Lecture note_01_Introduction to course.pdfVIP

1/42 N h i d Mi h ianomec an cs an cromec an cs H. L. Duan School of Engineering Peking University , 2/42 I t d ti t thn ro uc on o e course Wh t i i h i ?a s m cromec an cs Generally speaking, micromechanics is a scientific discipline that studies: (1) Mechanical, electrical, and, in general, thermodynamical behaviors of a material with microstruture or, (2) Materials’ behaviors at micro (nano) or mesoscale. 3/42 I t d ti t thn ro uc on o e course 4/42 I t d ti t thn ro uc on o e course 5/42 I t d ti t thn ro uc on o e course 6/42 I t d ti t thn ro uc on o e course 7/42 I t d ti t thn ro uc on o e course 8/42 I t d ti t thn ro uc on o e course 9/42 I t d ti t th Heterogeneous medium Equivalent homogeneous medium n ro uc on o e course ( ) ( ) ( )= ?J x K x F x = ?J K F F : field applied on a material -- cause J : response of the material to F -- effect K : coefficient 10/42 I t d ti t thn ro uc on o e course ( ) ( ) ( )= ?J x K x F x F : field applied on a material -- cause J f th t i l t F ff t : response o e ma er a o -- e ec K : coefficient 0 : ( )/2?? = = = ?? + ??σ σ C ε ε u u Basic equations for mechanics , , Basic equations for conductivity 11/42 Analogy between the steady state conduction Physical Subject φ F K J thermal temperature gradient thermal heat flux conduction conductivity electrical conduction potential intensity electrical conductivity current density electrostatics potential intensity permittivity electric induction magnetostatics potential intensity magnetic permeability magnetic induction elasticity displacement strain elastic moduli stress 12/42 Conceptual relation between elasticity and conduction El i i C d i ast c ty on uct on u: displacement φ: temperature ε: strain -φ,i : gradient σ: stress q: flux T :traction qn: normal flux component C l ti d li d ti iti: e as c mo u μ: con uc v es S: compliances ρ: resistivities rigid phase superconductor empty phase insulator 13/42 Motivations