The constitutive relation of Skorohod and Olevsky for viscous sintering is utilized to model the shrinkage and relative density evolution during the sintering process of ceramics. A new implicit integration scheme is presented and implemented. The computational cost is drastically reduced by combining this integration scheme with a solid-like shell element formulation, which also enables a faster and more accurate description of shape distortions, especially for thin geometries. The characterization and identification of the material viscosity is also improved via the Aquilanti–Mundim deformed Arrhenius description. The model robustness is examined with a spectrum of benchmark tests: ZnO sintering experiments from previous studies, as well as new lanthanum tungstate sintering tests. The model predictions for both dimensional shrinkage and relative density evolution are very accurate using the newly proposed material viscosity functions. The model improvements offer the possibility to simulate long-time sintering processes with higher accuracy and significantly reduced computational efforts.

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In this paper, we present a two dimensional model for modelling the hydraulic fracture process in anisotropic and heterogeneous rocks. The model is formulated using extended finite elements (XFEM) in combination with Newton-Raphson method for spatial and Euler's implicit scheme for time. The fracture is modelled with the help of cohesive zone method (CZM). Anisotropy arising due to orientation of grains in a specific direction in rocks is modelled to understand the influence of the degree of anisotropy and the grain orientation direction on fracture propagation. A combination of Tsai-Hill failure criterion and Camacho-Ortiz propagation criteria is used to predict mixed mode fracture propagation in anisotropic media. Effect of heterogeneities due to material inclusions, on fractures are modelled.@en

Plastic size effects in single crystals are investigated by using finite strain and small strain discrete dislocation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip systems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete dislocation plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. However, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bending stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations.

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