By Alexander of Aphrodisias, William E. Dooley
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Additional info for Alexander of Aphrodisias on Aristotles Metaphysics 1. Translated by W. E. Dooley
Deformations of cuboidal RSEs without rotation of principal axes belong to this group if only deviators are considered. 6) is zero. Thus the asterix may be dropped for strains, ε˙∗i = ε˙i . Their rates should be referred to the actual length for large deformations. Related evolutions of state and shape can be represented by associated stress and strain paths 20 2 Simple psammoids ε1* σ1* ασ 0 3,4 τ 3 1,2 A 3 σ3* a) 0 4 σ2* 1,2 ε3* 1 B 2 αε A 1 2 3 ε2* b) Fig. 2. Deviatoric stress paths (a) and related strain paths (b) of a pore-free solid in deviator planes, Fig.
Truesdell and Noll (1965) call materials simple if their stress tensor is a frame-indiﬀerent functional of a suitable stretching tensor. They give algebraic representations for ﬂuids and elastic solids, but leave aside plastic materials. Representative elements (RSEs) of a pore-free solid are considered in Sect. 1 for preparation in this ﬁrst chapter on constitutive relations for soils. e. dependence on pressure, density and amount of strain rate) are neglected. The only state variable is the deviatoric stress tensor.
Stationary (so-called critical) states are approached by isochoric deformations, otherwise the stress paths get proportional with increase or decrease of pressure. Only at state limits the void ratio is determined by the skeleton stress components. Psammoid skeletons are called simple if their state is fully characterized by stress components and void ratio. This implies that the memory of path reversals is swept out by suﬃciently big monotonous deformations (Gudehus et al. 1977). The consequences for strain cycles and ratcheting are shown more geometrico in Sects.
Alexander of Aphrodisias on Aristotles Metaphysics 1. Translated by W. E. Dooley by Alexander of Aphrodisias, William E. Dooley