Numerical analysis of history-dependent hemivariational inequalities and applications to viscoelastic contact problems with normal penetration

In this paper numerical approximation of history-dependent hemivariational inequalities with constraint is considered, and corresponding Céa’s type inequality is derived for error estimate. For a viscoelastic contact problem with normal penetration, an optimal order error estimate is obtained for the linear element method. A numerical experiment for the contact problem is reported which provides numerical evidence of the convergence order predicted by the theoretical analysis.     

Cost-based optimal history-dependent inspection strategy for random fatigue crack growth

Optimal inspection time for random fatigue crack growth is theoretically investigated based upon cost-minimization, by the use of a diffusive crack growth model. Assuming that a component is immediately replaced if a crack is detected by the inspection, we discuss a method to decide the optimal inspection schedule for a history-dependent strategy and newly propose an approximation method to derive it easily. By comparing the inspection schedule derived by the method with the optimal one through numerical calculations, we verify the appropriateness of it.     

History-dependent scheduling: Models and algorithms for scheduling with general precedence and sequence dependence

In this paper, we extend job scheduling models to include aspects of history-dependent scheduling, where setup times for a job are affected by the aggregate activities of all predecessors of that job. Traditional approaches to machine scheduling typically address objectives and constraints that govern the relative sequence of jobs being executed using available resources. This paper optimises the operations of multiple unrelated resources to address sequential and history-dependent job scheduling constraints along with time window restrictions. We denote this consolidated problem as the general precedence scheduling problem (GPSP). We present several applications of the GPSP and show that many problems in the literature can be represented as special cases of history-dependent scheduling. We design new ways to model this class of problems and then proceed to formulate it as an integer program. We develop specialized algorithms to solve such problems. An extensive computational analysis over a diverse family of problem data instances demonstrates the efficacy of the novel approaches and algorithms introduced in this paper.     

Dendrite Spacing Selection during Directional Solidification of Pivalic Acid-Ethanol System

Unidirectional solidification of pivalic acid （PVA）-ethanol （Eth） mixture was performed to examine whether an allowable range of primary dendrite spacing definitely exists at a given growth velocity and how the range is history-dependent. PVA-0.59 wt pct Eth was unidirectionally solidified in the range of growth velocity 0.5-64 μm/s at the temperature gradient of 2.3 K/ram. Sequential change in growth velocity was imposed to determine the upper and lower limits for the allowable range of stable spacing. An allowable range of the steady state primary spacing was observed at a given growth velocity, and the extent of the range seems to be dependent on the degree to which step-increase or step-decrease in growth velocity is accomplished. As the degree of sequential change in growth velocity increases, the history-dependence of the selection for the primary dendrite spacing tends to disappear.     

A penalty method for history-dependent variational–hemivariational inequalities

Penalty methods approximate a constrained variational or hemivariational inequality problem through a sequence of unconstrained ones as the penalty parameter approaches zero. The methods are useful in the numerical solution of constrained problems, and they are also useful as a tool in proving solution existence of constrained problems. This paper is devoted to a theoretical analysis of penalty methods for a general class of variational–hemivariational inequalities with history-dependent operators. Unique solvability of penalized problems is shown, as well as the convergence of their solutions to the solution of the original history-dependent variational–hemivariational inequality as the penalty parameter tends to zero. The convergence result proved here generalizes several existing convergence results of penalty methods. Finally, the theoretical results are applied to examples of history-dependent variational–hemivariational inequalities in mathematical models describing the quasistatic contact between a viscoelastic rod and a reactive foundation.     

Out-of-phase thermo-mechanical coupling behavior of proton exchange membranes

The thermal effects and mechanical effects on the durability of proton exchange membranes (PEMs) have been studied extensively in the literatures. However researches on the thermo-mechanical coupling behavior of PEMs are very limited. In this study, the interaction of mechanical and thermal effects in Nafion^® NRE-212 was investigated using experimental methods. The thermo-mechanical coupling experiments were conducted following the in-phase proportional loading path, where the maximum/minimum mechanical loads and temperatures occur simultaneously and out-of-phase non-proportional rectangular loading paths where a phase difference of 90° existed between thermal and mechanical loads. During the creep processes under a variable temperature in out-phase profiles, the creep strain was found to be history-dependent in the membrane. The effect of initial temperature on the creep was significant in the first cycle. Moreover, temperature cycles were applied as thermal loading conditions and the history-dependence was also observed for thermal stresses. The maximum thermal stress did not occur at the lowest temperature.     

Effect of deformation-dependent material parameters on forming limits of thin sheets

Material properties are deformation history dependent. To take this fact into consideration in forming limit analysis, the material parameters are defined as functions of strain using the Voce equation. These history-dependent material parameters are incorporated in the M–K analysis based on Hill's 1993 yield criterion in which all material parameters are independent, so that the effect of each of these history-dependent parameters on forming limits can be investigated individually. The analysis shows that history-dependent material properties have a significant influence on forming limits. An increasing r-value will increase the limit strain under plane strain (FLD₀), which is different from the traditional M–K analysis. Comparison of predicted results with experimental data illustrates that the consideration of history-dependent material properties can improve forming limit predictions considerably.