Conference Poster: Modeling, Testing, and Analysis of Impulse Response of Femoral Head Reduction in Ceramic Hip Prostheses

Kakarla, D., A. P. Sanders, S. Siskey, K. Ong, N. Ames, J. O. Ochoa, and R. M. Brannon. (2012). “Modeling, Testing, and Analysis of Impulse Response of Femoral Head Reduction in Ceramic Hip Prostheses.” Transactions of the Orthopaedic Research Society 2012 Annual Meeting, San Francisco, CA, Feb. 4-7, Poster 2076.


Hip simulator wear tests including micro-separation conditions have revealed that abnormal loading events can outweigh normal loading conditions in causing wear of hard-on-hard bearings. Yet, there is a paucity of data to describe the mechanics of abnormal events such as edge loading by femoral neck impingement or femoral head subluxation. Though the magnitude of head subluxation has been measured in-vivo for a variety of human activities, there are apparently no corresponding reports of the concurrent head-liner contact forces; accurate measurements of the same may be rendered difficult by the transient, impulsive nature of edge loading. This report provides initial laboratory results of an in-vitro and in-silico study of impulsive femoral head reduction whose ultimate aim is to quantify dynamic edge-loading contact forces and stresses. The study implements an engineering model of proximal-lateral head subluxation and edge loading as could occur in a lax hip during the swing phase of gait. Rapid reduction is caused by applying a sudden cranio-caudal motion to the acetabular liner. In the laboratory, the femur’s response to this input is measured with strain gages and a laser vibrometer.


Aldridge (AKA Blake) spherical source verification test for dynamic continuum codes

This post has the following aims:

  • Provide documentation and source code for a spherically symmetric wave propagation in a linear-elastic medium.
  • Tell a story illustrating how this simple verification problem helped to validate a complicated rate-dependent and history-dependent geomechanics model.
  • Warn against believing previously reported material parameters, since they might have been the result of constitutive parameter tweaking to compensate for unrelated errors in the host code. Continue reading

Presentation: Contact Mechanics of Impacting Slender Rods: Measurement and Analysis

Sanders, A., I. Tibbitts, D. Kakarla, S. Siskey, J. Ochoa, K. Ong, and R. Brannon. (2011). “Contact mechanics of impacting slender rods: measurement and analysis.” Society for Experimental Mechanics Annual Meeting. Uncasville, CT, June 13-16.


Images of a typical contact patch

To validate models of contact mechanics in low speed structural impact, slender rods with curved tips were impacted in a drop tower, and measurements of the contact and vibration were compared to analytical and finite element (FE) models. The contact area was recorded using a thin-film transfer technique, and the contact duration was measured using electrical continuity. Strain gages recorded the vibratory strain in one rod, and a laser Doppler vibrometer measured velocity. The experiment was modeled analytically using a quasi-static Hertzian contact law and a system of delay differential equations. The FE model used axisymmetric elements, a penalty contact  algorithm, and explicit time integration. A small submodel taken from the initial global model economically refined the analysis in the small contact region. Measured contact areas were within 6% of both models’ predictions, peak speeds within 2%, cyclic strains within 12 microstrain (RMS value), and contact durations within 2 µs. The accuracy of the predictions for this simple test, as well as the versatility of the diagnostic tools, validates the theoretical and computational models, corroborates instrument calibration, and establishes confidence thatthe same methods may be used in an experimental and computational study of the impact mechanics of artificial hip joint.

Available Online:

Global model results comparison with analytical and experimental results for speed at the midpoint of one of the rods

Publications: Nonuniqueness and instability of classical formulations of nonassociative plasticity

A plot of the frequency-dependent wave propagation velocity for the case study problem with an overlocal plasticity model, with the elastic and local hardening wave speeds shown for reference (left). Stress histories using an overlocal plasticity model with a nonlocal length scale of 1m and a mesh resolution of 0.125m (right)

The following series of three articles (with common authors J. Burghardt and R. Brannon of the University of Utah) describes a state of insufficient experimental validation of conventional formulations of nonassociative plasticity (AKA nonassociated and non-normality).  This work provides a confirmation that such models theoretically admit negative net work in closed strain cycles, but this simple prediction has never been validated or disproved in the laboratory!

