An inverse method for the determination of full field stresses from experimentally measured normal strains

Abstract

Certain diffraction-based techniques that measure strains in bulk samples are limited to determination of normal strains. A numerical inverse method is developed to determine full field stresses from the experimentally determined normal strains in isotropic solids under plane stress conditions. The method is based on satisfying the equations of equilibrium and the constitutive relations. The finite difference method is employed to solve the equations and to determine the complete stress field. Furthermore, a least-squares procedure is used to determine the unknown functions of integration in conjunction with known values of shear stress along a reference line. The method is verified by using the normal strain fields in various specimens obtained using both finite element analysis and exact elasticity solutions. It is found that the proposed method predicts the shear stresses accurately in the examples considered.

Keywords

neutron diffraction inverse problem finite difference method least square approximation

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References

Fitzpatrick

M. E.

Lodini

(Eds) Analysis of residual stress by diffraction using neutron and synchrotron radiation, 2004 (Taylor & Francis, London).

Hori

Kameda

Inversion of stress from strain without full knowledge of constitutive relations

J. Mechanics Physics Solids, 2001, 49, 1621–1638.

Yang

C. Y.

Chen

C. K.

The boundary estimation in two-dimensional inverse heat conduction problems

J. Phys. D: Appl. Phys., 1996, 29, 333–339.

Shaw

Noniterative solution of inverse problems by linear least square method

Appl. Math. Modeling, 2001, 25, 683–696.

Timoshenko

S. P.

Goodier

J. N.

Theory of elasticity, 3rd edition, 1971 (McGraw-Hill, New York).

Hertz

Gesammelte Werke (Collected works), 1895 (J. A. Barth, Leipzig).