This posting provides errata for an analytical solution that appeared in the following two publications:
Brannon, R. M. and S. Leelavanichkul (2010) A multi-stage return algorithm for solving the classical damage component of constitutive models for rocks, ceramics, and other rock-like media. Int. J. Fracture v. 163(1), pp. 133-149.
K.C. Kamojjala, R. Brannon, A. Sadeghirad, and J. Guilkey (2013) Verification tests in solid mechanics, Engineering with Computers, 1-21.
As pointed out by Dr. Andy Tonge, they both contain a the same transcription error that was not in the original unpublished working document where the details of the solution are archived. The following excerpt from the original unpublished working document contains correct formulas: PlasticityVerification2excerpt. See the red comment boxes in this file for details.
The presentation slides (downloadable as PowerPoint and PDF) describe the basic principles and application advantages of the material point method (MPM).
To follow this tutorial, you need to know basic equations for the finite-element method.
The enrichment discussion of the CPDI2 publication* provided the following figure to illustrate the CPDI2 basis functions:
This figure, however, has the shortcoming of not clearly depicting the partition of unity property.
In hindsight, we should have used…
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