Abstract : Structural and mechanical systems like bridges, buildings and defense systems play an essential role in modern societies. The maintenance of these structures must provide their safety and prevent the loss of life but at the same time be cost-efficient. Usually, the monitoring issue has been tackled from an engineering point of view. Consequently, the number of possible problem-solving algorithms is drastically reduced. In this minisymposium, the approaches from a mathematical and mechanical point of view are presented. These lead from methods for optimal sensor placements and applications of shape optimization to numerical simulations of damage detection, evolution, and prognosis.
[00271] Optimization aspects of experimental design approaches for sensor placement
Format : Talk at Waseda University
Author(s) :
Volker Schulz (Trier University)
Abstract : The information from sensors has to be treated in order to obtain properties of technical systems. The accuracy expressed in statistical concepts like covariance matrix and confidence regions depends on constituents of the measurement process. This talk discusses the effect of sensor placement and actuator design on these statistical properties and presents mathematical optimization approaches to optimize them.
[00272] Fracture propagation by using shape optimization techniques on Riemannian spaces
Format : Talk at Waseda University
Author(s) :
Tim Suchan (Helmut Schmidt University/University of the Federal Armed Forces Hamburg)
Kathrin Welker (TU Bergakademie Freiberg)
Winnifried Wollner (University of Hamburg)
Abstract : The concept of smooth phase fields has been used successfully to predict fracture propagation. However, it usually requires minimum two regularization parameters to be tuned. We present a novel approach for numerical fracture simulation which avoids the usage of phase fields. Instead, an objective functional that drives the evolution of the fracture is minimized with shape optimization techniques. We present the mathematical approach and numerical results for various commonly-used benchmarks.
[00246] Numerical modeling of crack propagation in concrete by means of cohesive zone modeling and a novel phase-field fracture approach
Format : Talk at Waseda University
Author(s) :
Rasoul Najafi Koopas (Helmut-Schmidt University)
Abstract : Two methodologies are developed for analyzing failure initiation and crack propagation in the highly inhomogeneous concrete mesostructure. By implementing efficient algorithms in Python, geometric features are generated and packed into a continuous phase. In the case of concrete, the continuous phase represents the mortar matrix, while the geometric features are the aggregates and voids of different sizes distributed randomly within the mortar matrix to represent the complex two-dimensional mesostructures of the concrete. The failure initiation and crack propagation of mesoscale concrete specimens are investigated using two different approaches, namely the Cohesive Zone Model and a novel Phase-Field fracture model. In the first approach, crack propagation is realized by generating zero-thickness Cohesive Interface Elements at the interfaces of solid elements. For this purpose, two-dimensional cohesive interface elements are generated $(i)$ within the constituent elements of the mortar matrix, $(ii)$ within the elements constituting the aggregates, and $(iii)$ at the Interfacial Transition Zone. Hence, all potential crack paths are simulated by assigning different Traction Separation laws to the cohesive interface elements generated in different regions of the mesoscale concrete specimen. In the second approach, a novel cohesive phase-field is developed by incorporating the idea proposed by Wu and Nguyen $(2018)$ and Geelen et al. $(2019)$ in which by a group of optimal characteristic functions, a phase-field regularized cohesive zone model with linear softening law is realized and applied to brittle fracture. Moreover, the implemented cohesive phase-field fracture is insensitive to the length scale parameter, which allows the use of a relatively coarser mesh, thereby significantly reducing the computational cost $[3]$. A series of mesoscale concrete specimens with identical properties $(volume density, size distribution, and aggregate shape)$ are simulated using the above approaches and the predicted crack paths are compared with each other.
References:
1- Wu, Jian-Ying, and Vinh Phu Nguyen. "A length scale insensitive phase-field damage model for brittle fracture." Journal of the Mechanics and Physics of Solids 119 (2018): 20-42.
2- Geelen, Rudy JM, et al. "A phase-field formulation for dynamic cohesive fracture." Computer Methods in Applied Mechanics and Engineering 348 (2019): 680-711.
3- Rezaei, Shahed, et al. "An anisotropic cohesive fracture model: Advantages and limitations of length-scale insensitive phase-field damage models." Engineering Fracture Mechanics 261 (2022): 108177.
