S-IGA with Consistent Jacobian-Based Formulation for Finite Strain Elastoplasticity
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This presentation introduces a consistent Jacobian-based formulation for applying S-IGA (s-version isogeometric analysis) to finite strain elastoplasticity. IGA, based on NURBS functions, has been proposed as a high-precision numerical analysis method that may be an alternative to the popular finite element method. In fracture mechanics, S-FEM (s-version finite element method) has been proposed as a flexible and efficient modelling technique. Adopting the concept of S-FEM, S-IGA can easily represent local features such as circular holes and cracks. Furthermore, the higher-order continuity of its basis functions is expected to reduce errors in integrating the coupling stiffness matrix. In applications to elastoplasticity, however, integration errors in evaluating internal forces and consistent tangent stiffness are a significant challenge for S-FEM. To address this, integration schemes using recursive mesh subdivision and octree meshes have been studied. However, these approaches can increase computational cost and memory usage. Therefore, we have introduced S-IGA using blending functions. Preliminary numerical tests suggest that unifying integration elements with blending functions yields quadratic convergence and high accuracy in small strain elastoplasticity. Nevertheless, extending this to finite strain problems has remained a challenge. In this study, we address the finite strain formulation by reformulating the Jacobian in S-IGA using mapping tensors defined on both initial global and local configurations. This formulation allows for the evaluation of a consistent B-matrix associated with shape updates. Numerical examples demonstrate the effectiveness of the proposed method, confirming that quadratic convergence of the Newton-Raphson method and high-precision results are achieved even in finite strain problems. Finally, we summarize the current status and future outlook of this research.
