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# Plasticity in Materials

By rstroup27
Sep 28, '11 2:34 PM EST

I would like to think as an architect that the materials on a building are permanent.  That, as I design a building, what I design will last forever.

It's not true, of course.  All materials, whether steel or concrete or composite, are destined to fail at some point in time.  Whether that failure point occurs five years or five hundred years down the line is the utmost priority for any designer to determine.  Sustainability isn't just about recycling; it's also about lifespan and durability.

In structures, we are taught how this material failure or collapse is reached.  This is critical for any architect to comprehend: if undue pressure or force is exerted on structural materials, no matter the modulus of elasticity, that material will succumb at some point to the load imposed upon it.

We call this point the yield point, and it is reached when the proportionality between stress and strain (per Hooke's Law) is no longer obeyed by the material given an increase in applied stress.  Experimentally, the yield point has a function, or criterion which must prove true for yielding to occur.

If we assume that any random material selected is isotropic (that is, has a similar grain pattern in all directions at an atomic level, i.e., steel, unalloyed metals) then five different theories are considered applicable:

• Maximum Principal Stress Theory - yielding occurs when a principal stress exceeds the tensile yield strength of a material.
• Maximum Principal Strain Theory - yielding occurs when a principal strain exceeds the tensile yield strain in a material.  (Both this theory and the maximum principal stress theory are typically determined by simple tension tests)
• Tresca / Shear Yield Theory - yielding occurs when the shear stress exceeds a shear yield point in a material.
• Von Mises / Distortional Theory - yielding occurs when the distortional strain energy (the change in shape) on a material exceeds the material's strain energy at the tensile yield point.
• Deformational Yield Theory - yielding occurs when the deformational strain energy (the change in volume) on a material exceeds the material's strain energy at the tensile yield point.

No matter the determination of this onset in plasticity, the central ideas remain the same: to determine when a material fails, we need human-based classifications of force per unit area or length.  And that is precisely why stress and strain are so critical for any architect to understand.  For instance, consider the flutes on the High Art Museum in Atlanta, GA designed by Richard Meier.

These "flute tips" sculpt the interior exhibition space lighting.  They are rounded at the ends and are most likely prefabricated and cut per the lighting specifications provided by Meier.  Although noticeable from afar, the importance of these tips are more fundamental for the ambience inside, so the curved metal serves a unique function explicitly.

To arrive at this design, the fabricator had to understand how each of these tips would behave under adverse loading conditions: wind, snow, rain all could damage the metals severely even in a hot/humid climate such as would be found in Atlanta.  Therefore, the alloys in these metals must behave so as to have elasticity contained within the yield surfaces created by the above yield design theories.

Is the stress going to induce yielding?  Is the strain going to cause yielding?  Will there be work-hardening in the materials, thereby expanding the yield surface of the materials?  If anything can be done for the protection of these tips, what particularly will allow for elastic/ductile behavior within any plausible loading constraints?

Questions like these are the questions one should ask as a designer.  The materials speak to us what these limits are.  It's important to listen.

• ## 1 Comment

• i could be wrong but based on a recent visit those flute tips and the image you show were designed by  Piano as part of his High Musuem expansion. The ceilings in the Meier half are more "traditional" so to speak. I wrote about the two buildings for Archinect here

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