A method for determining elastic constants and boundary conditions of three-dimensional hyperelastic materials

Identification of force loadings on the inner circumference of a finite‐length elastic cylinder

“…Making use of the method of homogeneous solutions developed on the basis of the biharmonic Love function along with a variational approach engaging the least-square fitting, the problem was reduced to an infinite system of linear algebraic Equations that appeared to be similar to the one obtained for the direct problem discussed by Сhekurin and Postolaki [38]. In view of the zero-asymptotic of the coefficients system (22), the simple reduction method has been used in order to derive the corresponding finite system (23). The key advantage of this algorithm is that reduced system ( 23) is of the same type as the one for the direct problem and thus provides stable solution, which was verified by the numerical case studies implementing small noise into the input data for the inverse problem.…”

“…Recently, Xu et al [21] presented a FEMbased approach for solving 3D inverse problems on determining Young's modulus and unknown loading on a part of the surface of a linearly elastic solid. For hyperelastic materials, this approach was presented by Xu et al [22]. A spatially onedimensional problem on the identification of transient linear force loading of a finite-length cylindrical rod was attempted by Vahterova and Fedotenkov [23] using the method of influence functions.…”

“…In view of the zero-asymptotic of the coefficients in system (22), it can be solved by implementing the simple reduction method [47] implying a finite number of terms in expressions (12). This leads to the following finite system of equations:…”

“…For hyperelastic materials, this approach was presented by Xu et al. [22]. A spatially one‐dimensional problem on the identification of transient linear force loading of a finite‐length cylindrical rod was attempted by Vahterova and Fedotenkov [23] using the method of influence functions.…”

Clamping force prediction based on deep spatio-temporal network for machining process of deformable parts

“…Other researchers have viewed force identification or load distribution identification as an inverse problem, such as Liaghat et al 18 modeled the inverse problem of load distribution identification as an optimization problem, proposed an efficient iterative inverse process for identifying the load distribution leading to a specific crack expansion path in fractured members. Xu et al 19 proposed a novel inverse method based on two different objective functions for identifying the unknown elastic constants and boundary conditions of three-dimensional hyperelastic materials. Nevertheless, the mechanistic analysis clearly indicates which factors affect the complex physical process.…”