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We propose a mathematical model and a numerical scheme to describe compaction processes in a sedimentary rock layer undergoing both mechanical and geochemical processes. We simulate the sedimentation process by providing a sedimentation rate, and we account for chemical reactions using simplified kinetics describing either the conversion of a solid matrix into a fluid, as in the case of kerogen degradation into oil, or the precipitation of a mineral solute on the solid matrix of the rock. We use a Lagrangian description that enables to recast the equations in a fixed frame of reference. We present an iterative splitting scheme that allows solving the set of governing equations efficiently in a sequential manner. We assess the performances of this strategy in terms of convergence and mass conservation. Some numerical experiments show the capability of the scheme to treat two test cases, one concerning the precipitation of a mineral, the other the dissolution of kerogen. [ABSTRACT FROM AUTHOR]

Slender beams are often employed as constituents in engineering materials and structures. Prior experiments on lattices of slender beams have highlighted their complex failure response, where the interplay between buckling and fracture plays a critical role. In this paper, we introduce a novel computational approach for modeling fracture in slender beams subjected to large deformations. We adopt a state-of-the-art geometrically exact Kirchhoff beam formulation to describe the finite deformations of beams in three-dimensions. We develop a discontinuous Galerkin finite element discretization of the beam governing equations, incorporating discontinuities in the position and tangent degrees of freedom at the inter-element boundaries of the finite elements. Before fracture initiation, we enforce compatibility of nodal positions and tangents weakly, via the exchange of variationally-consistent forces and moments at the interfaces between adjacent elements. At the onset of fracture, these forces and moments transition to cohesive laws modeling interface failure. We conduct a series of numerical tests to verify our computational framework against a set of benchmarks and we demonstrate its ability to capture the tensile and bending fracture modes in beams exhibiting large deformations. Finally, we present the validation of our framework against fracture experiments of dry spaghetti rods subjected to sudden relaxation of curvature. [ABSTRACT FROM AUTHOR]