Mixed displacement-pressure-phase field framework for finite strain fracture of nearly incompressible hyperelastic materials

The favored phase field method (PFM) has encountered challenges in the finite strain fracture modeling of nearly or truly incompressible hyperelastic materials. We identified that the underlying cause lies in the innate contradiction between incompressibility and smeared crack opening. Drawing on the stiffness-degradation idea in PFM, we resolved this contradiction through loosening incompressible constraint of the damaged phase without affecting the incompressibility of intact material. By modifying the perturbed Lagrangian approach, we derived a novel mixed formulation. In numerical aspects, the finite element discretization uses the classical Q1/P0 and high-order P2/P1 schemes, respectively. To ease the mesh distortion at large strains, an adaptive mesh deletion technology is also developed. The validity and robustness of the proposed mixed framework are corroborated by four representative numerical examples. By comparing the performance of Q1/P0 and P2/P1, we conclude that the Q1/P0 formulation is a better choice for finite strain fracture in nearly incompressible cases. Moreover, the numerical examples also show that the combination of the proposed framework and methodology has vast potential in simulating complex peeling and tearing problem

Numerical calculation of free-energy barriers for entangled polymer nucleation.

The crystallization of entangled polymers from their melt is investigated using computer simulation with a coarse-grained model. Using hybrid Monte Carlo simulations enables us to probe the behavior of long polymer chains. We identify solid-like beads with a centrosymmetry local order parameter and compute the nucleation free-energy barrier at relatively high supercooling with adaptive-bias windowed umbrella sampling. Our results demonstrate that the critical nucleus sizes and the heights of free-energy barriers do not significantly depend on the molecular weight of the polymer; however, the nucleation rate decreases with the increase in molecular weight. Moreover, an analysis of the composition of the critical nucleus suggests that intra-molecular growth of the nucleated cluster does not contribute significantly to crystallization for this system.National Key R&D Program of China (2016YFB0302500); National Natural Science Foundation of China (51633009); Royal Society Newton Mobility Grant (MBAG/240 RG82754

Absolute stability of time-varying delay Lurie indirect control systems with unbounded coefficients

This paper investigates the absolute stability problem of time-varying delay Lurie indirect control systems with variable coefficients. A positive-definite Lyapunov-Krasovskii functional is constructed. Some novel sufficient conditions for absolute stability of Lurie systems with single nonlinearity are obtained by estimating the negative upper bound on its total time derivative. Furthermore, the results are generalised to multiple nonlinearities. The derived criteria are especially suitable for time-varying delay Lurie indirect control systems with unbounded coefficients. The effectiveness of the proposed results is illustrated using simulation examples

Permeability Change Caused by Stress Damage of Gas Shale

Stress damage of shale during the uniaxial loading process will cause the change of permeability. The study of stress sensitivity of shale has focused on the influence of confining pressure on shale permeability and the change of shale permeability during the loading process of axial stress is lacking. The permeability of gas shale during loading process was tested. The results show that shale damage macroscopically reflects the process of axial micro-cracks generation and expansion, and the axial micro-cracks will cause permeability change during the loading process. There is a good corresponding relationship between damage development and micro-crack expansion during the process of shale loading. The damage factor will increase in the linear elastic stage and enlarge rapidly after entering the stage of unstable micro-crack expansion, and the permeability of shale increases with the increasing of shale damage. The research results provide a reliable test basis for further analysis of the borehole instability and hydraulic fracture mechanisms in shale gas reservoirs