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Chapter I2 A Theory of Nonlinear Finite Element Analysis 239
that if the strain is above a certain level, it is dependent on the deformation history along with
the stress. For an elasto-plastic solid, the incremental theory (or flow theory) is widely used to
account for the deformation history. However, for the simplification of calculation, the total
strain theory (or deformation theory) is also used when the finite element method is not
applied.
Figure A.3 Bauschinger's Effect
12.5.2 Relationship Between Stress and Strain in Elastic Region
The relationship between stress and strain in the elastic region can be repressed in a matrix
form as follows;
M = be kE1
(A.4)
[De] = [Ce
where,
For an isotropic material, [De], IC] are formulated with the Young's modulus, E, and
Poisson's ratio in the form,
