A stabilized discontinuous Galerkin method is developed for general hyperelastic materials at finite strains. Starting from a mixed method incorporating Lagrange multipliers along the interface, the displacement formulation is systematically derived through a variational multiscale approach whereby the numerical fine scales are modeled via edge bubble functions. Analytical expressions that are free from user-defined parameters arise for the weighted numerical flux and stability tensor. In particular, the specific form taken by these derived quantities naturally accounts for evolving geometric nonlinearity as well as discontinuous material properties. The method is applicable both to problems containing nonconforming meshes or different element types at specific interfaces and to problems consisting of fully discontinuous numerical approximations. Representative numerical tests involving large strains and rotations are performed to confirm the robustness of the method. FINITE STRAIN INTERFACE FORMULATION WITH EVOLVING STABILIZATION 279The key factors impacting the robustness and efficiency of the DG method are the design of the so-called numerical flux and the penalty or stabilization parameter. Regarding the penalty parameter, studies for embedded interface problems [5] as well as discontinuous discrete approximations [2,13] have shown that selecting a value outside of an optimal range leads to issues with accuracy and stability. Choosing a value that is too low leads to loss of coercivity and results in an ill-posed discrete problem. On the other hand, choosing a value that is too high leads to ill conditioning in the stiffness matrix as well as to overly strict enforcement of the displacement jump condition. When the jump condition is strictly enforced, the computed response approaches that of a continuous Galerkin method, and the rationale for employing DG is lost. Dimensional analyses indicate that the stability parameter is a function of the element geometry, polynomial order, material properties, and the local interface topology; however, its magnitude can be elusive. The classical approach in the context of linear problems is to estimate the parameter through eigenvalue analyses [14,15]. More recently, in the context of embedded interface problems [4], the values of the parameter for linear simplex elements were determined by conducting a mathematical analysis of the coercivity condition. In particular, definitions for the numerical flux and penalty parameter that involved a weighting of the element size and material properties across the interface emerged. In contrast, the standard definition for the numerical flux in DG methods [12] assumes an equal weighting of the flux field from each side of the interface, which is postulated based on the assumption of mesh uniformity. Other interface methods have previously employed either area weighting [16] or stiffness weighting [5] alone. Additional techniques for defining the penalty parameter for linear problems include developments using bubble functions [17,1...

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a b s t r a c tIn this work, algorithmic modifications are proposed and analyzed for a recently developed stabilized finite strain Discontinuous Galerkin (DG) method. The distinguishing feature of the original method, referred to as VMDG, is a consistently derived expression for the numerical flux and stability tensor that account for evolving material and geometric nonlinearity in the vicinity of the interface. Herein, the proposed modifications involve simplifications to the residual force vector and tangent stiffness matrix of the VMDG method that lead to formulations similar to other existing DG methods but retain the enhanced definition for the stability parameters. The primary objective is to reduce the costs associated with implementing the method as well as executing simulations while retaining accuracy and flexibility, thereby making the formulation amenable to boarder material classes such as inelasticity. Each simplification has associated implications on the mathematical and algorithmic properties of the method, such as L 2 convergence rate, solution accuracy, continuity enforcement, and stability of the nonlinear equation solver. These implications are carefully quantified and assessed through a comprehensive numerical performance study. The range of two and three dimensional problems under consideration involves both isotropic and anisotropic materials. Both triangular and quadrilateral element types are employed along with h and p refinement. The ability of the proposed methods to produce stable and accurate results for such a broad class of problems is highlighted.

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