Contact problems of the mechanics of bodies with accretion

Abstract

Contact problems of the mechanics of bodies with accretion are studied. A general formulation of the mixed problem is given for a viscoelastic ageing body during its continuous piecewise accretion. Complete systems of equations of the mixed problem are given in time intervals from the onset of loading to the onset of accretion, from the onset of accretion to the end of accretion, and beyond it. The characteristic feature of the basic relations in the case of a body with continuous accretion is the use not of the usual equations of compatibility of the deformations and the Cauchy relations, but of their analogues in the rates of change of the corresponding quantities /1–3/. Moreover, the given previous histories of the deformation tensor of the accruing elements form, at the instant of attachment, specific initial and boundary conditions /2/ on the accruing surface. In particular, the total stress tensor associated with external loads and characterizing the tightness of attachment of the accruing elements is determined at the accruing surface /2, 3/. The instant of attachment of the new elements to the main body represents an important characteristic of the process. The set of instants of attachment completely determines the configuration of the accruing body at any instant of time. Equations of state of the theory of creep of the inhomogeneously ageing bodies are used /4, 5/. The equations reflect the fundamental specific features of the accretion process where the times of preparation and onset of loading play an important part. A method of solving the mixed and initial-boundary value problems is given. Contact problems for a wedge under various methods of accretion are considered. Integral equations are derived and their solutions constructed. Numerical solutions of the contact problems for a wedge with accretion are given for the case when the influx of matter from outside results in increasing the wedge angle, and for an accruing quarter-plane. Qualitative and quantitative effects are discussed, especially the influence of the method and rate of accretion on the contact characteristics.