@article{LahmerIlgLerch, author = {Lahmer, Tom and Ilg, J. and Lerch, Reinhard}, title = {Variance-based sensitivity analyses of piezoelectric models}, series = {Computer Modeling in Engineering \& Sciences}, journal = {Computer Modeling in Engineering \& Sciences}, pages = {105 -- 126}, abstract = {Variance-based sensitivity analyses of piezoelectric models}, subject = {Angewandte Mathematik}, language = {en} } @article{VuBacRafieeZhuangetal., author = {Vu-Bac, N. and Rafiee, Roham and Zhuang, Xiaoying and Lahmer, Tom and Rabczuk, Timon}, title = {Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters}, series = {Composites Part B: Engineering}, journal = {Composites Part B: Engineering}, pages = {446 -- 464}, abstract = {Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters}, subject = {Angewandte Mathematik}, language = {en} } @inproceedings{JaouadiLahmer, author = {Jaouadi, Zouhour and Lahmer, Tom}, title = {Topology optimization of structures subjected to multiple load cases by introducing the Epsilon constraint method}, series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom}, organization = {Bauhaus-Universit{\"a}t Weimar}, issn = {1611-4086}, doi = {10.25643/bauhaus-universitaet.2804}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28042}, pages = {7}, abstract = {A topology optimization method has been developed for structures subjected to multiple load cases (Example of a bridge pier subjected to wind loads, traffic, superstructure...). We formulate the problem as a multi-criterial optimization problem, where the compliance is computed for each load case. Then, the Epsilon constraint method (method proposed by Chankong and Haimes, 1971) is adapted. The strategy of this method is based on the concept of minimizing the maximum compliance resulting from the critical load case while the other remaining compliances are considered in the constraints. In each iteration, the compliances of all load cases are computed and only the maximum one is minimized. The topology optimization process is switching from one load to another according to the variation of the resulting compliance. In this work we will motivate and explain the proposed methodology and provide some numerical examples.}, subject = {Angewandte Informatik}, language = {en} } @article{ZhaoLuRabczuk, author = {Zhao, Jiyun and Lu, Lixin and Rabczuk, Timon}, title = {The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {567 -- 572}, abstract = {The tensile and shear failure behavior dependence on chain length and temperature in amorphous polymers}, subject = {Angewandte Mathematik}, language = {en} } @article{BenZhaoZhangetal., author = {Ben, S. and Zhao, Jun-Hua and Zhang, Yancheng and Rabczuk, Timon}, title = {The interface strength and debonding for composite structures: review and recent developments}, series = {Composite Structures}, journal = {Composite Structures}, abstract = {The interface strength and debonding for composite structures: review and recent developments}, subject = {Angewandte Mathematik}, language = {en} } @article{GhorashiValizadehMohammadietal., author = {Ghorashi, Seyed Shahram and Valizadeh, Navid and Mohammadi, S. and Rabczuk, Timon}, title = {T-spline based XIGA for Fracture Analysis of Orthotropic Media}, series = {Computers \& Structures}, journal = {Computers \& Structures}, pages = {138 -- 146}, abstract = {T-spline based XIGA for Fracture Analysis of Orthotropic Media}, subject = {Angewandte Mathematik}, language = {en} } @phdthesis{Vu, author = {Vu, Bac Nam}, title = {Stochastic uncertainty quantification for multiscale modeling of polymeric nanocomposites}, doi = {10.25643/bauhaus-universitaet.2555}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20160322-25551}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {265}, abstract = {Nanostructured materials are extensively applied in many fields of material science for new industrial applications, particularly in the automotive, aerospace industry due to their exceptional physical and mechanical properties. Experimental testing of nanomaterials is expensive, timeconsuming,challenging and sometimes unfeasible. Therefore,computational simulations have been employed as alternative method to predict macroscopic material properties. The behavior of polymeric nanocomposites (PNCs) are highly complex. The origins of macroscopic material properties reside in the properties and interactions taking place on finer scales. It is therefore essential to use multiscale modeling strategy to properly account for all large length and time scales associated with these material systems, which across many orders of magnitude. Numerous multiscale models of PNCs have been established, however, most of them