Abstract: Deformation and Fracture of Heterogeneous Media using Boundary-Conforming Convected Particle Characteristic Functions in the Material Point Method

This is an abstract for

NWU2013: Advances in Computational Mechanics with Emphasis on Fracture and Multiscale Phenomena. Workshop honoring Professor Ted Belytschko’s 70th Birthday.  April 18, 2013 – April 20, 2013, Evanston, IL, USA

The organizers allocated only 10 minutes for each person’s talk (including big wigs like Tom Hughes), so we might just present this topic in the form of a puppet show with enough information to tickle the audience to chat with us about it in the hallway!


Rebecca Brannon*, Alireza Sadeghirad,  James Guilkey

Department of Mechanical Engineering

University of Utah

Salt Lake City, UT, 84112

*Email: Rebecca.Brannon@utah.edu

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Publication: On the thermodynamic requirement of elastic stiffness anisotropy in isotropic materials

Measure of anisotropy for Zircon, Quartz, Uranium, Titanium, Hornblende, and Copper.

T. Fuller and R.M. Brannon

In general, thermodynamic admissibility requires isotropic materials develop reversible deformation induced anisotropy (RDIA) in their elastic stiffnesses. Taking the elastic potential for an isotropic material to be a function of the strain invariants, isotropy of the elastic stiffness is possible under distortional loading if and only if the bulk modulus is independent of the strain deviator and the shear modulus is constant. Previous investigations of RDIA have been limited to applications in geomechanics where material non-linearityand large deformations are commonly observed. In the current paper, the degree of RDIA in other materials is investigated. It is found that the resultant anisotropy in materials whose strength does not vary appreciably with pressure, such as metals, is negligible, but in materials whose strength does vary with pressure, the degree of RDIA can be significant. Algorithms for incorporating RDIA in a classical elastic–plastic model are provided.

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Publication: Decomposition and Visualization of Fourth-Order Elastic-Plastic Tensors

A.G. Neeman; R.M. Brannon; B. Jeremic; A. Van Gelderand;  A. Pang

Top view (Z from above) of eigentensors for Drucker-Prager material, time step 124, colored by minimum stretch eigenvalue.

Visualization of fourth-order tensors from solid mechanics has not been explored in depth previously. Challenges include the large number of components (3x3x3x3 for 3D), loss of major symmetry and loss of positive definiteness(with possibly zero or negative eigenvalues). This paper presents a decomposition of fourth-order tensors that facilitates their visualization and understanding. Fourth-order tensors are used to represent a solid’s stiffness.The stiffness tensor represents the relationship between increments of stress and increments of strain. Visualizing stiffness is important to understand the changing state of solids during plastification and failure. In this work,we present a method to reduce the number of stiffness components to second-order 3×3 tensors for visualization.The reduction is based on polar decomposition, followed by eigen-decomposition on the polar “stretch”. If any resulting eigenvalue is significantly lower than the others, the material has softened in that eigen-direction. The associated second-order eigentensor represents the mode of stress (such as compression, tension, shear, or some combination of these) to which the material becomes vulnerable. Thus we can visualize the physical meaning of plastification with techniques for visualizing second-order symmetric tensors.

Available Online:

Publication: http://www.mech.utah.edu/~brannon/pubs/7-2008NeemanBrannonJeremicVanGelderPang.pdf

Poster: http://www.mech.utah.edu/~brannon/pubs/7-09NeemanBrannonEtAlNEESposter.pdf

Powder metal jet penetration into stressed rock

The Uintah computational framework (UCF) has been adopted for simulation of shaped charge jet penetration and subsequent damage to geological formations.  The Kayenta geomechanics model, as well as a simplified model for shakedown simulations has been  incorporated within the UCF and is undergoing extensive development to enhance it to account for fluid in pore space.

A generic penetration simulation using Uintah

The host code (Uintah) itself has been enhanced to accommodate  material variability and scale effects. Simulations have been performed that import flash X-ray data for the velocity and geometry of a particulated metallic jet so that uncertainty about the jet can be reduced to develop predictive models for target response.  Uintah’s analytical polar decomposition has been replaced with an iterative algorithm to dramatically improve accuracy under large deformations. Continue reading

Nonclassical plasticity validation

Analysis and computations have been performed by the Utah CSM group to support experimental investigations of unvalidated assumptions in plasticity theory. The primary untested assumption is that of a regular flow rule in which it is often assumed that the direction of the inelastic strain increment is unaffected by the total strain increment itself. To support laboratory testing of this hypothesis, the general equations of classical plasticity theory were simplified for the case of axisymmetric loading to provide experimentalists with two-parameter control of the axial and lateral stress increments corresponding to a specified loading trajectory in stress space. Loading programs involving changes in loading directions were designed. New methods for analyzing the data via a moving least squares fit to tensor-valued input-output data were used to quantitatively infer the apparent plastic tangent modulus matrix and thereby detect violations of the regular flow rule. Loading programs were designed for validating isotropic cap hardening models by directly measuring the effect of shear loading on the hydrostatic elastic limit.

UofU Contributors/collaborators:
Michael Braginski (postdoc, Mech. Engr., UofU)
Jeff Burghardt (PhD student, Mech. Engr., UofU)

External collaborators/mentors:
Stephen Bauer (Manager, Sandia National Labs geomechanics testing lab)
David Bronowski (Sandia geomechanics lab technician)
Erik Strack (Manager, Sandia Labs Computational Physics)

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

A.F. Fossum and R.M. Brannon (2006)

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.

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