摘要
This paper proposes the approximate methods of calculation for research on inhomogeneous finite strain fields in geologic bodies by means of the 'Principal Axis' theory of continuum mechanics. The methods are to obtain the principal strain orientations at finite points in the earth's crust based on the information and data provided by the actual strain measurements of deformation marked objects in the field, or by the research on crystalline fabrics in rocks, and then to obtain two sets of smooth orthogonal principal strain trajectories through mathematical treatments. A network composed of two sets of orthogonal curves shows the deformation character of the rock, and correspondent strain components satisfy compatibility conditions. The curvatures of curves are used to describe the compatibility conditions in this paper. An analytic solution of a strain field is obtained when the two sets of lines can be simulated by analytic function; the magnitudes of principal strains at every point may be obtained by means of the discrete method when the simulation by analytic functions fails.
This paper proposes the approximate methods of calculation for research on inhomogeneous finite strain fields in geologic bodies by means of the "Principal Axis" theory of continuum mechanics. The methods are to obtain the principal strain orientations at finite points in the earth’s crust based on the information and data provided by the actual strain measurements of deformation marked objects in the field, or by the research on crystalline fabrics in rocks, and then to obtain two sets of smooth orthogonal principal strain trajectories through mathematical treatments. A network composed of two sets of orthogonal curves shows the deformation character of the rock, and correspondent strain components satisfy compatibility conditions. The curvatures of curves are used to describe the compatibility conditions in this paper. An analytic solution of a strain field is obtained when the two sets of lines can be simulated by analytic function; the magnitudes of principal strains at every point may be obtained
基金
Project supported by the National Natural Science Foundation of China.
