# ENGRMAE 258 Mechanical Behavior of Solids – Continuum Theories (2017-2018)

#### ENGRMAE 258 Mechanical Behavior of Solids – Continuum Theories

**ENGRMAE 258 Mechanical Behavior of Solids – Continuum Theories (Credit Units: 4)** Presents a continuum, macroscopic view of deformation and failure of solids. The course covers elasticity, plasticity, visco-elasticity, visco-plasticity, fracture and fatigue. Topics include discussions of physical behavior, mathematical formalism and measurement techniques. Prerequisite: ENGRMAE 254. Graduate students only. (Design units: 0)

Mase and Mase, Continuum Mechanics for Engineers, CRC.

W. Slaughter, The Linearized Theory of Elasticity, Birkhauser, 2001.

J. Lubliner, Plasticity Theory, Dover Publications.

R. Hill, The Mathematical Theory of Plasticity, Oxford Univ. Press, 1998.

R. Lakes, Viscoelastic Materials, Cambridge University Press, 2009.

R.M. Christensen, Theory of Viscoelasticity, Dover Publications, 2010.

T.L. Anderson, Fracture Mechanics, 2nd Ed., CRC.

S. Suresh, Fatigue of Materials, 2nd Ed., Cambridge University Press.

The mathematics of tensors and indicial notation. Continuum mechanics of small deformations: the stress tensor, fundamental kinematics, conservation laws.

Week 1 Review of mathematical fundamentals: Indicial notation. Tensors. Coordinate transformations. Principal values and principal directions. Gauss and Stokes theorems.

Week 2 Review of fundamental concepts of continuum mechanics: Conservation of mass. Stress tensor. Conservation of linear and angular momentum. Hydrostatic and deviator stress. Strain tensor for infinitesimal deformations.

Week 3 Linear elastic behavior: Elastic strain energy and hyperelastic behavior. Isotropic materials: Lame’ constants. Anisotropic materials. Plane Elasticity and Airy stress function.

Weeks 4-5 Yielding and fundamentals of plasticity theory: Yield criteria (Von Mises, Tresca, …). Deformation and flow theories. Flow rules for isotropic and kinematic hardening. Drucker’s postulate. Normality and convexity of yield surfaces with associated flow rules.

Weeks 6-7 Time-dependent deformation: Visco-elasticity and creep: Linear visco-elasticity. Boltzmann superposition integrals. Particular creep and relaxation functions (Maxwell, Voigt and Standard Linear Solid Models). Effect of temperature. Response to sinusoidal stimuli (storage and loss modulus, loss coefficient). Resonance of structural members. Damping. Experimental methods. Physical mechanisms for damping in materials.

Weeks 8-9 Fundamentals of fracture mechanics: Linear Elastic Fracture Mechanics. Griffith criterion. Strain energy release rate. Energy considerations. R curve and crack stability. The K field. Small-scale yielding. Fracture toughness. Elastic-Plastic Fracture Mechanics. The J integral. Experimental measurements of fracture toughness: K testing VS J testing.

Week 10 Fundamentals of fatigue: Crack growth rate. Fatigue threshold. Life prediction for a structure. Experimental measurements of fatigue crack growth.

Meets for 3 hours of lecture each week for 10 weeks.

none.

none.

Contributes toward the Mechanical Engineering Topics courses.

Approach:

Lectures: 100%

Laboratory Portion: 0%

HW: 30%

Final Presentation: 30%

Final Exam: 40%

Total: 100%

Mathematics and Basic Science: 0.0 credit units

Computing: 0.0 credit units

Engineering Topics: 4.0 credit units

Engineering Science: 4.0 credit units

Engineering Design: 0.0 credit units