A nonlocal approach to graded surface modeling in topology optimization - Singh, Sukhminder; Pflug, Lukas; Wein, Fabian; Stingl, Michael (Structural and Multidisciplinary Optimization, 2025)
Additively manufactured structures often exhibit a correlation between their mechanical properties, such as stiffness, strength, and porosity, and their wall thickness. This correlation stems from the interplay between the manufacturing process and the properties of the filler material. In this study, we investigate the thickness-dependent effect on structural stiffness and propose a nonlocal integral model that introduces surface grading of Young’s modulus to capture this phenomenon. We incorporate this model into topology optimization for designing structures with optimized compliance subject to a volume constraint. Notably, elastically degraded surfaces penalize excessively thin features, effectively eliminating them from the optimized design. The effectiveness of the proposed framework is demonstrated through two- and three-dimensional examples.
CRIS-Team Scopus Importer:2025-05-16
Keywords: Additive manufacturing; Nonlocal integral model; Surface grading; Topology optimization

Material optimization for controlling interfacial damage in composite structures - Singh, Sukhminder; Stingl, Michael (Proceedings in Applied Mathematics and Mechanics, 2021)
Advances in the computational modeling of fracture in solid structures have opened up possibilities for structural design optimization. The rate‐independent structural problem considering damage in its original form is ill‐posed due to the non‐unique nature of the solution, that poses difficulty in using gradient‐based algorithms for material optimization. To overcome this issue, this work introduces a viscosity parameter in the governing state equations and, thus renders the structural problem well‐posed. Material interfaces are modeled using an exponential, initially‐elastic cohesive law and linear elasticity is assumed throughout the structural domain. The time‐dependent fracture problem is solved via incremental variational approach with finite element discretization of the displacement field. Finally, the effectiveness of the method is illustrated by a material optimization example using a smooth gradient‐based solver with first‐order material sensitivities.<br

Material optimization to enhance delamination resistance of composite structures using viscous regularization - Singh, Sukhminder; Pflug, Lukas; Stingl, Michael (Computer Methods in Applied Mechanics and Engineering, 2021)
Advances in the computational modeling of fracture of solids have opened up new possibilities for structural design optimization to enhance fracture properties. Here, we investigate material optimization and design to improve fracture behavior of composite structures under quasi-static conditions. The rate-independent structural problem considering cohesive fracture is ill-posed in its original form due to the non-unique nature of the solution. This renders the use of gradient-based optimization algorithms problematic. To overcome this issue, we introduce viscous regularization and a local approximation of the cohesive law into the governing state equations, and study the impact with the help of interfacial fracture of composite structures consisting of two or more materials. The fracture problem is then integrated into a material optimization framework. We study the effect of viscous regularization on the global landscape of the proposed objective function using a 2-dimensional delamination example with one design parameter and discuss difficulties resulting from the stabilization of inherently unstable crack states. In view of these issues, we finally propose considering multiple state problems, each limited to a single crack, with different predefined crack paths. In the end, we optimize the orientations of orthotropic inclusions embedded in a double-cantilever beam for the worst case of the potential crack paths.

On optimization of heterogeneous materials for enhanced resistance to bulk fracture - Singh, Sukhminder; Pflug, Lukas; Mergheim, Julia; Stingl, Michael (Forces in Mechanics, 2023)
We propose a novel approach to optimize the design of heterogeneous materials, with the goal of enhancing their effective fracture toughness under mode-I loading. The method employs a Gaussian processes-based Bayesian optimization framework to determine the optimal shapes and locations of stiff elliptical inclusions within a periodic microstructure in two dimensions. To model crack propagation, the phase-field fracture method with an efficient interior-point monolithic solver and adaptive mesh refinement, is used. To account for the high sensitivity of fracture properties to initial crack location with respect to heterogeneities, we consider multiple cases of initial crack and optimize the material for the worst-case scenario. We also impose a minimum clearance constraint between the inclusions to ensure design feasibility. Numerical experiments demonstrate that the method significantly improves the fracture toughness of the material compared to the homogeneous case.
CRIS-Team Scopus Importer:2023-07-07
Keywords: Bayesian optimization; Fracture toughness; Heterogeneous materials; Phase-field method

Robust design optimization for enhancing delamination resistance of composites - Singh, Sukhminder; Pflug, Lukas; Mergheim, Julia; Stingl, Michael (International Journal for Numerical Methods in Engineering, 2022)
Recent developments in the field of computational modeling of fracture have opened up possibilities for designing structures against failure. A special case, called interfacial fracture or delamination, can occur in loaded composite structures where two or more materials are bonded together at comparatively weak interfaces. Due to the potential crack growth along these interfaces, the structural problem suffers from snap-back/snap-through instabilities and bifurcations with respect to the model parameters, leading to noisy and discontinuous responses. For such a case, the design optimization problem for a selected quantity of interest is ill-posed, since small variations in the design parameters can lead to large jumps in the structural response. To this end, this article presents a stochastic optimization approach to maximize delamination resistance that is less sensitive to small perturbations of the design and thereby leads to a robust solution. To overcome the intractability of Monte Carlo methods for estimating the expected value of the expensive-to-evaluate response function, a global, piecewise-constant surrogate is constructed based on nearest-neighbor interpolation that is iteratively refined during the optimization run. We found that by taking a large stochastic region at the beginning of the optimization and gradually reducing it to the desired one can help overcome poor local optima. Our results demonstrate the effectiveness of the proposed framework using an example of shape optimization of hard inclusions embedded in a double-cantilever beam, which significantly enhances delamination resistance.
CRIS-Team WoS Importer:2022-12-16