Advanced Scaled Boundary Finite Element Framework for Complex and Biological Materials

Dec 20, 2025
NL-SBFEM framework

Description This project focuses on the development of the Scaled Boundary Finite Element Method (SBFEM) for complex material behavior, extending the classical formulation to nonlinear, viscoelastic, and anisotropic hyperelastic responses. The framework preserves the boundary-only discretization of SBFEM while enabling robust treatment of material and geometric nonlinearities.

Key Contributions

  • Nonlinear SBFEM (NL-SBFEM) formulation for large deformations.
  • Viscoelastic SBFEM for time-dependent material response.
  • Modular material interface enabling automatic differentiation.
  • Extension to anisotropic hyperelastic models for soft tissues.

Biomechanics Focus

The final objective is biomechanical modeling of soft tissues, particularly fiber-reinforced materials relevant to ligaments, tendons, and vascular tissues, avoiding volumetric meshing while retaining high accuracy.

Numerical Methods SBFEM Nonlinear Solid Mechanics Viscoelasticity Biomechanics

Publications

NL-SBFEM: A pure SBFEM formulation for geometrically and materially nonlinear problems
A novel nonlinear SBFEM formulation preserving its advantages without hybrid methods.
Seyed Sadjad Abedi-Shahri, Farzan Ghalichi, Iman Zoljanahi Oskui
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A Scaled Boundary Finite Element Formulation for Solving Plane-Strain Viscoelastic Problems
A new scaled boundary finite element formulation is developed to solve plane-strain viscoelastic problems. The scaled boundary finite element formulation for plane-stress viscoelastic problems is also presented in the appendix.
Seyed Sadjad Abedi-Shahri, Farzan Ghalichi, Iman Zoljanahi Oskui
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