A novel test configuration design method for inverse identification of in‐plane moduli of a composite plate under the PFEUM framework

We propose a novel sensitivity based approach that predicts and explains the accuracy of material parameter identification for a composite plate using the Projected Finite Element Update Method. A typical experiment using the Projected Finite Element Update Method technique involves a plate specimen held at 3 or 4 supports and bent under the application of a point load. Two‐Dimensional Digital Image Correlation is used to measure the pseudo displacements resulting from the projection of out‐of‐plane deflection of the plate onto the image plane. A cost function relating the projected numerical and experimental displacement fields is then minimised to obtain the material parameters. It is shown that the contribution of a specific material parameter in the observed displacement field influences the accuracy of its identification. The contributions from material parameters are first quantified in terms of sensitivity criterion that may be tailored by changing the elements of test configuration such as location of supports, the load application point, and the specimen geometry. Several test configurations are designed by maximising the sensitivities corresponding to individual material parameters. The relevance of proposed sensitivity criterion in these configurations is then validated through material identification in simulated experiments with added Gaussian noise. Finally, a thin CFRP plate is tested under these configurations to demonstrate the practical use of this approach. The proposed approach helps in robust estimation of the in‐plane elastic moduli from a bent composite plate with a simple Two‐Dimensional Digital Image Correlation setup without requiring measurement of the actual plate deflection or curvatures.     

Towards Material Testing 2.0. A review of test design for identification of constitutive parameters from full‐field measurements

Full‐field optical measurements like digital image correlation or the grid method have brought a paradigm shift in the experimental mechanics community. While inverse identification techniques like finite element model updating or the virtual fields method have been the object of significant developments, current test methods, inherited from the age of strain gauges or linear variable displacement transducers, are generally not well adapted to the rich information provided by these new measurement tools. This paper provides a review of the research dealing with the design and optimization of heterogeneous mechanical tests for the identification of material parameters from full‐field measurements, christened here Material Testing 2.0 (MT2.0).     

Global 2D digital image correlation for motion estimation in a finite element framework: a variational formulation and a regularized,pyramidal, multi‐grid implementation

In this study, the inverse problem of reconstructing the in‐plane (2D) displacements of a monitored surface through a sequence of two‐dimensional digital images, severely ill‐posed in Hadamard's sense, is deeply investigated. A novel variational formulation is presented for the continuum 2D digital image correlation problem, and critical issues such as semi‐coercivity and solution multiplicity are discussed by functional analysis tools. In the framework of a Galerkin, finite element discretization of the displacement field, a robust implementation for 2D digital image correlation is outlined, aiming to attenuate the spurious oscillations which corrupt the deformation scenario, especially when very fine meshes are adopted. Recourse is made to a hierarchical family of grids linked by suitable restriction and prolongation operators and defined over an image pyramid. Multi‐grid cycles are performed ascending and descending along the pyramid, with only one Newton iteration per level irrespective of the tolerance satisfaction, as if the problem were linear. At each level, the conventional least‐square matching functional is herein enriched by a Tychonoff regularization provision, preserving the solution against an unstable response. The algorithm is assessed on the basis of both synthetic and truly experimental image pairs. Copyright © 2013 John Wiley & Sons, Ltd.     

A second‐order decoupled implicit/explicit method of the 3D primitive equations of ocean II: finite element spatial discretization

A fully discrete second‐order decoupled implicit/explicit method is proposed for solving 3D primitive equations of ocean in the case of Dirichlet boundary conditions on the side, where a second‐order decoupled implicit/explicit scheme is used for time discretization, and a finite element method based on the P₁(P₁) ? P₁?P₁(P₁) elements for velocity, pressure and density is used for spatial discretization of these primitive equations. Optimal H¹?L²?H¹ error estimates for numerical solution and an optimal L² error estimate for are established under the convergence condition of 0 < h≤β₁,0 < τ≤β₂, and τ≤β₃h for some positive constants β₁,β₂, and β₃. Furthermore, numerical computations show that the H¹?L²?H¹ convergence rate for numerical solution is of O(h + τ²) and an L² convergence rate for is O(h²+τ²) with the assumed convergence condition, where h is a mesh size and τ is a time step size. More practical calculations are performed as a further validation of the numerical method. Copyright © 2016 John Wiley & Sons, Ltd.