[00231] Sequential subspace optimization for recovering stored-energy functions in hyperelastic materials
Format : Talk at Waseda University
Author(s) :
Lukas Vierus (Saarland University)
Rebecca Rothermel (Saarland University)
Thomas Schuster (Saarland University)
Anne Wald (University of Göttingen)
Abstract : Structural Health Monitoring demands for an efficient computation of parameters which characterize the mechanical behavior of elastic materials. Hyperelasticity describes a nonlinear elastic behavior where the second Piola-Kirchhoff stress tensor is given as a derivative of a scalar function representing the stored strain energy that encodes all mechanical properties of the underlying material. The mathematical model is represented by a high-dimensional parameter identification problem for a nonlinear, hyperbolic system with given initial and boundary values. We present an iterative method based on sequential subspace optimization leading to a significant acceleration compared to the Landweber method.
[00230] A low power autonomous SHM node for aerospace applications
Format : Talk at Waseda University
Author(s) :
Carol Featherston (School of Engineering, Cardiff University)
Rhys Pullin (School of Engineering, Cardiff University)
Stepehn Griggs (School of Engineering, Cardiff University)
Matthew Pearson (School of Engineering, Cardiff University)
Abstract : Acoustic emission(AE) monitors the release of energy resulting from the growth of damage to determine structural integrity. It is difficult to apply in low‐power systems as sensors must either be wired together or time synchronised, which is power intensive. A method based on three piezoelectric sensors in a small triangular array is proposed. Hardware is developed and the feasibility of powering the unit through energy harvesting explored. Results are obtained for a complex composite structure.
[00270] Damage parameter estimation in composite materials using data assimilation with reduced order models
Format : Online Talk on Zoom
Author(s) :
Nanda Kishore Bellam Muralidhar (TU Braunschweig)
Carmen Gräßle (TU Braunschweig)
Natalie Rauter (HSU Hamburg)
Rolf Lammering (HSU Hamburg)
Andrey Mikhaylenko (HSU Hamburg)
Dirk Lorenz (TU Braunschweig)
Abstract : In this work, we are concerned with estimating parameters that describe damage in composite materials. In particular, we consider fiber metal laminates which consist of metals and fiber reinforced plastics. Such materials are of great interest in e.g. aviation and automotive industries. We study structural health monitoring using guided ultrasonic waves utilizing an integrated sensor. In order to determine the damage parameters, we use techniques from Bayesian inference and data assimilation together with model order reduction which enables to alleviate the computational efforts. Numerical simulations illustrate the approaches.
[00256] Coefficient Control for Variational Inequalities
Format : Talk at Waseda University
Author(s) :
Nicolai Simon (Universität Hamburg)
Winnifried Wollner (Universität Hamburg)
Abstract : We consider the effects of introducing a control variable into the coefficients of a variational inequality in an optimal control problem with complementarity constraints.
The novelty of this talk is the utilization of H-convergence methods to formulate limit arguments as the basis for a bootstrapping approach, used to prove strong $L^p$ convergence of the coefficient control variable. Using the example of an obstacle problem, we compute a set of limiting optimality conditions using these arguments.
[00269] Optimal sparse sensor location for structural health monitoring
Format : Online Talk on Zoom
Author(s) :
Olga Weiß (Helmut Schmidt University/ University of the Federal Armed Forces Hamburg)
Kathrin Welker (TU Bergakademie Freiberg)
Volker Schulz (Trier University)
Abstract : Bridge structures are indispensable components of the infrastructure of modern industrial societies, and maintaining their functionality and reliability is essential.
Hence, monitoring processes of the structure and health of bridges are indispensable. For this purpose, the efficient and optimal placement of appropriate sensors for the non-destructive permanent monitoring of the structures is an important component.
Determining the number and placement of sensors to provide valuable information about damage and impact to the structure is essential for cost-efficient monitoring and for minimizing the volume of data, however, to this date represents a challenge.
We consider this issue from a mathematical point of view and derive a suitable optimization problem in infinite-dimensional function spaces. This modeled optimization problem is to be solved numerically by adapted optimization methods. As a special feature, the desired resulting sparsity of the solution for the positioning of the sensors is to be incorporated and considered in the solving method.
