Abstract

Abstract

This article presents the first application of the Finite Calculus (FIC) in a Ritz-FEM variational framework. FIC provides a steplength parametrization of mesh dimensions, which is used to modify the shape functions. This approach is applied to the FEM discretization of the steady-state, one-dimensional, diffusion–absorption and Helmholtz equations. Parametrized linear shape functions are directly inserted into a FIC functional. The resulting Ritz-FIC equations are symmetric and carry a element-level free parameter coming from the function modification process. Both constant- and variable-coefficient cases are studied. It is shown that the parameter can be used to produce nodally exact solutions for the constant coefficient case. The optimal value is found by matching the finite-order modified differential equation (FOMoDE) of the Ritz-FIC equations with the original field equation. The inclusion of the Ritz-FIC models in the context of templates is examined. This inclusion shows that there is an infinite number of nodally exact models for the constant coefficient case. The ingredients of these methods (FIC, Ritz, MoDE and templates) can be extended to multiple dimensions

Abstract

This article presents the first application of the Finite Calculus (FIC) in a Ritz-FEM variational framework. FIC provides a steplength parametrization of mesh dimensions, which is used to modify the shape functions. This approach is applied to the FEM discretization of the steady-state, one-dimensional, diffusion–absorption and Helmholtz equations. Parametrized linear shape functions are directly inserted into a FIC functional. The resulting Ritz-FIC equations are symmetric and carry a element-level free parameter coming from the function modification process. Both constant- and variable-coefficient cases are studied. It is shown that the parameter can be used to produce nodally exact solutions for the constant coefficient case. The optimal value is found by matching the finite-order modified differential equation (FOMoDE) of the Ritz-FIC equations with the original field equation. The inclusion of the Ritz-FIC models in the context of templates is examined. This inclusion shows that there is an infinite number of nodally exact models for the constant coefficient case. The ingredients of these methods (FIC, Ritz, MoDE and templates) can be extended to multiple dimensions

Abstract

To evaluate the feasibility of the safe use of existing gas grids for the transport and storage of hydrogen gas, the phenomenon of hydrogen assisted degradation of steel used in the pipeline grid has to be examined. A finite element based framework developed for describing this phenomenon at the continuum scale is used to assist in the design and analysis of experimental characterisation of the tearing resistance. The framework is based on the complete Gurson model for ductile damage and takes into account damage acceleration due to the local hydrogen concentration, and the diffusion of hydrogen. Simulations representing single edge notched tension (SENT) fracture toughness tests of an API 5L X70 grade steel are performed and results are discussed in terms of crack growth resistance curves. Side grooves are included in the geometry of the SENT model to promote uniform crack growth. Different boundary conditions are employed, simulating ex-situ and in-situ hydrogen charging of specimens. Moreover, the effect of the applied deformation rate on the dynamics of hydrogen diffusion and the resulting toughness values is investigated. Accordingly, guidance regarding experimental SENT testing for the hydrogen assisted tearing resistance degradation is provided, in terms of test conditions (in-situ/ex-situ) and deformation rate.

Abstract

Enabling and establishing both an understanding and simulation of the process of environment-induced damage are crucial for the prediction of remaining service life of engineering structures and components, sound reliability analysis, and design for the purpose of enhancing overall resistance of the material to environment-induced damage. A fully coupled mechano-chemical peridynamic (PD) model for environment-induced degradation or corrosion was established by using both the peridynamic corrosion theory and the mechano-chemical effect theory. The model is capable of simulating the occurrence of degradation caused by the conjoint and mutually interactive influences of mechano-chemical phenomena. Both in-situ electrochemical tests and stress corrosion cracking tests were carried out, and the test results used to explore the effects of stress and/or load on the kinetics of environment-induced damage to an aluminum alloy. The model predictions are in good agreement with the experimental observations. Results of this novel research study demonstrate that the fully coupled mechano-chemical peridynamic corrosion model can capture the environment-induced damage and can be used to study propagation and/or growth of the damage upon exposure to an aggressive environment.