RIKS and Arc length method in ABAQUS

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The given below is a brief introduction about the Riks Method and Arc length, used in ABAQUS. The details are taken from ABAQUS-Mannual and Nikolaos Vasios(PhD Student, Materials Science & Mechanical Engineering) article.

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The Riks method-

· is generally used to predict unstable, geometrically nonlinear collapse of a structure;

· can include nonlinear materials and boundary conditions;

· often follows an eigenvalue buckling analysis to provide complete information about a structure's collapse; and

· Can be used to speed convergence of ill-conditioned or snap-through problems that do not exhibit instability.

In simple cases linear eigenvalue analysis may be sufficient for design evaluation; but if there is concern about material nonlinearity, geometric nonlinearity prior to buckling, or unstable post-buckling response, a load-deflection (Riks) analysis must be performed to investigate the problem further.

The Riks method uses the load magnitude as an additional unknown; it solves simultaneously for loads and displacements. Therefore, another quantity must be used to measure the progress of the solution; Abaqus/Standard uses the “arc length,” l, along the static equilibrium path in load-displacement space. This approach provides solutions regardless of whether the response is stable or unstable.

Arc length method- Efficient method in solving non-linear systems of equations when the problem under consideration exhibits one or more critical points. In terms of a simple mechanical loading-unloading problem, a critical point could be interpreted as the point at which the loaded body cannot support an increase of the external forces and an instability occurs.