ABSTRACT
V a r i a t i o n a l M u l t i s c a l e M e t h o d s t o
E m b e d M a c r o m e c h a n i c a l F o r m u l a t i o n s
w i t h F i n e S c a l e P h y s i c s
A s deformation phenomena approach the length scales of grains (1/ im and lower i n most polycrys ta l l ine solids), the interactions between defects (dislo cations, microvoids and microcracks) and the effects of their elastic fields play increasingly impor tan t roles. Convent iona l macroscopic con t inuum theories
of ine las t ic i ty-such as p las t ic i ty or damage-fai l at resolving this effect. A
t reatment of interactions between i n d i v i d u a l defects is, however, ru led out;
their densities are too h igh to warrant such an approach even at these finer
scales. O n the other hand, the hardening effects at crack t ips , results of
nanoindenta t ion tests ( N i x , 1989; M c E l h a n e y et a/., 1998), micro tors iona l and mic robend ing experiments (Fleck et a/., 1994; S to lken & Evans , 1998) can be expla ined w i t h notable success by various classes of s t ra in gradient
p las t ic i ty theories (Fleck & Hutch inson , 1997; G a o et a/., 1999; Arsenl i s & Parks , 1999). T h e observed finite w i d t h of shear bands is also represented by these theories since they introduce a length scale to the p rob lem. A separate
approach to incorpora t ing the influence of micros t ruc ture is seen i n the for
m a l t reatment of configurat ional microforces ( G u r t i n , 1995). A related work is ( G u r t i n , 2000), which treats c rys ta l p las t ic i ty i n the framework of mic roforces and encompasses plast ic s t ra in gradient effects. A t h i r d class of models
opera t ing at microscopic length scales consists of t ract ion-displacement laws
specified on in ternal surfaces. Included i n this category are laws specifying
the evolu t ion of tangential t rac t ion dr iven by sl ip on shear bands (Armero & G a r i k i p a t i , 1996) and embedded fracture zone models [see (Tvergaard & Hutch inson , 1992), for example].
