On the Design of Innovative Heterogeneous Sheet Metal Tests Using a Shape Optimization Approach

Abstract

The development of full-field measurement methods has enabled a new trend of heterogeneous mechanical tests. The inhomogeneous strain fields retrieved from these tests are being widely used in the calibration of constitutive models for sheet metals. However, today, there is no mechanical test able to characterize the material in a large range of strain states. The aim of this work is to present a heterogeneous mechanical test with an innovative tool/specimen shape, capable of producing rich heterogeneous strain paths and thus providing extensive information on material behavior. The proposed specimen is found using a shape optimization process where an index that evaluates the richness of strain information is used. In this work, the methodology and results are extended to non-specimen geometry dependence and to the non-dependence of the geometry parametrization through the use of the Ritz method for boundary value problems. Different curve models, such as splines, B-splines, and NURBS, are used, and C1 continuity throughout the specimen is guaranteed. Moreover, several deterministic and stochastic optimization methods are used in order to find the method or the combination of methods able to minimize the cost function effectively. Results demonstrated that the solution is dependent on the geometry definition, as well as on the optimization methodology. Nevertheless, the obtained solutions provided a wider spectrum of strain states than standard tests.

Testing methodologies for the calibration of advanced plasticity models for sheet metals: A review

“…In order to minimize the cost function that provides the optimum heterogeneous specimen shape for a uniaxial tensile test, based on the indicator developed by Souto et al, [ 98 ] Andrade‐Campos et al investigated the best curve parameterization and optimization algorithm. [ 99 ] Seven optimization strategies were used, but only four of them were able to converge to a solution: the Nelder–Mead, pattern search, SDBOX (globally‐convergent derivative‐free algorithm for the minimization of a continuously differentiable function), and CMA‐ES (covariance Matrix Adaptation Evolution Strategy). The number of control points that minimizes the cost function regarding the different curve parameterization was also determined.…”

In Situ Monitoring of Additive Manufacturing Using Digital Image Correlation: A Review

“…This information was relevant to enhance finite element analysis by considering both real geometry and boundary conditions, in contrast with prescribing idealised displacements at the boundary domain [ 34 , 35 ]. Full-field data were conveniently used in other studies for advanced inverse material characterisation, particularly dealing with heterogeneous stress and strain states that can be generated by geometric discontinuities, loading configurations or material structure [ 16 , 32 , 36 ]. In situ DIC measurements have also been playing an important role in fracture and fatigue problems.…”

On the topology design of a mechanical heterogeneous specimen using geometric and material nonlinearities

“…The design of a mechanical test based on the empirical knowledge of the authors was addressed in [1][2][3], for example. The strain field heterogeneity was used as a criterion to lead the design process using optimization methodologies [4][5][6][7]. A step further relies on evaluating the uncertainty of the identified parameters [8][9][10].…”