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Xuanhe Zhao's picture

Xuanhe Zhao

My name is Xuanhe Zhao, and I'm a first year student in DEAS. Before joining Harvard, I got my Master Degree in Materials Engineering from University of British Columbia, Canand. I have took one course on Computational Mechanics, and read a couple of books on theory of elasticity.

 The major goal for me taking ES 240 is to learn how to understand and solve engineering problems, both familiar and unfamiliar, in a intuitive way. In addition, I will further consolidate my background in solid mechanics.

Megan McCain's picture

Megan McCain

I am a first year grad student in bioengineering working in Dr. Parker's Disesase Biophysics Group ( I attended Washington University in St. Louis for undergrad, where I double majored in biomedical engineering and biology and minored in chemistry. The only courses I have taken related to solid mechanics are Biomechanics and Transport Phenomena, both of which covered basic mechanics. As an undergrad, I worked in a research lab that focused on cardiac electrophysiology. The lab I am in now is interested in how the mechanical and electrical behaviors of cardiac cells are related, so I need to gain a stronger background in mechanics to match my background in electrophysiology. I hope that this class will help me develop an intuition about the mechanical behavior of objects, which I can apply to the mechanics of cellular events.

Ken P. Chong's picture

National Medal of Science

The nomination of colleagues for awards is one of the most important and gratifying aspects of participating in the scientific community. Help celebrate the contributions of your colleagues by submitting a nomination for The National Medal of Science.

The National Medal of Science was established in 1959 as a Presidential Award to be given to individuals "deserving of special recognition by reason of their outstanding contributions to knowledge in the physical, biological, mathematical, or engineering sciences." In 1980 Congress expanded this recognition to include the social and behavioral sciences. The National Medal of Science is the highest honor the President bestows on scientists. A Committee of 12 scientists and engineers is appointed by the President to evaluate the nominees for the Award. Since its establishment, the National Medal of Science has been awarded to 425 distinguished scientists and engineers whose careers spanned decades of research and development.

Michael Petralia

I completed my undergraduate degree in Mechanical Engineering at The Cooper Union for the Advancement of Science and Art, in New York City. At the undergraduate level, I have taken two courses related to solid mechanics: Solid Mechanics and Stress & Applied Elasticity. Though these courses covered most of the same topics, the focus was not on working with developing the equations for different situations. The majority of the work was in knowing when to apply the equations and coming up with quantitative solutions. Thus my weaknesses will be related to coming up with equations to model various stress situations.

Concerning my research, I am working with Prof. Robert Wood in the microrobotics laboratory. My focus will be on aquatic robots on the order of several centimeters in length. Because of the restrictions inherent in working at this scale, it will be important not to over-design the systems. From studying solid mechanics, I hope to gain the ability to analyze the states of stress and strain in materials such that I can effectively develop efficient systems for microrobotics.

will adams

My name is Will Adams and I am a first year grad student in BME. I have no previous courses in solid mechanics or strength of materials but I have taken two fluid mechanics courses, ES220 and ES123, as an undergrad which contain many of the same lines of thinking. Hopefully the math formalisms of these classes will help in ES240 but having no solids background leaves me with little intuition about experimental results. Hopefully I can acquire this here. I was a BME major as an undergrad here in DEAS.

Adrian Podpirka's picture

Adrian Podpirka

My name is Adrian Podpirka and I am a first year grad student studying applied physics. I came to Harvard after finishing my Bachelors in Material Science and Engineering at Columbia University. As an undergraduate I took Mechanics of Solids with Professor Xi Chen and Mechanical Properties of Materials with Professor Noyan.

Related to this course, my main weakness is the mathematics involved since it has been more then 3 years since I took differential equations. Also, both my undergraduate courses were not tensor based. My main strength in this course would be my understanding of material properties and the phenomenas involved.

My likely research direction will probably be in the field of fuel cell membranes with Professor Ramanathan.

Zhigang Suo's picture

Solid Mechanics Homework 11-15

This set of homework relies on a few elementary facts of the algebra of vectors and tensors.  If you are vague about these facts, see some old notes I wrote when I taught ES 240 in 2006:  node/205/revisions/1385/view

11. Positive-definite elastic energy density
12. The coefficient of thermal expansion (CTE) is a second-rank tensor.
13. Hooke's law for anisotropic, linearly elastic solids
14. Invariants of a tensor
15. A "derivation" of the Mises (1913) yield criterion

Xiao-Yan Gong's picture

Pushing Mechanics to the Up Front of Design

When a mechanical engineer and a material scientist were asked for the root cause of an in-vivo fracture. Mechanical engineer pointed to the loading and the material scientist pointed to the processing. While they both are correct, they both also missed the real ROOT cause, the design.

