covariance

Material strength is a classical concept that has recently found renewed applications in fracture mechanics, especially in models for crack nucleation in brittle solids. In this paper, we formulate material strength in the setting of finite elasticity and examine its geometric, constitutive, and symmetry-theoretic foundations. We show that spatial covariance requires a strength function to depend on both stress and the corresponding strain measure, so that strength is not controlled by stress alone, but by the pair (stress,strain).

This paper studies the invariance of balance of

energy for a system of interacting particles under groups of

transformations. Balance of energy and its invariance is first

examined in Euclidean space. Unlike the case of continuous media,

it is shown that conservation and balance laws do not follow

from the assumption of invariance of balance of energy under

time-dependent isometries of the ambient space. However, the

postulate of invariance of balance of energy under arbitrary