Constitutive Model and Finite Element Procedure for Dilatant Contact Problems

Abstract

A constitutive law for dilatant frictional behavior is reviewed. It is developed by distinguishing between the macrostructural and raicrostructural features of a material discontinuity. Macrostructural considerations provide the general form of the constitutive equations, while microstructural considerations ailow the inclusion of an appropriate surface idealization. The result is an incremental relation between contact stresses (traction) and relative surface deformation that accounts for phenomena such as surface damage due to wear and arbitrary cyclic sliding. A quadratic‐displacement‐isoparametric finite element is derived that permits modeling of curved‐contact surfaces and crack surfaces terminating at a tip with a surrounding medium that is modeled with quarter‐point quadratic elements. Emphasis is on the use of established finite‐element‐solution methodologies and program architecture for material‐nonlinear problems. Several examples are considered. The resulting methodology is useful for modeling geologic discontinuities, crack‐shear transfer in concrete, and dilatancy‐induced mixed‐mode fracture mechanics.s