The notion of constitutive equations (or laws) is elucidated together with the meaning of related notions such as material constants, calibration and response envelopes. Also discussed is why a comparison of constitutive equations is conceptually difficult.

Several tensors that describe deformation are introduced, as well as stretching and spin. As an example, they are presented for the special case of simple shear. The compatibility equations are discussed together with non-Boltzmann continua.

The mechanical behaviour of soil is introduced by presenting and discussing the typical outcomes of element tests with soil.

The main principles of plasticity theory are introduced. The collapse theorems are presented as one of the principal applications of plasticity theory in soil mechanics. Some special plasticity theories for soil (Cam-clay theory and Mohr–Coulomb applications) are also presented.

For civil engineering, calculations are of central importance; they provide a sense of security. However, in soil mechanics the reliability of calculations is reduced for several reasons: aside from incomplete constitutive equations and their calibration based on experiments burdened with errors, some other problems are the spatial scatter of soil properties, missing knowledge of the initial stress field and infinite extending of the considered bodies. Validations reveal the poor reliability of computation results. To cope with such problems increased margins of safety, cautious building (observational method) and reliance upon authorities like experts, computer codes and codes of practice are used.

Barodesy is developed on the basis of the relation between proportional strain paths and proportional stress paths and of the fading memory of soil. This relation is mathematically described by means of a matrix exponential. The fine tuning of barodesy is obtained by consideration of limit states and the dilatancy prevailing there. A new approach to critical states is presented which leaves the hitherto considered critical state line unchanged but introduces an evolution equation for the critical void ratio at non-critical states. It is shown that barodesy includes basic and well-known concepts of soil behaviour. It is shown that the same equation of barodesy holds for sand and clay. Simulations of element tests, oedometric, triaxial drained and undrained ones, show that barodesy is capable of describing them in a satisfactory way, though using equations of outstanding simplicity. In addition, the simulations of cyclic tests exhibiting liquefaction and cyclic mobility are satisfactory.

Brief overview of the importance and peculiarities of granular materials.

Conservation laws (or balance equations) are introduced together with their representation as field and integral equations, jump relations. Some special stress fields are introduced as examples.

Hypoplasticity as an alternative to elastoplasticity theory is introduced. The description of irreversibility with non-linear rate equations is explained, and the incremental non-linearity is elucidated. The emergence and development of hypoplasticity is discussed together with its links to elastoplasticity.

A very short and simple introduction to continuous and discontinuous fields and some related quantities.

The problem of uniqueness in solving initial boundary value problems is considered together with its implications for the simulation of element tests. Some general theorems holding for linear constitutive equations are discussed together with some applications to soil. The formation of shear bands ('faults’ in geology) is described as a special case of loss of uniqueness. Vortices are also introduced as patterns of loss of uniqueness.

Friction is discussed as the main source of strength of granular media. The Mohr–Coulomb strength criterion is introduced. Cohesion as an additional source of strength is discussed together with its controversial physical origin.

This appendix introduces the classification of physical properties according to their behaviour under rotation (scalars, vectors, and in general tensors of a certain rank). Cartesian and spherical representations are presented and explicit expressions for the tensors of second and fourth rank needed when studying liquid crystals are given.

The application of molecular and mesophase symmetries to identify the minimal set of order parameters required to treat single-particle properties for different mesophases and mesogens or solutes is discussed. The use of symmetry to build rotational invariants (Stone S functions) to describe pairwise properties is described and explicit expressions of invariants are provided for uniaxial and biaxial particles.