A mathematical model is established to describe a contact problem between a deformable body and a foundation. The contact is bilateral and modelled with a nonlocal friction law, in which adhesion is taken into account...A mathematical model is established to describe a contact problem between a deformable body and a foundation. The contact is bilateral and modelled with a nonlocal friction law, in which adhesion is taken into account. Evolution of the bonding field is described by a first-order differential equation. The materials behavior is modelled with a nonlinear viscoelastic constitutive law. A variational formulation of the mechanical problem is derived, and the existence and uniqueness of the weak solution can be proven if the coefficient of friction is sufficiently small. The proof is based on arguments of time-dependent variational inequalities, differential equations, and the Banach fixed-point theorem.展开更多
The nonlocal friction law proposed by Oden et al. was adopted in order to consider the nonlocal friction effect of the asperities on the rough contact surface between the die and the workpiece in several kinds of meta...The nonlocal friction law proposed by Oden et al. was adopted in order to consider the nonlocal friction effect of the asperities on the rough contact surface between the die and the workpiece in several kinds of metal plastic forming problems. The mechanical equilibrium equations with the integral-differential form were obtained by using the engineering method or slab method, and solved approximately by using the perturbation method. The normal stress distributions on the contact surfaces in metal forming problems with nonlocal friction were obtained, and the factors which affect the nonlocal friction effect were analyzed.展开更多
We deal with a variational inequality describing the motion of incompressible fluids, whose viscous stress tensors belong to the subdifferential of a functional at the point given by the symmetric part of the velocity...We deal with a variational inequality describing the motion of incompressible fluids, whose viscous stress tensors belong to the subdifferential of a functional at the point given by the symmetric part of the velocity gradient, with a nonlocal friction condition on a part of the boundary obtained by a generalized mollification of the stresses. We establish an existence result of a solution to the nonlocal friction problem for this class of non-Newtonian flows. The result is based on the Faedo-Galerkin and Moreau Yosida methods, the duality theory of convex analysis and the Tychonov-Kakutani-Glicksberg fixed point theorem for multi-valued mappings in an appropriate functional space framework.展开更多
A steady-state, rigid-plastic rolling problem for temperature and strain-rate dependent materials with nonlocal friction is considered. A variational formulation is derived, coupling a nonlinear variational inequality...A steady-state, rigid-plastic rolling problem for temperature and strain-rate dependent materials with nonlocal friction is considered. A variational formulation is derived, coupling a nonlinear variational inequality for the velocity and a nonlinear vari- ational equation for the temperature. The existence and uniqueness results are obtained by a proposed fixed point method.展开更多
A class of quasisteady metalforming problems under nonlocal contact and Coulomb＇s friction boundary conditions is considered with an incompressible, rigid plastic, strainrate dependent, isotropic, and kinematic harde...A class of quasisteady metalforming problems under nonlocal contact and Coulomb＇s friction boundary conditions is considered with an incompressible, rigid plastic, strainrate dependent, isotropic, and kinematic hardening material model. A coupled variational formulation is derived, the convergence of a variable stiffness parame ter method with time retardation is proved, and the existence and uniqueness results are obtained.展开更多
We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation.A non linear electro-elastic constitutive law is used to model the piezoelectric ...We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation.A non linear electro-elastic constitutive law is used to model the piezoelectric material.The unilateral contact is modelled using the Signorini condition,nonlocal Coulomb friction law with slip dependent friction coefficient and a regularized electrical conductivity condition.Existence and uniqueness of a weak solution is established.A finite elements approximation of the problem is presented,a priori error estimates of the solutions are derived and a convergent successive iteration technique is proposed.展开更多
A class of steady-state metal-forming problems,with rigid-plastic,incompressible,strain-rate dependent material model and nonlocal Coulomb’s friction,is considered.Primal,mixed and penalty variational formulations,co...A class of steady-state metal-forming problems,with rigid-plastic,incompressible,strain-rate dependent material model and nonlocal Coulomb’s friction,is considered.Primal,mixed and penalty variational formulations,containing variational inequalities with nonlinear and nondifferentiable terms,are derived and studied.Existence,uniqueness and convergence results are obtained and shortly presented.A priori finite element error estimates are derived and an algorithm,combining the finite element and secant-modulus methods,is utilized to solve an illustrative extrusion problem.展开更多
文摘A mathematical model is established to describe a contact problem between a deformable body and a foundation. The contact is bilateral and modelled with a nonlocal friction law, in which adhesion is taken into account. Evolution of the bonding field is described by a first-order differential equation. The materials behavior is modelled with a nonlinear viscoelastic constitutive law. A variational formulation of the mechanical problem is derived, and the existence and uniqueness of the weak solution can be proven if the coefficient of friction is sufficiently small. The proof is based on arguments of time-dependent variational inequalities, differential equations, and the Banach fixed-point theorem.
文摘The nonlocal friction law proposed by Oden et al. was adopted in order to consider the nonlocal friction effect of the asperities on the rough contact surface between the die and the workpiece in several kinds of metal plastic forming problems. The mechanical equilibrium equations with the integral-differential form were obtained by using the engineering method or slab method, and solved approximately by using the perturbation method. The normal stress distributions on the contact surfaces in metal forming problems with nonlocal friction were obtained, and the factors which affect the nonlocal friction effect were analyzed.
基金Partial support, from FCT research programme POCTI(Portugal/FEDER-EU).
文摘We deal with a variational inequality describing the motion of incompressible fluids, whose viscous stress tensors belong to the subdifferential of a functional at the point given by the symmetric part of the velocity gradient, with a nonlocal friction condition on a part of the boundary obtained by a generalized mollification of the stresses. We establish an existence result of a solution to the nonlocal friction problem for this class of non-Newtonian flows. The result is based on the Faedo-Galerkin and Moreau Yosida methods, the duality theory of convex analysis and the Tychonov-Kakutani-Glicksberg fixed point theorem for multi-valued mappings in an appropriate functional space framework.
文摘A steady-state, rigid-plastic rolling problem for temperature and strain-rate dependent materials with nonlocal friction is considered. A variational formulation is derived, coupling a nonlinear variational inequality for the velocity and a nonlinear vari- ational equation for the temperature. The existence and uniqueness results are obtained by a proposed fixed point method.
文摘A class of quasisteady metalforming problems under nonlocal contact and Coulomb＇s friction boundary conditions is considered with an incompressible, rigid plastic, strainrate dependent, isotropic, and kinematic hardening material model. A coupled variational formulation is derived, the convergence of a variable stiffness parame ter method with time retardation is proved, and the existence and uniqueness results are obtained.
文摘We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation.A non linear electro-elastic constitutive law is used to model the piezoelectric material.The unilateral contact is modelled using the Signorini condition,nonlocal Coulomb friction law with slip dependent friction coefficient and a regularized electrical conductivity condition.Existence and uniqueness of a weak solution is established.A finite elements approximation of the problem is presented,a priori error estimates of the solutions are derived and a convergent successive iteration technique is proposed.
文摘A class of steady-state metal-forming problems,with rigid-plastic,incompressible,strain-rate dependent material model and nonlocal Coulomb’s friction,is considered.Primal,mixed and penalty variational formulations,containing variational inequalities with nonlinear and nondifferentiable terms,are derived and studied.Existence,uniqueness and convergence results are obtained and shortly presented.A priori finite element error estimates are derived and an algorithm,combining the finite element and secant-modulus methods,is utilized to solve an illustrative extrusion problem.
