Eshelby “driving” forces on interacting defects at the microscale and their homogenized effect on the macro: examples in microcrack/hole interaction and damage amplification
Xanthippi Markenscoff (University of California, San )
SES Medal Symposium in honor of D.J. Steigmann
Tue 2:40 - 4:00
MacMillan 115
The equation of motion of defects is governed by Noether’s theorem on the energy functional in a variable domain, as a necessary and sufficient condition for equilibrium (---or conservation of linear momentum in elastodynamics--) to be maintained in the domain under translation of the defect in both linear and nonlinear elasticity[1]. By the use of the path independent J and M integrals and asymptotic homogenization, this dissipation of energy is carried to the macro-scale and this is illustrated in a particular example of macroscopic damage acceleration due to nearby microcrack / hole interaction respectively[2,3]. [1]. Gupta, A. and X. Markenscoff “A New Interpretation of Configurational Forces,” J. Elast. 108, 225, 228, 2012. [2]. Markenscoff,, X and Dascalu, C. “Asymptotic Homogenization Analysis for DamageAmplification due to Interaction of Micro-cracks,” J. Mech. Phys. Sol. 60, 1478-1485, 2012. [3] Markenscoff, X. Growth of holes and damage amplification by asymptotic homogenization, J. Math. Mech. Sol. (to appear)