We present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.
In finite element simulations, not all of the data are of equal importance. In fact, the primary purpose of a numerical study is often to accurately assess only one or two engineering output quantities that can be expressed as functionals. Adjoint-based error estimation provides a means to approximate the discretization error in functional quantities and mesh adaptation provides the ability to control this discretization error by locally modifying the finite element mesh. In the past, adjoint-based error estimation has only been accessible to expert practitioners in the field of solid mechanics. In this work, we present an approach to automate the process of adjoint-based error estimation and mesh adaptation on parallel machines. This process is intended to lower the barrier of entry to adjoint-based error estimation and mesh adaptation for solid mechanics practitioners. We demonstrate that this approach is effective for example problems in Poisson’s equation, nonlinear elasticity, and thermomechanical elastoplasticity.
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.