem. It is shown in this paper that the fluid medium encompassing the absorber can be modeled as an elastic medium with equivalent Lamé constants. Quarter symmetry conditions within the periodic unit cell are exploited. The finite element results are compared with analytical results, and with results published elsewhere in the literature. It is shown in the process that meshing of the fluid domain can be obviated if the transmission coefficients or reflection coefficients only are desired as is often the case. Finally, some design curves for thin resonant absorbers with water closure are presented in this paper.

Finite element estimation of elastic interlaminar stresses in laminates

Low interlaminar strength and the consequent possibility of interlaminar failures in composite laminates demand an examination of interlaminar stresses and/or strains to ensure their satisfactory performance. As a first approximation, these stresses can be obtained from thickness-wise integration of ply equilibrium equations using in-plane stresses from the classical laminated plate theory. Implementation of this approach in the finite element form requires evaluation of third and fourth order derivatives of the displacement functions in an element. Hence, a high precision element developed by Jayachandrabose and Kirkhope (1985) is used here and the required derivatives are obtained in two ways. (i) from direct differentiation of element shape functions; and (ii) by adapting a finite difference technique applied to the nodal strains and curvatures obtained from the finite element analysis. Numerical results obtained for a three-layered symmetric and a two-layered asymmetric laminate show that the second scheme is quite effective compared to the first scheme particularly for the case of asymmetric laminates.

Decoupled three-dimensional finite element computation of thermoelastic damping using Zener's approximation

We consider three dimensional finite element computations of thermoelastic damping ratios of arbitrary bodies using Zener's approach. In our small-damping formulation, unlike existing fully coupled formulations, the calculation is split into three smaller parts. Of these, the first sub-calculation involves routine undamped modal analysis using ANSYS. The second sub-calculation takes the mode shape, and solves on the same mesh a periodic heat conduction problem. Finally, the damping coefficient is a volume integral, evaluated elementwise. In the only other decoupled three dimensional computation of thermoelastic damping reported in the literature, the heat conduction problem is solved much less efficiently, using a modal expansion. We provide numerical examples using some beam-like geometries, for which Zener's and similar formulas are valid. Among these we examine tapered beams, including the limiting case of a sharp tip. The latter's higher-mode damping ratios dramatically exceed those of a comparable uniform beam.

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J(2) flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.

Finite element simulations of ductile rupture in a constrained metal foil

A numerical study of the ductile rupture in a metal foil constrained between two stiff ceramic blocks is performed. The finite element analysis is carried out under the conditions of mode I, plane strain, small-scale yielding. The rate-independent version of the Gurson model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed to represent the behavior of the metal foil. Different distributions of void nucleating sites in the metal foil are considered for triggering the initiation of discrete voids. The results clearly show that far-field triaxiality-induced cavitation is the dominant failure mode when the spacing of the void nucleating sites is large. On the contrary, void coalescence near the notch tip is found to be the operative failure mechanism when closely spaced void nucleating sites are considered.

Violin string shape functions for finite element analysis of rotating Timoshenko beams

Violin strings are relatively short and stiff and are well modeled by Timoshenko beam theory. We use the static part of the homogeneous differential equation of violin strings to obtain new shape functions for the finite element analysis of rotating Timoshenko beams. For deriving the shape functions, the rotating beam is considered as a sequence of violin strings. The violin string shape functions depend on rotation speed and element position along the beam length and account for centrifugal stiffening effects as well as rotary inertia and shear deformation on dynamic characteristics of rotating Timoshenko beams. Numerical results show that the violin string basis functions perform much better than the conventional polynomials at high rotation speeds and are thus useful for turbo machine applications. (C) 2011 Elsevier B.V. All rights reserved.

A finite element assessment of flexural strength of prestressed concrete beams with fiber reinforcement

This paper presents an assessment of the flexural behavior of 15 fully/partially prestressed high strength concrete beams containing steel fibers investigated using three-dimensional nonlinear finite elemental analysis. The experimental results consisted of eight fully and seven partially prestressed beams, which were designed to be flexure dominant in the absence of fibers. The main parameters varied in the tests were: the levels of prestressing force (i.e, in partially prestressed beams 50% of the prestress was reduced with the introduction of two high strength deformed bars instead), fiber volume fractions (0%, 0.5%, 1.0% and 1.5%), fiber location (full depth and partial depth over full length and half the depth over the shear span only). A three-dimensional nonlinear finite element analysis was conducted using ANSYS 5.5 [Theory Reference Manual. In: Kohnke P, editor. Elements Reference Manual. 8th ed. September 1998] general purpose finite element software to study the flexural behavior of both fully and partially prestressed fiber reinforced concrete beams. Influence of fibers on the concrete failure surface and stress-strain response of high strength concrete and the nonlinear stress-strain curves of prestressing wire and deformed bar were considered in the present analysis. In the finite element model. tension stiffening and bond slip between concrete and reinforcement (fibers., prestressing wire, and conventional reinforcing steel bar) have also been considered explicitly. The fraction of the entire volume of the fiber present along the longitudinal axis of the prestressed beams alone has been modeled explicitly as it is expected that these fibers would contribute to the mobilization of forces required to sustain the applied loads across the crack interfaces through their bridging action. A comparison of results from both tests and analysis on all 15 specimens confirm that, inclusion of fibers over a partial depth in the tensile side of the prestressed flexural structural members was economical and led to considerable cost saving without sacrificing on the desired performance. However. beams having fibers over half the depth in only the shear span, did not show any increase in the ultimate load or deformational characteristics when compared to plain concrete beams. (C) 2002 Published by Elsevier Science Ltd.

