We introduce an improved position-based dynamics method with corrected smoothed particle hydrodynamics (SPH) kernel to simulate deformable solids. Using a strain energy constraint that follows the continuum mechanics, the method can maintain the efficiency and stability of the position-based approach while improving the physical plausibility of the simulation. We can easily simulate the behavior of anisotropic and plastic materials because the method is based on physics. Unlike the previous position-based simulations of continuous materials, we use weakly structured particles to discretize the model for the convenience of deformable object cutting. In this case, a corrected SPH kernel function is adopted to measure the deformation gradient and calculate the strain energy on each particle. We also propose a solution for the interparticle inversion and penetration in large deformation. To perform complex interaction scenarios, we provide a simple method for collision detection. We demonstrate the flexibility, efficiency, and robustness of the proposed method by simulating various scenes, including anisotropic elastic deformation, plastic deformation, model cutting, and large-scale elastic collision.