I am interested in devising techniques for modeling nonlinear materials.
For scale homogenization, you mean size effect predicted by homogenization techniques? You should check my last publications about it.
Is for linear elasticity but it may give you some inspiration for non-linear materials.
Good luck!
Mat
Hello, you can linearize numerically and provide it in step-by-step mode. What we need is a precise knowledge about stress-strain relationship for the original components of the composite.
Dear Jawad,
We might be able to give you an answer that is more specific, but we might need some information about the problem you're interested in. Regarding the "how" part of your question, most standard commercial and free FEM packages can deal with homogenization problems, but since you, I assume, want to study the nonlinear mechanical behaviour of materials, you may want to look into Abaqus (industry-oriented) or Z-Set (academy-oriented, www.zset-software.com).
Cheers,
Justin
Hello everyone,
about the "what is" question, I think Brett gave a good simple definition. Regarding the "how" to non.linear material I also think we need more information. First, do you mean non-linear material or structures with non-linear behaviours? Because I have been working on corrugated core sandwich structures for the last 3 years and I am applying homogenization techniques to the core. The homogenized material has a non-linear plastic behaviour. So, I think we need a bit more details.
CIAO!
Giorgio
Hi! Answer is quite long but I believe that the best way to understand something is to do it! Hope it works!
Intro.
First of all, scale homogenization is a mathematical technique which was developed mainly by French and Russian mathematicians in the mid 70's (see Benssousan et al., 1975 and 1978).
From a physical point of view, this concept deals with what we understand by physical properties and how can we define a composite material as a mixture/aggregate of homogeneus constituents.
As a practical example, think about wood or steel. In a "macroscopical" scale, namely X, we can see with our eyes a continuum and "practically homogeneus material". However, as you may already been noticed, we know that internally these kind of materials are heterogeneous.
A natural question is, how we can even think about in material properties when we know that internally, in a "different scale", namely Y, they are heterogeneus?
After some reflections, you may notice that this theory relies on the assumption, until some extent, that material heterogenities may exhibit a sort of periodicity.
To clarify the idea, think about crystals. They are often modeled as "periodic arrangement of atoms in a crystal-lattice".
For the effective properties of a composite material, analysis is limited to a "periodic model", "representative volume of analysis" or "periodic element" in the Y-scale.
The key here is to choose this "periodic object" in manner that ALL the physical and geometrical (distribution) characteristics of each constituent are present.
Such periodic object will contain, as in a crystal, all the information needed to compute their physical properties (elastic, thermal, electrical and magnetic).
With the above mentioned elements, it is possible to state a connection (both, geometrical and physical) between the scales X and Y. This is:
(1) Y = X/e
where e is a small (e
Thanks everyone.
I am looking into dynamic analysis of wire rope (non linear material with hysteresis).
Hello,
I suggest you to read my dissertation on the ULB site (ulb.ac.be). I discussed largely the situation of (pseudo) homogeneous situations in biotechnical systems. It may help you.
Good luck.
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