AN INCREMENTAL RELAXATION FINITE-ELEMENT ANALYSIS OF VISCOELASTIC PROBLEMS WITH CONTACT AND FRICTION

Based on the principle of virtual work, a general but effective finite element technique associated with an incremental relaxation procedure is established for the analysis of viscoelastic contact problems with friction. A generalized Maxwell model is used to model the viscoelast ic constitutive equations of which the relaxation function is represen ted by the sum of a series of decaying exponential functions of time. The contact behaviors are accurately performed through a transformatio n matrix method. By the incremental relaxation procedure developed, th e stress of each element of the generalized Maxwell model at instant t ((N+1)) includes two parts: (I) the part decaying from the stress at i nstant t((N)) during the time interval [t((N)), t((N+1))], and (2) the incremental stress induced from the incremental strain applied at ins tant t((N)). The total stress at instant t((N+1)) can thus be computed by the sum of the stress of the elements of the generalized Maxwell m odel and is only dependent on the previous stress level and the increm ental strain applied at instant t((N)). Hence, both the total strain a nd displacement at each instant are not used in the total stress calcu lation. In addition, the numerical errors caused by selecting larger t ime increments can also be avoided. Finally, the influence of friction on the contact traction distributed on the contact surface at various time instants is presented.