Using parabolic maximum principle, we apply the analytic method to obtain lower comparison inequalities for non-negative weak supersolutions of the heat equation associated with a regular strongly p-local Dirichlet fo...Using parabolic maximum principle, we apply the analytic method to obtain lower comparison inequalities for non-negative weak supersolutions of the heat equation associated with a regular strongly p-local Dirichlet form on the abstract metric measure space. As an application we obtain lower estimates for heat kernels on some Riemannian manifolds.展开更多
A large number of criteria has been developed to predict material instabilities, but their choice is limited by the lack of existing comparison of their theoretical basis and application domains. To overcome this limi...A large number of criteria has been developed to predict material instabilities, but their choice is limited by the lack of existing comparison of their theoretical basis and application domains. To overcome this limitation, a theoretical and numerical comparison of two major models used to predict diffuse necking is present in this paper. Limit Point Bifurcation criterion is first introduced. An original formulation of the Maximum Force Criterion (MFC), taking into account the effects of damage and isotropic and kinematic hardenings, is then proposed. Strong connections are shown between them by comparing their theoretical basis. Numerical Forming Limit Diagrams at diffuse necking obtained with these criteria for different metallic materials are given. They illustrate the theoretical link and similar predictions are shown for both models.展开更多
文摘Using parabolic maximum principle, we apply the analytic method to obtain lower comparison inequalities for non-negative weak supersolutions of the heat equation associated with a regular strongly p-local Dirichlet form on the abstract metric measure space. As an application we obtain lower estimates for heat kernels on some Riemannian manifolds.
文摘A large number of criteria has been developed to predict material instabilities, but their choice is limited by the lack of existing comparison of their theoretical basis and application domains. To overcome this limitation, a theoretical and numerical comparison of two major models used to predict diffuse necking is present in this paper. Limit Point Bifurcation criterion is first introduced. An original formulation of the Maximum Force Criterion (MFC), taking into account the effects of damage and isotropic and kinematic hardenings, is then proposed. Strong connections are shown between them by comparing their theoretical basis. Numerical Forming Limit Diagrams at diffuse necking obtained with these criteria for different metallic materials are given. They illustrate the theoretical link and similar predictions are shown for both models.
