Papers by Tomasz Wierzbicki
In the present work a comprehensive experimental/numerical study on a 6060 T6 bumper profile subj... more In the present work a comprehensive experimental/numerical study on a 6060 T6 bumper profile subjected to combined shear-compression (shear-punch test) load is carried out. A set of key plasticity and fracture parameters to predict correctly the mechanical response of the structural component is required. Fracture initiation tests on lab scale specimens provide the sufficient data needed to calibrate the newly extended non-quadratic yield function Yld2000-3d and the isotropic Modified Mohr-Coulomb (MMC) fracture model. The calibrated plasticity and fracture constitutive model is then validated upon disk-shaped specimen. Moreover, test results are reported on full-scale extruded aluminum bumper subjected to shear-punch load. A detailed FE model of the bumper and the supporting structure was built. The numerical simulation outcomes demonstrate that the calibrated material model predicts correctly not only the global force-displacement response but also the local fracture behavior at multiple initiation points. It was shown that various part of the multi-cell cross-section of the extruded profile underwent different loading histories. Thus, in one single test a wide range of stress triaxialities develop which requires to introduce a very complete plasticity and fracture model.
International Journal of Solids and Structures, 1970
Engineering Fracture Mechanics, 2008
Ductile fracture is often considered as the consequences of the accumulation of plastic damage. T... more Ductile fracture is often considered as the consequences of the accumulation of plastic damage. This paper is concerned with the application of a recently developed damage plasticity theory incorporates the pressure sensitivity and the Lode angle dependence into a nonlinear damage rule and the material deterioration. The ductile damaging process is calculated through the so-called “cylindrical decomposition” method. The constitutive
Journal of Constructional Steel Research, 1995
This paper examines the crushing characteristics of web griders subjected to local in-plane crush... more This paper examines the crushing characteristics of web griders subjected to local in-plane crushing loads. First, a simplified model of the post-buckling deformation of the web girder is developed. This model is then used to derive an approximate solution for the plastic behavior of the deforming web girder under localized in-plane loading. Finally, the results of small-scale crushing tests of
Computers & Structures, 1984
... 11. N. Aya and K. Takahashi, Energy absorption characteristics of vehicle body structure. Tra... more ... 11. N. Aya and K. Takahashi, Energy absorption characteristics of vehicle body structure. Trans. Soc. ... 46, 377-385 (1979). 17. W. Johnson, PD Soden and STS Al-Hassani, Inextensional collapse of thin-walled tubes under axial compression. J. Strain Anal. 12, 317-330 (1977). ...
Journal of Strain Analysis for Engineering Design, 1982
Page 1. CRUSHING ANALYSIS OF ROTATIONALLY SYMMETRIC PLASTIC SHELLS J. G. DE OLIVEIRA T. WIERZBICK... more Page 1. CRUSHING ANALYSIS OF ROTATIONALLY SYMMETRIC PLASTIC SHELLS J. G. DE OLIVEIRA T. WIERZBICKIt Massachusetts Institute of Technology Massachusetts Insritute of Technology The crushing analysis of ...
International Journal of Mechanical Sciences, 1993
A simple kinematic model is developed which describes the main features of the process of the cut... more A simple kinematic model is developed which describes the main features of the process of the cutting of a plate by a rigid wedge. It is assumed in this model that the plate material curls up into two inclined cylinders as the wedge advances into the plate. This results in membrane stretching up to fracture of the material near the wedge tip, while the "flaps" in the wake of the cut undergo cylindrical bending. Self-consistent, single-term formulas for the indentation force and the energy absorption are arrived at by relating the "far-field" and "near-tip" deformation events through a single geometric parameter, the instantaneous rolling radius. Further analysis of this solution reveals a weak dependence on the wedge angle and a strong dependence on friction coefficient. The final equation for the approximate cutting force over a range of wedge semiangles l0 ° < 0 < 30 ° and friction coefficients 0.1 </~ _< 0.4 is: F = 3.28ao(3t)°'21°'*t t'6/./°"4,
International Journal of Impact Engineering, 1997
A closed form solution to the problem of steady-state wedge cutting through a ductile metal plate... more A closed form solution to the problem of steady-state wedge cutting through a ductile metal plate is presented. The considered problem is an idealization of a ship bottom raking process, i.e. a continuous cutting damage of a ship bottom by a hard knife-like rock in a grounding event A new kinematic model is proposed for the strain and displacement fields and it is demonstrated that the analysis is greatly simplified if the strain field is assumed to be dominated by plastic shear strains and moving hinge lines. Also, it is shown that the present shear model offers the basis for a convenient extension of the presented plate model to include more structural members as for example the stiffeners attached to a ship bottom plating. The fracture process is discussed and the model is formulated partly on the basis of the material fracture toughness. The effect of friction and the reaction force perpendicular to the direction of motion is derived theoretically in a consistent manner. The perpendicular reaction force is of paramount importance for predicting the structural damage of a ship hull because it governs the vertical ship motion and rock penetration which is strongly coupled with the horizontal resistance and thus with the damaged length. The derived expressions are discussed and compared with previously published experimental results and formulas.
