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# What are the current research areas in computational mechanics?

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Hello mechanicians,

What are the current research areas in computational mechanics? What is the future of CM? Where can one find such information on the net? Is there a central location?

Thank you,

Mahadevu

Forums:

## suggetion

sugession for gaining confidence in analysys

## multiscale simulation?

Hi Mahadevu,

Multiscale simulation might be one of the interesting areas in compuational mechanics, although the progress on this topic seems to slow down somehow recently. It seems to me that nowdays people are more interested in biomechanics/materials. I would like to see more people talking about CM. Maybe CM people can do some computational biomechanics research.

Luming

## Multi-scale simulation of biological materials

Hi Mahadevu

An exciting area of computational mechanics are methods that include an atomistic description of materials. Some of these ideas fall into the general realm of 'multi-scale modeling'. Such methods attempt to link the 'material scale' with the 'structural scale', a tremendously challenging problem. I personally work primarily at the material scale, studying mechanical properties of biological materials, in particular those made out of proteins. I find this a very interesting area of research that brings in chemistry to the more traditional mechanics fields. Chemistry is particularly important for large deformation or fracture, when atomic bonds are stretched heavily and broken. It is not hard to imagine that this critically important if we would like to predict how protein materials fail.

We now realize that this link between mechanics and chemistry is vital to come up with accurate models of the behavior of materials and structures.

In addition to feature the chemical component, these materials are intriguing because of their hierarchical structure. At this interface 'structure' and 'material' merge and become indistinguishable.

In this area, computational mechanics has great future - with many outstanding, exciting and important problems: For example, many biological processes are related to mechanics; the cell's shape/stiffness, adhesion problems, tunable elasticity of biopolymers, mechanical properties of tissues and many others. Here mechanics can be a true asset to do very interesting science. Being able to carry out simulations is sometimes advantageous over experiment - as it is easier to control experiments, to manipulate such small structures as proteins, and to set up studies with different boundary conditions.

Markus

## take a look at paper of Oden, Belytschko and Hughes

Obviously, the following paper is suited to your needs:

J.T. Oden, T. Belytschko, I. Babuska, T.J.R. Hughes, "Research directions in computational mechanics," Computer Methods in Applied Mechanics and Engineering, 192: 913-922 (2003)

You can get it via http://www.tam.northwestern.edu/tb/TBPublications.htm

Phuonos

## "You can also take a look at this NSF report"

The web link is

http://www.nsf.gov/pubs/reports/sbes_final_report.pdf

## The Unique Value of Computational Mechanics

I expect everyone will have a "slightly" different view on this, Personally, I can see the value of CM at least in the following areas:

(1) Obtaining microscopic understanding of “mechanical behavior” down to the atomic scale

Mechanics is conventionally developed within the framework of continuum theory neglecting the details of atomic structure and chemical bonding. However, when the size and dimension are reduced, the relevant length scale controlling the mechanical behavior becomes smaller and smaller even down to the atomic scale. In this regime, Computational Mechanics becomes a powerful tool of study. Therefore, we can expect CM to be widely applied in small and low dimensional systems, such as nanostructures and biomolecules, and this has been happening already.

(2) Predicting fundamental “mechanical constants”

First-principles (or Ab initio) quantum-mechanics based computational methods are capable of predicting fundamental materials properties with a high degree of accuracy, such as predicting the crystal lattice constants within a couple of percent and the elastic constants within a few percent of experimental value. On the other, many “mechanical constants” are difficult (if not impossible) to measure by experiments, such as dislocation core energy, surface stress, etc.. In this regard, first-principles CM will make a unique contribution to predict these fundamental constants. Such prediction can be further used as inputs for larger-scale simulations and continuum modeling. (This is now sometimes referred to as “sequential” multiscale simulation.) For example, we have recently combined first-principles surface energy and surface stress calculations with continuum modeling to predict on the critical nucleation size of quantum dots (strained islands) in heteroepitaxial growth of semiconductor thin films [Lu & Liu, Phys. Rev. Lett. 94, 176103 (2005)]

Note: First-principles computational methods are already very popular in Physics, Chemistry, and Material community, but it seemed to me this is not the case in Mechanics community.

(3) Employing CM as a designing tool for new materials and structures

Another very interesting and exciting area is to employ CM not only to study the mechanical behavior of materials and structures, but also to apply the mechanical behavior to make new materials and structures. For example, the bending of thin film is possibly the simplest mechanical behavior we know. Recently, we have carried out CM simulations to design nanotubes and nanocoils from bending of nanometer thick ultrathin films [Huang et al, Adv. Mater. 17, 2860 (2005)].

## Stochastics

An area that is likely to blossom in the years ahead is stochastic computational mechanics, with the emergence of possibly new paradigms and computational approaches. Due to the limited predictive power of deterministic models (given the variabilities in material/failure properties for instance), the need for conceiving better computer models that incorporate elements of uncertainty is apparent. This applies to simulating phenomena in structural and biological materials at the meso/continuum scales and also in multiscale modeling endeavors. With ever-increasing computational power, costs will be less of an issue and render such simulations tractable in the near future.

## "Stochastic" processes and biology

The dictionary definition of "stochastic" associates the word with randomness first, and statistically described processes second. The antonym of stochastic is "deterministic" or caused by something. I wonder if it is really appropriate to describe biological materials as stochastic-- uncertain or random, as opposed to just inhomogeneous and therefore perplexing. I agree completely that the computational modeling of inhomogeneous biological materials presents a serious computational challenge in coming years, and that the true understanding of the mechanical behavior of such materials necessarily includes the recognition of point-to-point variability. However, it's unclear to me that this variability is truly stochastic, as opposed to biologically determined!

## Re: Stochastic processes

True. This is how I see it. Stochastics typically refers to processes in which certain parameters are random variables or random functions (not deterministic). Stochastic computations refers to analysis wherein one or more parameters, coefficients, or boundary conditions are described by a random variable or function in the governing equation (ODE/PDE typically). Point-to-point variability in material properties (porous media, polycrystals, bio-materials) produces heterogeneity. This c'd be known (deterministic function) or be non-deterministic (random function). `Random' here is not to be taken literally: there is variability at a point and we need to somehow account for this in a numerical model. In modeling, we attempt to best capture the behavior/response of all members that belong to a certain class. For example, at a given point

x, the Young's modulus E, might have a scatter: this is accounted for in a model by assuming that E atxcan be described by alog-normal distribution(a choice you make) with certain mean and variance. What results in the randomness is that at everyxthere is `spread' of E from specimen-to-specimen (i.e., microstructure to microstructure). We know that E varies in the domain but to characterize this variability through a single deterministic function E(x) would not be apropos. In essence, this choice would amount to using the sample mean value (on average that's what you w'd obtain) atxfrom the ensemble distribution. Very often, material/system performance is not characterized by the mean-value of parameters, but by extremes (e.g., weakest links in failure is a case in point). Of course, for biological materials/systems, there is a lot more beyond this (epistemically) I w'd reckon when it comes to uncertainty quantification.