Syllabus for MSE 541, Heterogeneous and multiphase materials
Department of Materials Science and Engineering
Cross listed as EMA 541, Engineering Mechanics and Astronautics
University of Wisconsin-Madison
Offered Fall 2012; Fall 2014; Fall 2016; Fall 2018
Time and place: MWF 9:55-10:45, room MSE 265 moved to MSE 235. Timetable
. Final quiz, Fri. Dec. 14, 10:05-12:05.
Use control or command click for new tab or window.
Prerequisites: Mechanics of materials, such as the following.
MSE 441 co-requisite or EMA 303 prerequisite or equivalent or consent of instructor.
Instructor: Rod Lakes
, Professor. Office-541 ERB. Office phone (608) 265-8697; fax: (608) 263-7451.
Principles of the mechanics of solid multiphase systems. Role of heterogeneity and anisotropy in determining physical properties including elastic, dielectric and piezoelectric properties. Applications in lightweight structures, ultra-strong materials, materials for protection of the body, and materials for the replacement of human tissues. Materials with fibrous, lamellar, particulate, and cellular structures. Heterogeneous materials of biological origin. Metamaterials and biomimetic and bio-inspired materials.
To prepare seniors and graduate students to understand physical properties, particularly mechanical properties of heterogeneous and multiphase materials; and the cultivation of physical insight in that regard.
A course pack will be provided.
: Grading is based on homework (15%), projects (20%) and quizzes (65%). There are typically two one hour quizzes and a two hour final. The scale is 90-100% - A, etc. Homework grades will be reduced by 5% per working day (Monday-Friday) of additional delay
. All assignments must be submitted in paper form, not electronic. Short assignments may be hand written. Project reports may be single space, double side: your choice.
Homework is due one week after it is assigned unless otherwise stated. Project reports are due two weeks after they are assigned unless otherwise stated.
Bring a calculator to quizzes. Use phones and laptops outside class only to avoid distraction
. Do not take photographs of human beings without permission. If you wish a scan of class notes, please ask and one will be provided. Keep in mind writing it down enhances comprehension. If you feel that you need to use a device for substantive reasons, please discuss prior to class.
I: Introduction. Material heterogeneity. Survey of laminated, fibrous, particulate, cellular and porous, platelet structures. Single crystal properties and polycrystal properties. Heterogeneity of biological materials and designed heterogeneity. Strength of fibers. Constituent materials. Griffith's experiments, stress concentrations. Concept of equivalent homogeneity. Micro and nanotructures.
II: Structure, properties and bounds. Unidirectional fibrous media. Bounds on physical properties: Voigt and Reuss bounds; Hashin-Shtrikman bounds. Realization of extremal properties. Prediction of stiffness and strength for different directions.
III: Symmetry and anisotropy. Symmetry and physical properties. Crystal symmetry classes. Isotropy, cubic, hexagonal, orthorhombic, monoclinic, triclinic symmetry. Application of anisotropic elasticity to composites. Generalized Hooke's law of elasticity. Modulus and compliance matrices. Anisotropy and dielectric and piezoelectric properties. Thermal expansion. Experimental methods.
IV: Coupled fields; smart materials Piezoelectric properties, symmetry, causes. Elastic moduli of piezoelectric solids. Piezoelectric materials. Pyroelectric and ferroelectric materials. Thermal expansion. Fluid-solid composites.
V: Practical particulate, fibrous and platelet filled materials. Structure. Particulate materials. Dental composites, metal matrix composites, asphalt. Toughened polymers via compliant inclusions. Stiffness vs. volume fraction. Self healing polymers. Attainment of the Hashin-Shtrikman bounds. Unidirectional fibrous materials; stiffness, strength, thermal expansion. Fibrous solids with short-fibers. Nano-tubes as fibers. Platelet reinforcement. Shear lag model. Laminates. Polycrystalline aggregates. Piezoelectric composites. Metal matrix composites. In situ composites; eutectic structure.
VI: Cellular solids. Structure property relations of cellular solids. Lightweight cellular solids. Foams, structural honeycombs, sandwich structures. Polymer lattice structures. Dense foams; syntactic foams. Poisson's ratio of composites and foams. Hierarchical honeycomb, foam and lattices. Design of hierarchical solids. Applications.
VII: Biological materials Hierarchical structure: structure within structure. Bone, wood, tendon and other materials of biological origin. Fibrous aspects of bone structure. Tendon and ligament as fibrous biological materials. Biological cellular solids. Cellular architecture of bone, wood, bamboo. Enhancement of physical properties.
VIII: Size of heterogeneity. Fracture mechanics, stress concentrations, free-edge effects. Role of microstructure size. Gradient effects. Generalized continuum models; Cosserat elasticity; size effects. Toughness: empirical criteria; causal mechanisms.
IX: Viscoelasticity. Creep, relaxation, vibration damping. Bounds on stiffness-loss map. Role of the shape of the heterogeneity. Experimental methods. Applications.
References and resources
R. S. Lakes, Multiphase materials, to be provided in class.
L. J. Gibson, and M. F. Ashby, Cellular Solids, Cambridge, (1999).
M. F. Ashby and D. R. H. Jones, Engineering Materials, 2nd ed. Butterworth, (1998).
J. F. Nye, Physical Properties of Crystals, Oxford, (1976).
B. D. Agarwal and L. J. Broutman, Analysis and Performance of Fiber Composites, J. Wiley, 2nd ed. (1990).
For those who use KaleidaGraph to draw graphs, this software can import data from text files or from Excel. The rationale is to achieve better quality of graphs
. Here are links to
tutorial 2 pdf
Develop clear understanding of the role of material heterogeneity; develop physical insight; develop ability to design systems with heterogeneous materials.