Some necessary conditions at an internal boundary for minimizers in finite elasticity

✍ Scribed by Henry C. Simpson; Scott J. Spector

• Publisher: Springer Netherlands
• Year: 1991
• Tongue: English
• Weight: 618 KB
• Volume: 26
• Category: Article
• ISSN: 0374-3535
• DOI: 10.1007/bf00041890

✦ Synopsis

Consider a deformed body that contains surfaces across which the material properties are not continuous such as a twin boundary in a crystal, a boundary between shear bands in a metal or polymer, or a boundary at which two distinct materials have been joined. Given that the body is elastic at equilibrium it is of interest to determine constitutive restrictions upon the stored-energy density that are consequences of the observed stability of the body.

In this paper we address the problem of finding pointwise algebraic conditions upon the elasticity tensors C+ (xo, Vf+(xo)) and C- (xo, Vf-(xo)) that are necessary for a continuous, piecewise smooth deformation f to be a weak relative minimizer, i.e., a local minimizer of the energy in the CLtopology. In particular we show that the Legendre-Hadamard condition, Agrnon's condition, and two new conditions: if for some vector e e ® no" CO+ [e ® no] = e ® no" Co [e ® no] = 0 then CO+ [e ® no] = C o [e ® no]; and if for some vector a a ® to" C? [a ® to] = a ® to" Co [a ® to] = 0 then CO + [a ® to]n o = Co [a ® to]no