It is very common that medical device design engineers are so focused on the device functionality that often the very basic mechanics is overlooked. Lack of knowledge on the in-vivo environment (Design Requirements) is another subject to blame. However, it is common that even technology driven companies have gaps between design department and duarability deparment. Up front design engineers do not necessarily keep up with the fast paces of material advances. On the other hand, downstram subject matter experts, device tesing teams or often the R&D departments are not informed of design changes before the design is fixed. The problem is worse often in industrial leaders than in start-ups, but the sympton is the same, problem found in animal studies and/or clinical trials before they reached industrial subject matter experts.

Xiao-Yan Gong's picture

Mechanics in Medical Implant Industry

The major challenge in medical implant industry is the knowledge about human body. Had we know the human body and its functions better, we can make better and reliable implants. Below are two examples that I have learned.

Let's start from stent, a small, lattice-shaped, metal tube that is inserted permanently into an artery. The stent opens the narrowed artery so that an adequate supply of blood can be restored. See this FDA site for further detail.

Stent has revolutionized the treatments for cardiovascular disease and the interventional system. However, stent fractures are commonly observed in-vivo in the past years and has become a concern for patient wellness and therefore a challenge/opportunity for mechanical engineering. Both the engineering and the medical care societies have to work together to solve this issue. It is very surprising that little publications are available to study the key issues such as artery deformation, motion, its mechanical properties and its variations among patient age, race, and other factors. As a result, current stents, even they have been proven to be lifesavers for many patients, they are not necessarily a satisfactory product for a mechanical engineer. We can not wait for the medical care society to give us the information because they often concern and focus on different issues than us. In addition, they can not work alone to come up with the necessary equipments. Therefore, we need proactive to interact and help each other to get what we want. The day we know our interventional system better is the day that we can make better stents because stents can only be as good as our knowledge to the interventional system.

Xuanhe Zhao's picture

University of Michigan, tenure-track faculty positions

 University of Michigan, tenure-track faculty positions

The Department of Mechanical Engineering, University of Michigan, Ann Arbor, invites applications for tenure-track faculty positions in various areas of mechanical engineering including design and manufacturing, dynamics, systems and controls, materials and solid mechanics and thermal/fluid sciences. Candidates with research interests in automotive engineering, biotechnology, eco/sustainable systems, energy-systems, manufacturing, and micro/nano systems are particularly encouraged to apply.

Applicants should have an earned Ph.D. in Mechanical Engineering or related fields, a demonstrated record for conducting independent research, and the potential for leadership and impact in teaching and research. Appointments at all levels will be considered. For best consideration, candidates should apply by February 28, 2007, but the positions will remain open until filled.

Konstantin Volokh's picture

Prediction of femoral head collapse in osteonecrosis

OSTEONECROSIS is the death of bone that results in the collapse of the bony structure, leading to joint pain, bone destruction, and loss of function. Destruction of the bone frequently is severe enough to require joint replacement surgery. Osteonecrosis is a common disorder and accounts for 10% or more of the 500,000 total joint replacement procedures performed annually in the United States. Approximately 75% of patients with osteonecrosis are between 30 and 60 years of age.

From the point of view of mechanics, osteonecrosis means deterioration of mechanical properties of the bone. Decrease of the magnitude of the elastic modulus of the bone leads to its inability to bear the external load and culminates in bone damage and fracturing. For a couple of decades the engineers were trying to estimate the critical stress-strain state of the femoral head using the available data on the osteonecrotic bone properties, finite element analysis based on 3D elasticity, and Von Mises stress as a criticality condition. The fact that the cortical shell of the femoral head is significantly stiffer than the underlying cancellous bone did not attract much attention yet. However, from the solid mechanics point of view the difference in the stiffness of the cortical and cancellous parts of the femoral head under both normal and necrotic conditions is important. This difference allows for considering the femoral head as an elastic cortical shell on an elastic cancellous foundation. This, in its turn, suggests the buckling of the cortical shell as a possible starting point of the overall head collapse. The purpose of the study, described here, was to assess the cortical shell buckling scenario as a possible mechanism of the femoral head collapse at the various stages of osteonecrosis.

