TITLE:

Using the Spectral Decomposition of the Compliance Tensor to Treat Locking Finite Elements in Anisotropic Elasticity

DATE:

Friday, November 14 2014

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Dr. Stephen P. Oberrecht. PhD. Department of Structural Engineering University of California, San Diego

ABSTRACT:

Certain anisotropic elastic materials, such as the homogenized model of a fiber-reinforced matrix, are nearly rigid under stresses applied in a direction of material rigidity—the resulting strains are comparatively small when viewed against the strains that would occur in response to otherwise directed stresses.This leads to underestimated deformations when modeled with basic finite element techniques.

Splitting the material compliance into two terms allows the separation, and targeted treatment, of troublesome strain modes. This is illustrated most clearly with the dilational-deviatoric split used to treat so-called ‘volumetric locking. The spectral decomposition of the material compliance provides a generalized split of the material elasticity, naturally parsing the material response into six strain modes with decreasing propensity for locking.

Using this split, we generalize fundamental techniques such as Selective Reduced Integration (SRI) and B-bar method. We use this split material compliance to remedy the element locking suffered by lower order finite elements when they are used to discretize locking materials. While its application to the dilational-deviatoric split is trivial, the compliance spectrum’s ability to naturally separate stiff material response modes makes it a valuable general tool for homogenized anisotropic materials which also lock with lower order elements.

Applying the split as defined by the first compliance mode has recently been shown to give rise to similar, generalized, SRI and B-bar methods to treat the locking of anisotropic materials.

We also show that this generalization can be broadened to treat materials with multiple rigid fiber directions. While up to five constrained modes can be separated for special treatment, some attention must be paid to the stability of the resulting finite element stiffness matrices. A framework for assessing the element stability is delineated, commonly arising instabilities are analyzed, and a stabilization method is offered. This stabilization leads to a variable treatment model that also offers improved convergence performance for isotropic materials that do not have rigid strain modes.

HOST:

Dr. Satchi Venkataraman

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