Nonlinear Finite-Element Modeling of Batter Piles under Lateral Load

In this paper, a finite-element model is developed in which the nonlinear soil behavior is represented by a hyperbolic relation for static load condition and modified hyperbolic relation, which includes both degradation and gap for a cyclic load condition. Although batter piles are subjected to lateral load, the soil resistance is also governed by axial load, which is incorporated by considering the P-Δ moment and geometric stiffness matrix. By adopting the developed numerical model, static and cyclic load analyses are performed adopting an incremental-iterative procedure where the pile is idealized as beam elements and the soil as elastoplastic spring elements. The proposed numerical model is validated with published laboratory and field pile test results under both static and cyclic load conditions. This paper highlights the importance of the degradation factor and its influence on the soil resistance-displacement (p-y) curve, number of cycles of loading, and cyclic load response.

A new beam finite element for the analysis of functionally graded materials

A new beam element is developed to study the thermoelastic behavior of functionally graded beam structures. The element is based on the first-order shear deformation theory and it accounts for varying elastic and thermal properties along its thickness. The exact solution of static part of the governing differential equations is used to construct interpolating polynomials for the element formulation. Consequently, the stiffness matrix has super-convergent property and the element is free of shear locking. Both exponential and power-law variations of material property distribution are used to examine different stress variations. Static, free vibration and wave propagation problems are considered to highlight the behavioral difference of functionally graded material beam with pure metal or pure ceramic beams. (C) 2003 Elsevier Science Ltd. All rights reserved.

Reconstructing Solid Model from 2D Scanned Images of Biological Organs for Finite Element Simulation

This work presents a methodology to reconstruct 3D biological organs from image sequences or other scan data using readily available free softwares with the final goal of using the organs (3D solids) for finite element analysis. The methodology deals with issues such as segmentation, conversion to polygonal surface meshes, and finally conversion of these meshes to 3D solids. The user is able to control the detail or the level of complexity of the solid constructed. The methodology is illustrated using 3D reconstruction of a porcine liver as an example. Finally, the reconstructed liver is imported into the commercial software ANSYS, and together with a cyst inside the liver, a nonlinear analysis performed. The results confirm that the methodology can be used for obtaining 3D geometry of biological organs. The results also demonstrate that the geometry obtained by following this methodology can be used for the nonlinear finite element analysis of organs. The methodology (or the procedure) would be of use in surgery planning and surgery simulation since both of these extensively use finite elements for numerical simulations and it is better if these simulations are carried out on patient specific organ geometries. Instead of following the present methodology, it would cost a lot to buy a commercial software which can reconstruct 3D biological organs from scanned image sequences.

A nonlinear spectral finite element model for analysis of wave propagation in solid with internal friction and dissipation

A geometrically non-linear Spectral Finite Flement Model (SFEM) including hysteresis, internal friction and viscous dissipation in the material is developed and is used to study non-linear dissipative wave propagation in elementary rod under high amplitude pulse loading. The solution to non-linear dispersive dissipative equation constitutes one of the most difficult problems in contemporary mathematical physics. Although intensive research towards analytical developments are on, a general purpose cumputational discretization technique for complex applications, such as finite element, but with all the features of travelling wave (TW) solutions is not available. The present effort is aimed towards development of such computational framework. Fast Fourier Transform (FFT) is used for transformation between temporal and frequency domain. SFEM for the associated linear system is used as initial state for vector iteration. General purpose procedure involving matrix computation and frequency domain convolution operators are used and implemented in a finite element code. Convergnence of the spectral residual force vector ensures the solution accuracy. Important conclusions are drawn from the numerical simulations. Future course of developments are highlighted.

Finite element simulation of BAW propagation in inhomogeneous plate due to piezoelectric actuation

A set of finite elements (FEs) is formulated to analyze wave propagation through inhomogeneous material when subjected to mechanical, thermal loading or piezo-electric actuation. Elastic, thermal and electrical properties of the materials axe allowed to vary in length and thickness direction. The elements can act both as sensors and actuators. These elements are used to model wave propagation in functionally graded materials (FGM) and the effect of inhomogeneity in the wave is demonstrated. Further, a surface acoustic wave (SAW) device is modeled and wave propagation due to piezo-electric actuation from interdigital transducers (IDTs) is studied.