When a long slender structure such as a wire, strut or rope is loaded under tension all the way t... more When a long slender structure such as a wire, strut or rope is loaded under tension all the way to fracture, upon failure an elastic unloading wave propagates down the wire and reflects as a compressive wave from the distant clamp end. The compressive effect of dynamic pulse buckling, amplitude and wave length depend on material properties and geometry features of the problem. Small scale experiments were performed on thin stainless steel wires of 0.127 mm diameter and varying lengths. The theory of dynamic pulse buckling, developed in the 1980s at the Stanford Research Institute, is used to study the initial phase of the deformation of the wire. In order to obtain a deeper insight in the mechanism of structural collapse, numerical simulations and high speed photography on small scale tests were employed. Both techniques revealed propagation of the bending disturbance (with increasing amplitude) and formation of the periodic helical shape wave with varying amplitude in space. A considerable axial momentum brings the wire into a complex process of elastic–plastic deformation with strain reversal. The numerical simulation was compared to high speed snapshots, showing good agreement. The implication of the presented results to structural integrity of deep water installations is also discussed.
Thin-Walled Structures, 1992
A simple computational model of a thin-walled prismatic column is developed, which describes a tr... more A simple computational model of a thin-walled prismatic column is developed, which describes a transition from the postbuckling to the pos~'ailure and crushing deformation phase. Energy methods are used to analyze the elastic post-buckling response of the column. Ultimate strength is calculated, using the first yield criterion. Limit analysis methods, properly generalized to large displacement and rotation problems, are employed in the postfailure range. The new model explains, with some realism, the process of strain localization and the formation of a plastic folding mechanism in the column. It also leads to a prediction of the entire load-deformation characteristics up to the internal touching and stiffening.
Thin-Walled Structures, 2000
Torsional collapse of thin-walled prismatic columns is studied analytically and numerically. Simp... more Torsional collapse of thin-walled prismatic columns is studied analytically and numerically. Simple torsional collapse models are developed to predict the collapse behavior of square columns under large plastic rotation using energy method. By considering the combined effect of geometry and material, the onset of the sectional plastic buckling is predicted and the critical twisting rotation for sectional buckling is obtained. Next, an analytical expression is derived for the moment-rotation relation valid for rotation up to 180°. The analytical solution is shown to compare well with the numerical results. The solutions are then extended for rectangular and hexagonal thin-walled columns. Numerical simulations for rectangular and hexagonal columns are also carried out and the results are presented in this paper for the purpose of comparison.
The effect of low-density metal filler, such as aluminum foam or honeycomb, is studied on the ben... more The effect of low-density metal filler, such as aluminum foam or honeycomb, is studied on the bending collapse resistance of thin-walled prismatic columns. A combination of analytical and numerical results is used to predict the initial and post collapse response of empty and filled columns. Closed-formed solutions for the bending-rotation characteristics are constructed in terms of the geometrical parameters and the filler strength. The low-density metal core retards sectional collapse of the thin-wall column, and increases bending resistance for the same rotation angle. Numerical simulations show that, in terms of achieving the highest energy absorption to weight ratio, columns with aluminum honeycomb or foam core are preferable to thickening the column wall. Moreover, the presence of adhesive improved the specific energy absorption significantly.
The present paper investigates the mechanics of the crushing of sandwich proÿles through componen... more The present paper investigates the mechanics of the crushing of sandwich proÿles through component testing and theoretical analysis. Experiments were run showing that the underlying folding mechanism of sandwich proÿles is very di erent from that of solid-section thin-walled structures. In particular, the shear behavior of the core material was found to strongly in uence the mechanics of energy absorption. The analysis focuses on the crushing behavior of double-cell proÿles that are made of soft-core hybrid stainless steel assembly (HSSA) sheets. Both material and structural tests were performed. It is demonstrated that the shear strength of the HSSA ÿber core is small as compared to the face sheet properties. When subjected to bending, the core deformed in the shear mode, whereas the facings bent independently. Based on this mechanism, a new shear-folding model for sandwich proÿles is derived, incorporating the "shear crushing" of the sandwich core material. Theoretical predictions of the mean crushing force based on the present model compared very well with the experimental data. ?
The perforation response of a thin or intermediately thick beam/plate struck by a rigid, heavy, f... more The perforation response of a thin or intermediately thick beam/plate struck by a rigid, heavy, flat-nosed projectile traveling at a high velocity is studied analytically. Based on a newly developed expression relating indentation depth to crack length, a shear-plugging model including two stages: indentation and crack growth, is proposed. In this model, shear resistance in the ligament decreases as the cracks propagate through the target thickness. The closed-form solutions for residual velocities, plastic energy, shear zone width, crack propagation speeds, and temperature rise are derived. A coupled shear-tension solution that takes into account global deformation of the plate is also developed. The coupled solution improves prediction for the case with the initial impact velocity near the ballistic limit. Comparisons with experimental results presented in the open literature are made showing rather good correlation, which validates the accuracy of the present solution. r
A bifurcation method is proposed to solve a class of steady-state propagation problems in plastic... more A bifurcation method is proposed to solve a class of steady-state propagation problems in plastic shells. The method is explained on a simple one-dimensional example of a collapsing underwater pipeline. The pipe is modeled as a rigid-plastic beam/string resting on a plastic strain-softening foundation and is subjected to uniform pressure loading. The unknowns in the problem are the critical pressure for the buckle to propagate and the length and shape of the so-called transition zone. Using the method of local equilibrium closed-form solutions are derived for three different structural models: beam, string, and beam/ string.
... a function of x. However, an average parabolic function that closely fits the exact function ... more ... a function of x. However, an average parabolic function that closely fits the exact function was ... 3. T. WIERZBICKI and S. BHAT, A moving hinge solution for axisymmetric crushing of tubes ... RJ HAYDUK, Dynamic response of visco-plastic circular plates to Gaussian pressure loading ...
International Journal of Mechanical Sciences, 1988
International Journal of Solids and Structures, 1992
Journal of Applied Mechanics-transactions of The Asme, 1989
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Papers by Tomasz Wierzbicki