Non-linear constitutive relations for unstable materials

Non-linear constitutive relations to describe the rheological properties of unstable materials in the one-dimensional case are proposed, where the properties of instability, in particular ageing (i.e., the increase in stiffness and toughness of the material with time), are described by experimentally determined “instability functions”, which depend on the “age” of a given batch of material and, possibly, on invariance of the stress or strain tensors, which affect the rate of physical-chemical processes in the materials. Taking into account the instability of the material, a “fast” time is introduced, measured from the beginning of a short-term test with a material of a given age, and a “slow” time, measured from the instant when the material is produced. An exact solution of the problem of identifying the model, i.e., a determination of the material instability functions from experimental data, is constructed.