Original paper(Vol.48 No.4 pp.323)
A Incremental Formulation of FLEM Based on the Objective Stress-Rate for Large Deformation Analysis
Nishimura Tsuyoshi; Kiyama Hideo; Fujimura Hisashi
Abstract:The numerical methods of analysis can provide useful information for engineering in rock. One of the most important components of these methods is the mathematical description of a relationship between stress and strain. For example, the response which is typified by relatively brittle behavior becomes apparently ductile as the confining pressure is increased. Strain may be larger to reach failure, which is particularly observed in soft rock. In such cases, numerical methods should be formulated referring to the frame of large strain theory which can explain a result of material rotation.
This paper describes a formulation of FLEM (Flow Element Method) for large deformation analysis of continua. An analytical area is divided into conceptual sub sections. The explicit time marching scheme of the equation of motion is adopted to get displacements of the centroid of the section. The basic idea of this method has originated from DEM (Distinct Element Method). Another sub division into individual elements of finite size is prepared to calculate forces acting to the centroid. This procedure is based on FEM (Finite Element Method).
A two dimensional elastic block subjected to end displacement in a plain strain condition was simulated by FLEM incorporating the Jaumann rate. The same problem was analyzed by FEM to check the FLEM simulations. The results obtained in this paper are as follows. (1) This method can be applied to quasi static problems by which the damping factor and the time increment are set to be the optimum values. (2) The objective stress rate plays an important role in large deformation analysis. However, the response of the external shear stress acting on the block to shear deformation indicates an unrealistic curve, further development of appropriate laws involving material rotation or a new procedure must be needed.
Key Words:FLEM, DEM, large shear deformation, jaumann stress-rate