We use the augmented Lagrangian formalism to derive discontinuous Galerkin formulations for problems in nonlinear elasticity. In elasticity stress is typically a symmetric function of strain, leading to symmetric tangent stiffness matrices in Newtons method when conforming finite elements are used for discretization. By use of the augmented Lagrangian framework, we can also obtain symmetric tangent stiffness matrices in discontinuous Galerkin methods. We suggest two different approaches and give examples from plasticity and from large deformation hyperelasticity.

翻译：在弹性压力中,弹性压力通常是压力的对称函数,在牛顿斯方法中,当对齐的定点元素被用于分解时,导致牛顿斯法中对齐的正正正度硬度矩阵。通过使用增强的拉格朗加框架,我们还可以在不连续的加勒金方法中获取对齐的正正度硬度矩阵。我们建议采取两种不同的方法,并举例说明可塑性和大规模变形超弹性。