Ashkan Vaziri's picture

Metallic sandwich plates subject to intense air shocks (by Ashkan Vaziri and John W. Hutchinson)

Recent results on fluid-structure interaction for plates subject to high intensity air shocks are employed to assess the performance of all-metal sandwich plates compared to monolithic solid plates of the same material and mass per area. For a planar shock wave striking the plate, the new results enable the structural analysis to be decoupled from an analysis of shock propagation in the air. The study complements prior work on the role of fluid-structure interaction in the design and assessment of sandwich plates subject to water shocks. Square honeycomb and folded plate core topologies are considered. Fluid-structure interaction enhances the performance of sandwich plates relative to solid plates under intense air shocks, but not as significantly as for water blasts. The paper investigates two methods for applying the loading to the sandwich plate-responses are contrasted for loads applied as a time-dependent pressure history versus imposition of an initial velocity. Click here for the full paper.

Zhigang Suo's picture

Solid Mechanics Homework 6-10

6. Post an entry in iMechanica to explain to your teaching staff and classmates why you take this class.

7. Residual stress around an inclusion
8. Lame Solution in Cylindrical Shape
9. Stress Concentration around a Circular Hole
10. Back-of-Envelope Calculation

Return to the outline of the course.

Dhirendra Kubair's picture

Finite element simulations of microvoid growth due to selective oxidation in binary alloys.

Selective oxidation induced void growth is observed in thermal barrier coating (TBC) systems used in gas turbines. These voids occur at the interface between the bond coat and the thermally grown oxide layer. In this article we develop the modeling framework to simulate microvoid growth due to coupled diffusion and creeping in binary alloys. We have implemented the modeling framework into an existing finite element program. The developed modeling framework and program is used to simulate microvoid growth driven by selective oxidation in a binary beta-NiAl alloy. Axisymmetric void growth due to the combined action of interdiffusion and creeping is simulated. The sharpness of the void and direction of creeping are considered as parameters in our study. Our simulations show that the voids dilate without any change in shape when creeping is equally likely in all the directions (isotropic). Void growth patterns similar to those observed in experiments are predicted when the creeping is restricted to occur only along the radial and tangential directions. A hemispherical void grows faster compared to a sharp void. The sharpness increases in the case of a sharp void and could lead to interactions with the neighboring voids leading to spallation of the thermally grown oxide layer as observed in experiments.

Xi Chen's picture

Mystical materials in indentation

As an indenter penetrates an elastoplastic material, the indentation load P can be measured as a continuous function of the indentation displacement δ, to obtain the so-called P-δ curve. A primary goal of the indentation analysis is to relate the material elastoplastic properties (such as the Young's modulus, yield stress, and work-hardening exponent) with the indentation response (i.e. the shape factors of the P-δ curve, including its curvature, unloading stiffness, loading work, unloading work, maximum penetration, residual penetration, maximum load, etc.). The sharp indenters (e.g.

Dynamics of wrinkle growth and coarsening in stressed thin films

Rui Huang and Se Hyuk Im, Physical Review E 74, 026214 (2006).

A stressed thin film on a soft substrate can develop complex wrinkle patterns. The onset of wrinkling and initial growth is well described by a linear perturbation analysis, and the equilibrium wrinkles can be analyzed using an energy approach. In between, the wrinkle pattern undergoes a coarsening process with a peculiar dynamics. By using a proper scaling and two-dimensional numerical simulations, this paper develops a quantitative understanding of the wrinkling dynamics from initial growth through coarsening till equilibrium. It is found that, during the initial growth, a stress-dependent wavelength is selected and the wrinkle amplitude grows exponentially over time. During coarsening, both the wrinkle wavelength and amplitude increases, following a simple scaling law under uniaxial compression. Slightly different dynamics is observed under equi-biaxial stresses, which starts with a faster coarsening rate before asymptotically approaching the same scaling under uniaxial stresses. At equilibrium, a parallel stripe pattern is obtained under uniaxial stresses and a labyrinth pattern under equi-biaxial stresses. Both have the same wavelength, independent of the initial stress. On the other hand, the wrinkle amplitude depends on the initial stress state, which is higher under an equi-biaxial stress than that under a uniaxial stress of the same magnitude.

Nanshu Lu's picture

Office Hour for ES 240

Zhigang Suo: Wed. 3pm Pierce 309

Nanshu Lu: Thur. 4~6pm Pierce 403

Valid for every week except special notification is published.

