arXiv subjects

Frans P. van der Meer

Publications and source records attributed to Frans P. van der Meer.

3 recordsLinked to original sources

arXiv2026

A Shell-to-Shell Cohesive Line Element for Efficient Modeling of Interfacial Cracking in Overmolded Stiffened Panels

The growing use of thermoplastics in lightweight structures requires efficient numerical methods to predict debonding in overmolded parts. In this work, a novel structural cohesive element is proposed as an efficient alternative to conventional cohesive elements for modeling debonding in thermoplastic composite panels with overmolded stiffeners. Three-node, higher-order hybrid/mixed shell elements based on the Kirchhoff hypothesis are used to model thin panels and stiffeners. The novel kinematics allows to obtain the jump vector at any point over the cohesive surface from the shell displacement approximations evaluated at the element edges. The weakly enforced higher-order continuity in skin and stiffener displacements enables debonding analysis on coarse meshes. The framework is suitable for analyzing debonding in skin-stiffener structures with non-constant damage through the stiffener thickness. The model is verified for mode I, mode II and mixed-mode benchmark problems. A debonding problem is analyzed with both standard 3D cohesive elements and the proposed element. The results show that the element size in the proposed models can be much larger than that in the standard model, with more than 95% reduction in CPU time. The debonding analysis of a complex stiffened panel is also presented to demonstrate the intended use of the proposed element for simulating debonding in structural components.

cs.CE↗

arXiv2026

Piecewise Deterministic Markov Processes for Bayesian Inference of PDE Coefficients

We develop a general framework for piecewise deterministic Markov process (PDMP) samplers that enables efficient Bayesian inference in non-linear inverse problems with expensive likelihoods. The key ingredient is a surrogate-assisted thinning scheme in which a surrogate model provides a proposal event rate and a robust correction mechanism enforces an upper bound on the true rate by dynamically adjusting an additive offset whenever violations are detected. This construction is agnostic to the choice of surrogate and PDMP, and we demonstrate it for the Zig-Zag sampler and the Bouncy particle sampler with constant, Laplace, and Gaussian process (GP) surrogates, including gradient-informed and adaptively refined GP variants. As a representative application, we consider Bayesian inference of a spatially varying Young's modulus in a one-dimensional linear elasticity problem. Across dimensions, PDMP samplers equipped with GP-based surrogates achieve substantially higher accuracy and effective sample size per forward model evaluation than Random Walk Metropolis algorithm and the No-U-Turn sampler. The Bouncy particle sampler exhibits the most favorable overall efficiency and scaling, illustrating the potential of the proposed PDMP framework beyond this particular setting.

stat.CO↗

arXiv2024

Integration of Active Learning and MCMC Sampling for Efficient Bayesian Calibration of Mechanical Properties

Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models and cutting-edge MCMC algorithms, often depend on ad-hoc decisions. A systematic assessment of their combined influence on analytical accuracy and efficiency is notably lacking. The present work offers a comprehensive comparative study, employing a scalable case study in computational mechanics focused on the inference of spatially varying material parameters, that sheds light on the impact of methodological choices for surrogate modelling and sampling. We show that a priori training of the surrogate model introduces large errors in the posterior estimation even in low to moderate dimensions. We introduce a simple active learning strategy based on the path of the MCMC algorithm that is superior to all a priori trained models, and determine its training data requirements. We demonstrate that the choice of the MCMC algorithm has only a small influence on the amount of training data but no significant influence on the accuracy of the resulting surrogate model. Further, we show that the accuracy of the posterior estimation largely depends on the surrogate model, but not even a tailored surrogate guarantees convergence of the MCMC.Finally, we identify the forward model as the bottleneck in the inference process, not the MCMC algorithm. While related works focus on employing advanced MCMC algorithms, we demonstrate that the training data requirements render the surrogate modelling approach infeasible before the benefits of these gradient-based MCMC algorithms on cheap models can be reaped.

physics.comp-ph↗