A data‐driven framework for evolutionary problems in solid mechanics

Poelstra, Klaas; Bartel, Thorsten; Schweizer, Ben

doi:10.1002/zamm.202100538

Cited by 3 publications

(1 citation statement)

References 19 publications

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“…Forays into the application of data-driven mechanics to inelastic material behavior have been been achieved by [14] and [15], among others. In this context, [16] present a sophisticated methodology to address the involved challenges by using a neural network to capture the material's history.…”

Section: Introductionmentioning

confidence: 99%

Aspects of accuracy and uniqueness of solutions in data‐driven mechanics

Bartel

Harnisch

Menzel

et al. 2023

Proc Appl Math and Mech

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Data‐driven methods provide great potential for future applications in engineering, for example in terms of more efficient simulations. Conventional material models and the associated constitutive equations are substituted by a minimization of a distance between so‐called material and mechanical states, which, however, leads to non‐unique solutions. The aim of this paper is to analyze the influence of the chosen initial values on the accuracy of the obtained results. Furthermore, Mixed Integer Quadratic Programming (MIQP) is implemented and its applicability to data‐driven mechanics is assessed.

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Section: Introductionmentioning

confidence: 99%

Aspects of accuracy and uniqueness of solutions in data‐driven mechanics

Bartel

Harnisch

Menzel

et al. 2023

Proc Appl Math and Mech

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Data‐driven simulation of functional fatigue in shape memory alloy wires

Harnisch,

Bartel,

Weyergraf

et al. 2024

Proc Appl Math and Mech

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Data‐driven mechanics offers great potential in engineering applications, where the efficient simulation of complex and, in particular, path‐dependent material behavior is often challenging. Within this approach, conventional material models are replaced by data sets containing snapshots of stress, strain and the history of both assumed to be sufficiently accurate representations of the underlying material behavior. Based on these snapshots and on physical admissibility, a distance function is built which is minimized to yield the boundary value problems' solution. The aim of this paper is to apply this framework to accurately simulate the complex behavior of shape memory alloy wires under cyclic loading, under which these materials exhibit a degradation of their features, denoted functional fatigue. The constructed synthetic data sets are enriched by real experimental data, showcasing that the data‐driven method is capable of combining both approaches of classic material modeling and modern methods which directly incorporate experimental data.

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Data-driven confidence bound for structural response using segmented least squares: a mixed-integer programming approach

Kanno

2024

Japan J. Indust. Appl. Math.

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As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures.

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A data‐driven framework for evolutionary problems in solid mechanics

Cited by 3 publications

References 19 publications

Aspects of accuracy and uniqueness of solutions in data‐driven mechanics

Aspects of accuracy and uniqueness of solutions in data‐driven mechanics

Data‐driven simulation of functional fatigue in shape memory alloy wires

Data-driven confidence bound for structural response using segmented least squares: a mixed-integer programming approach

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