RESEARCH ON DEFORMATION OF HYPERELASTIC MATERIALS BASED ON A NEW VIRTUAL ELEMENT METHOD

The virtual element method is an advanced numerical method for solving solid mechanics problems. In the past ten years, the numerical method has been widely developed and applied in linear elasticity problems. This work attempts to give a general high-order virtual element method format that can be used to calculate hyperelastic problems and more general nonlinear problems. Different from the traditional virtual element method for solving mechanical problems, its main idea is to solve the projection operator for the Poisson equation and use the projection operator directly for the approximation of the displacement field, so that it can solve many nonlinear mechanical problems. Since the projection operator of the scalar field is used to approximate the vector field, the method has a simple format and can be easily extended to high-order formats or three-dimensional problems. This work will start from the Poisson equation and introduce the calculation method of the elliptical projection operator in the virtual element method. On this basis, the specific format of the virtual element method in solving hyperelastic problems will be derived in detail, and the calculation of the tangent stiffness matrix will be given. Finally, this paper gives several typical hyperelastic numerical examples to prove the effectiveness of the virtual element method format.