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

Course Outline Offered Fall 2012; Fall 2014; Fall 2016; Fall 2018 Time and place: MWF 9:55-10:45, room MSE 265. Timetable               Search tool
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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. mail

Description: 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, ultrastrong 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. Biomimetic and bio-inspired materials.
material structures for class
Goals: 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.
Textbook: A course pack will be provided.
Grading: Grading is based on homework (15%), projects and labs (20%) and quizzes (65%). 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.

Course Outline
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.

VI: Cellular solids. Structure property relations of cellular solids. Lightweight cellular solids. Foams, structural honeycombs, sandwich structures. Polymer lattice structures. Syntactic foams. Poisson's ratio of composites and foams. Applications.

VII: Hierarchical structure. Structure within structure. Hierarchical honeycomb, foam and lattices. 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. Design of hierarchical solids. Enhancement of physical properties.

VIII: Design considerations. Fracture mechanics, stress concentrations, free-edge effects. In situ composites; eutectic structure. Gradient effects. Role of microstructure size. Generalized continuum models; Cosserat elasticity; size effects. Toughness: empirical criteria; causal mechanisms. Spongy impact absorber, bone cement.

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).

Graphs
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 1 tutorial 2 pdf

Expected outcome
Develop clear understanding of the role of material heterogeneity; develop physical insight; develop ability to design systems with heterogeneous materials.

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"For a successful technology, reality must take precedence over public relations, for Nature cannot be fooled", Richard Feynman.