【正文】 extensively in the solution of contact problems. From a purely putational standpoint, detection of contact and subsequent satisfaction of the imperability constraint are the two key issues to be addressed in the development of a general algorithmic framework. Numerous methodologies have been proposed in the literature of pulational contact mechanics since the early works of Conry and Seircg,1 and Chan and Tuba. 2 A fairly prehensive survey on the topic is found in The present work is concerned with the development of finite element methods suitable for the solution of twobody contact problems in the presence of large motions and deformations. This class of problems is of particular significance in numerous practical applications, such as metal forming processes and vehicular crash analyses. Various mercial and research puter codes employ algorithms for the solution of such problems. Lagrange multiplier method, 4 and their regularizations (penalty and augmented Lagrangian methods ) are typically used in enforcing imperability. The choice of integration method for the worklike term associated with the contact tractions in the weak form of linear momentumbalance plays a pivotal role in the 8 construction of contact elements. Use of nodal quadrature involving the contacting nodes of one of (resp. both) surfaces yields the standard onepass (resp. twopass) nodeonsurface algorithms. 7 Other integration rules are also applicable, provided there exists a continuous discretization of the contact interface. The main contribution of the present paper is in the identification of a genneral procedure according to which the twobody problem is approached as a sequence of two simultaneous subproblems. As in the traditional twopass algorithms, the surfaces of both interacting bodies are used in the analysis without need for introduction of an (often arbitrarily chosen) intermediate contact surface. The main advantage of the proposed approach over the twopass nodeonsurface algorithms if that it allows for a straightforward interpretation of the integration rules used on the contacting surfaces and, for appropriate choices of admissible fields, permits the exact transmission of constant pressure from one body to another. In the spirit of the patch test originating in the work of Irons, 10 and its subsequent generalizations, capability for exact representation of constant pressure (in both magnitude and direction) is viewed as a necessary condition for robustness and convergence of the overall contact algorithm. A brief exposition to contact mechanics is presented in Section 2, with particular emphasis on formulations to be used in the ensuing algorithmic developments. A twodimensional contact element is proposed and analysed in Section 3,while the results of selected numerical simulations using this element are presented and discussed in Section remarks are given in Section 5. 2. THE TWOBODY CONTACT PROBLEM Consider bodies ,2,1, ?? ?? identified with open and connected sets ?? in linear space 3? , equipped with canonical basis ( 1E , 2E , 3E ) and the usual Euclidean norm. At least one of the bodies is assumed to be deformable. A typical material point of ?? in the reference configuration is algebraically specified by vector ?? of material point ?? in the current configuration is given by ),( t??? ? ??? at each time t, and the displacement 9 vector ?u is defined according to ????? ? ????? ),(:),( ttu The mapping ?? is assumed smooth throughout its domain and invertible at least on ?? .Body ?and its boundary in the current configuration (at time t) are identified with ?t? and ?t?? ,respectively, hence ),(: tt ??? ? ??? and ),(: tt ??? ? ????? .Also, the outer unit normal to ?t?? is denoted by ?n . The motion of any system of bodies (including a single body) is subject to the principle of imperability of matter, as stated by Truesdell and Toypin in Reference11 ().This implies for the twobo