Materials with Memory

Real materials exhibit a continuing strain rate (creep) under persistent constant stress and decay of stress (relaxation) under constant strain. The analogue occurs for electric current or electric polarization and electric field. In this connection, here the mathematical framework of materials with fading memory is developed along with the thermodynamic consistency and the wave propagation properties. First, thermoelastic materials are modelled through histories and summed histories. Next, the wide topic of viscoelasticity is developed; the linear viscoelastic solid with emphasis on free energies; viscoelastic solids with unbounded relaxation functions; viscoelastic fluids. Attention is then addressed to electromagnetism in deformable bodies: dielectrics with memory, magneto-viscoelastic materials.