  1. An early (mostly failed) attempt at experimental investigation of unvalidated plasticity assumptions (click to view),
  2. A simple case study confirming that nonassociativity can cause non-unique and unstable solutions to wave motion problems (click to view),
  3. An extensive study showing that features like rate dependence, hardening, etc. do not eliminate the instability and also showing that it is NOT related to conventional localization (click to view).

Continue reading

Publication: Validating Theories for Brittle Damage

R.M. Brannon, J.M. Wells, and O.E. Strack

Realistic-looking, uneven damage zones in Brazilian simulations compare favorably with laboratory data for observable damage

Validating simulated predictions of internal damage within armor ceramics is preferable to simply assessing a models ability to predict penetration depth, especially if one hopes to perform subsequent ‘‘second strike’’ analyses. We present the results of a study in which crack networks are seeded by using a statistically perturbed strength, the median of which is inherited from a deterministic ‘‘smeared damage’’ model, with adjustments to reflect experimentally established size effects. This minor alteration of an otherwise conventional damage model noticeably mitigates mesh dependencies and, at virtually no computational cost, produces far more realistic cracking patterns that are well suited for validation against X-ray computed tomography (XCT) images of internal damage patterns. For Brazilian, spall, and indentation tests, simulations share qualitative features with externally visible damage. However, the need for more stringent quantitative validation, software quality testing, and subsurface XCT validation, is emphasized.

Continue reading

Publication: On a viscoplastic model for rocks with mechanism-dependent characteristic times

A. F. Fossum and R. M. Brannon

Rate Dependance

This paper summarizes the results of a theoretical and experimental program at Sandia National Laboratories aimed at identifying and modeling key physical features of rocks and rock-like materials at the laboratory scale over a broad range of strain rates. The mathematical development of a constitutive model is discussed and model predictions versus experimental data are given for a suite of laboratory tests. Concurrent pore collapse and cracking at the microscale are seen as competitive micromechanisms that give rise to the well-known macroscale phenomenon of a transition from volumetric compaction to dilatation under quasistatic triaxial compression. For high-rate loading, this competition between pore collapse and microcracking also seems to account for recently identified differences in strain-rate sensitivity between uniaxial-strain ‘‘plate slap’’ data compared to uniaxial-stress Kolsky bar data. A description is given of how this work supports ongoing efforts to develop a predictive capability in simulating deformation and failure of natural geological materials, including those that contain structural features such as joints and other spatial heterogeneities.

Available Online:


Publication: Assessment of the applicability of the Hertzian contact theory to edge-loaded prosthetic hip bearings.

Sanders, A. P. and R. M. Brannon (2011). “Assessment of the applicability of the Hertzian contact theory to edge-loaded prosthetic hip bearings.” Journal of Biomechanics 44(16): 2802-2808.


The components of prosthetic hip bearings may experience in-vivo subluxation and edge loading on the acetabular socket as a result of joint laxity, causing abnormally high, damaging contact stresses. In this research, edge-loaded contact of prosthetic hips is examined analytically and experimentally in the most commonly used categories of material pairs. In edge-loaded ceramic-on-ceramic hips, the Hertzian contact theory yields accurate (conservatively, <10% error) predictions of the contact dimensions. Moreover, the Hertzian theory successfully captures slope and curvature trends in the dependence of contact patch geometry on the applied load. In an edge-loaded ceramic-on-metal pair, a similar degree of accuracy is observed in the contact patch length; however, the contact width is less accurately predicted due to the onset of subsurface plasticity, which is predicted for loads >400N. The Hertzian contact theory is shown to be ill-suited to edge-loaded ceramic-on-polyethylene pairs due to polyethylene’s nonlinear material behavior. This work elucidates the methods and the accuracy of applying classical contact theory to edge-loaded hip bearings. The results help to define the applicability of the Hertzian theory to the design of new components and materials to better resist severe edge loading contact stresses.

Available online:;