Zhenyu Xue's picture

International Conference on Computational & Experimental Engineering and the Sciences (ICCES07) 

The Aim of ICCES'07 is to bring researchers from the world's acdemia, industry, and the governments, for a few days, to the ambience of Miami, USA, in January 2007, to discuss the recent advances in computational and experimental engineering & sciences, and to facilitate collaborative research efforts.

The Main Themes of the Conference are:

1. Multidisciplinary Analysis & Synthesis of Complex Systems
2. Mechanics of Composite Materials and Structures
3. Plasticity; Steel Structures; Computational & Experimental Aspects
4. Mechanics of Fluids, Gases, and Fluidics/MEMS
5. Nanoengineering in Medicine and Biology
6. Computational Biology, Biomechanics
7. Geomechanics, Geomaterials
8. Smart Structures
9. Computational Fracture Mechanics; Structural Integrity & Health Monitoring
10. Nanomechanics, Nanostructured Materials, & Materials by Design
11. Dynamics of Materials & Structures: Computations & Experiments
12. Meshless and other novel methods of computer modeling in engineering and the sciences
13. Computational Solid Mechanics

If you are interested in organizing a special Symposium in one of the above themes, please contact the organizing committee at

Ju Li's picture

Localization Lengthscale in Metallic Glass

See an accompanying powerpoint presentation: The aged-rejuvenation-glue-liquid (ARGL) shear band model has been proposed for bulk metallic glasses (Acta Mater. 54 (2006) 4293), based on small-scale molecular dynamics simulations and thermomechanical analysis. The model predicts the existence of a critical lengthscale ~100 nm and timescale ~100 ps, above which melting occurs in shear-alienated glass. Large-scale molecular dynamics simulations with up to 5 million atoms have directly verified these predictions. When the applied stress exceeds the glue traction (computed separately before), we indeed observe maturation of the shear band embryo into bona fide shear crack, accompanied by melting.

A message from Dr. Ken P. Chong

The deadline of October 1, 2006 for my program of Mechanics & Structures of Materials was inadvertently omitted in our website. However, at the beginning of our CMS home page there are 2 deadlines listed for all programs. In the meantime any unsolicited proposals for my program, please put in GPG 04-23 as the Program Announcement [1st box]. In the 2nd box put in my program name [Mechanics & Structures of Materials].

Rui Huang's picture

Surface effects on thin film wrinkling

A recent discussion here about the effect of surface stress on vibrations of microcantilever has gained some interest from our members. A few years ago, Zhigang and I looked at surface effect on buckling of a thin elastic film on a viscous layer (Huang and Suo, Thin Solid Films 429, 273-281, 2003). Although the physical phenomena (buckling vs vibrations) are different, the conclusion is quite consistent with Wei Hong and Pradeep's comments toward the end of the discussion. That is, surface stress only contributes as a residual stress and thus does not affect the buckling wavelength (frequency in space in analogy to frequency in time for vibrations).

Yaoyu Pang's picture

Nonlinear effect of stress and wetting on surface evolution of epitaxial thin films

Y. Pang and R. Huang, Physical Review B 74, 075413 (2006).

An epitaxial thin film can undergo surface instability and break up into discrete islands. The stress field and the interface interaction have profound effects on the dynamics of surface evolution. In this work, we develop a nonlinear evolution equation with a second-order approximation for the stress field and a nonlinear wetting potential for the interface. The equation is solved numerically in both two-dimensional (2D) and three-dimensional (3D) configurations using a spectral method. The effects of stress and wetting are examined. It is found that the nonlinear stress field alone induces "blow-up" instability, leading to crack-like grooving in 2D and circular pit-like morphology in 3D. For thin films, the blow-up is suppressed by the wetting effect, leading to a thin wetting layer and an array of discrete islands. The dynamics of island formation and coarsening over a large area is well captured by the interplay of the nonlinear stress field and the wetting effect.

Zhigang Suo's picture

7 reasons to post your original ideas in iMechanica

1. iMechanica is free for all to use. iMechanica is hosted on a server at the School of Engineering and Applied Sciences, of Harvard University, and is managed by a team of volunteers -- mechanicians just like you. You pay nothing to post, and readers pay nothing to read. The limit of each upload file is 50MB, and each user is given 1GB server space.

Ting Tsui's picture

Constraint Effects on Thin Film Channel Cracking Behavior

Channel CrackOne of the most common forms of cohesive failure observed in brittle thin film subjected to a tensile residual stress is channel cracking, a fracture mode in which through-film cracks propagate in the film. The crack growth rate depends on intrinsic film properties, residual stress, the presence of reactive species in the environments, and the precise film stack.


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