Hi
I want to know is this suitable to use large deformation theory, for small elastic deformation from different points of view, include: accuracy, implementation in code, computational cost and .... .
Deformation or strain, both are different quantities. In general, there can be large deformations but small local strains.
Coming to your question, you can use it for small strains but there might be added computational cost, which wouldn't be much!
Dear Fayyaz,
You may use large strain codes for small strain problems but not the other way around. The accuracy of the large strain formulation is generally higher, however in the small strain domain both material formulations will be really similar.
Large strain models are formulated in terms of the Green strain for instance. In contrast small strain models use the linearized form of the Green strain, usually called epsilon. Epsilon will become inaccurate only for large strains/deformations.
Since the latter is already linear you don't need the linearization of epsilon in your code and therefore there is no geometric part of the stiffness matrix. This saves some computational cost and makes the implementation easier.
I hope these comments answer your question.
Best regards,
Markus
For elastic solids, there is mechanical consistency between the nonlinear (large, finite) strain and the linear (small, infinitesimal) strain theories:
https://www.researchgate.net/project/Nonlinear-Constitutive-Parameters-in-Finite-Elasticity
Various finite element methods for the numerical approximation of problems in linear elasticity are well understood in terms of convergence analysis and error estimation, and are well established. Many of them have also been successfully implemented and validated in practice for a wide range of industrial applications.
See also:
Article Reliability of computational science
Nonlinear elasticity problems are more challenging both theoretically and computationally. For these, the most popular finite element method involves compressible or nearly incompressible materials and uses first-order isoparametric finite elements and a standard Newton's algorithm. More sophisticated approaches involve incompressible models, higher-order elements and adaptive mesh refinement. These methods are very expensive for three-dimensional complex geometries, but are relevant for industrial and biological applications where large deformations are expected (although for biological materials, constitutive modelling is another open challenge).
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