Scientific knowledge and engineering tools for predicting coastal erosion are largely confined to temperate climate zones that are dominated by non-cohesive sediments. The pattern of erosion exhibited by the ice-bonded permafrost bluffs in Arctic Alaska, however, is not well-explained by these tools. Investigation of the oceanographic, thermal, and mechanical processes that are relevant to permafrost bluff failure along Arctic coastlines is needed. We conducted physics-based numerical simulations of mechanical response that focus on the impact of geometric and material variability on permafrost bluff stress states for a coastal setting in Arctic Alaska that is prone to toppling mode block failure. Our three-dimensional geomechanical boundary-value problems output static realizations of compressive and tensile stresses. We use these results to quantify variability in the loci of potential instability. We observe that niche dimension affects the location and magnitude of the simulated maximum tensile stress more strongly than the bluff height, ice wedge polygon size, ice wedge geometry, bulk density, Young's Modulus, and Poisson's Ratio. Our simulations indicate that variations in niche dimension can produce radically different potential failure areas and that even relatively shallow vertical cracks can concentrate displacement within ice-bonded permafrost bluffs. These findings suggest that stability assessment approaches, for which the geometry of the failure plane is delineated a priori, may not be ideal for coastlines similar to our study area and could hamper predictions of erosion rates and nearshore sediment/biogeochemical loading.
Tetrahedral finite element workflows have the potential to drastically reduce time to solution for computational solid mechanics simulations when compared to traditional hexahedral finite element analogues. A recently developed, higher-order composite tetrahedral element has shown promise in the space of incompressible computational plasticity. Mesh adaptivity has the potential to increase solution accuracy and increase solution robustness. In this work, we demonstrate an initial strategy to perform conformal mesh adaptivity for this higher-order composite tetrahedral element using well-established mesh modification operations for linear tetrahedra. We propose potential extensions to improve this initial strategy in terms of robustness and accuracy.
This corrigendum clarifies the conditions under which the proof of convergence of Theorem 1 from the original article is valid. We erroneously stated as one of the conditions for the Schwarz alternating method to converge that the energy functional be strictly convex for the solid mechanics problem. We have relaxed that assumption and changed the corresponding parts of the text. None of the results or other parts of the original article are affected.
The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. To resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. In this study, the authors demonstrate the use of concurrent multiscale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J2 plasticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. In this study, the framework is applied to model incipient localization in tensile specimens during necking.