TAM Seminar - On the Impact Response of Prismatic Bars Subjected to a Dropped Weight: Linear Elasticity, Elastoplasticity, and Hyperelasticity - Vlado Lubarda

The maximum stress and displacement in a cylindrical bar subjected to impact by a dropped weight are determined for linearly elastic, elastoplastic (metallic), and hyperelastic (rubber-like) materials. Both tensile and compressive impacts are considered for different impact velocities. The analysis is based on an extension of the classical energy approach of infinitesimal linear elasticity. It is assumed that the work done on the bar by the falling weight is equal to its initial kinetic energy plus the change in its gravitational potential energy, evaluated with respect to the deformed configuration of the bar when the velocity of the dropped weight becomes zero. The mass of the impacted bar is assumed to be much smaller than that of the falling weight, so that the inertia of the bar and wave-propagation effects can be neglected.  
After reviewing the classical analysis for linear elasticity, the approach is extended to a bilinear elastoplastic material model and subsequently to the nonlinear Ramberg–Osgood, Ludwik, and Rasmussen material models. For tensile impact, the threshold velocity for the onset of necking is determined as a function of the mass, material, and geometric properties of the bar, assuming that the impact velocity is sufficiently low that strain-rate effects can be neglected. For compressive impact of slender bars, the buckling stress and corresponding critical impact velocity are determined using Engesser's tangent-modulus theory and von Kármán's reduced-modulus theory.  
The analysis is then extended to incompressible rubber-like materials described by the Mooney–Rivlin, neo-Hookean, Gent, Yeoh, Ogden, and Arruda–Boyce hyperelasticity models, as well as to compressible foam-like materials described by the Blatz–Ko, Hill–Storäkers, and compressible neo-Hookean models. Other coupled and uncoupled compressible hyperelastic models are also considered and discussed. For a linearly elastic bar, the maximum stress at zero impact velocity is twice the corresponding static stress. For nonlinear bars the dynamic factor can differ substantially from 2, depending on the magnitude of the dropped weight and the degree and type of material nonlinearity. 
The seminar will address both the research and teaching aspects of this mechanics problem, including energy considerations, wave propagation, material nonlinearity, instability, and constitutive modeling. 

Add Event To My Group

Please sign-in