connect only two scales. There are a few multiscale models for PNCs bridging four length scales (nano-, micro-, meso- and macro-scales). In addition, nanomaterials are stochastic in nature and the prediction of macroscopic mechanical properties are influenced by many factors such as fine-scale features. The predicted mechanical properties obtained by traditional approaches significantly deviate from the measured values in experiments due to neglecting uncertainty of material features. This discrepancy is indicated that the effective macroscopic properties of materials are highly sensitive to various sources of uncertainty, such as loading and boundary conditions and material characteristics, etc., while very few stochastic multiscale models for PNCs have been developed. Therefore, it is essential to construct PNC models within the framework of stochastic modeling and quantify the stochastic effect of the input parameters on the macroscopic mechanical properties of those materials. This study aims to develop computational models at four length scales (nano-, micro-, meso- and macro-scales) and hierarchical upscaling approaches bridging length scales from nano- to macro-scales. A framework for uncertainty quantification (UQ) applied to predict the mechanical properties of the PNCs in dependence of material features at different scales is studied. Sensitivity and uncertainty analysis are of great helps in quantifying the effect of input parameters, considering both main and interaction effects, on the mechanical properties of the PNCs. To achieve this major goal, the following tasks are carried out: At nano-scale, molecular dynamics (MD) were used to investigate deformation mechanism of glassy amorphous polyethylene (PE) in dependence of temperature and strain rate. Steered molecular dynamics (SMD)were also employed to investigate interfacial characteristic of the PNCs. At mico-scale, we developed an atomistic-based continuum model represented by a representative volume element (RVE) in which the SWNT's properties and the SWNT/polymer interphase are modeled at nano-scale, the surrounding polymer matrix is modeled by solid elements. Then, a two-parameter model was employed at meso-scale. A hierarchical multiscale approach has been developed to obtain the structure-property relations at one length scale and transfer the effect to the higher length scales. In particular, we homogenized the RVE into an equivalent fiber. The equivalent fiber was then employed in a micromechanical analysis (i.e. Mori-Tanaka model) to predict the effective macroscopic properties of the PNC. Furthermore, an averaging homogenization process was also used to obtain the effective stiffness of the PCN at meso-scale. Stochastic modeling and uncertainty quantification consist of the following ingredients: - Simple random sampling, Latin hypercube sampling, Sobol' quasirandom sequences, Iman and Conover's method (inducing correlation in Latin hypercube sampling) are employed to generate independent and dependent sample data, respectively. - Surrogate models, such as polynomial regression, moving least squares (MLS), hybrid method combining polynomial regression and MLS, Kriging regression, and penalized spline regression, are employed as an approximation of a mechanical model. The advantage of the surrogate models is the high computational efficiency and robust as they can be constructed from a limited amount of available data. - Global sensitivity analysis (SA) methods, such as variance-based methods for models with independent and dependent input parameters, Fourier-based techniques for performing variance-based methods and partial derivatives, elementary effects in the context of local SA, are used to quantify the effects of input parameters and their interactions on the mechanical properties of the PNCs. A bootstrap technique is used to assess the robustness of the global SA methods with respect to their performance. In addition, the probability distribution of mechanical properties are determined by using the probability plot method. The upper and lower bounds of the predicted Young's modulus according to 95 \% prediction intervals were provided. The above-mentioned methods study on the behaviour of intact materials. Novel numerical methods such as a node-based smoothed extended finite element method (NS-XFEM) and an edge-based smoothed phantom node method (ES-Phantom node) were developed for fracture problems. These methods can be used to account for crack at macro-scale for future works. The predicted mechanical properties were validated and verified. They show good agreement with previous experimental and simulations results.}, subject = {Polymere}, language = {en} } @misc{Almasi, type = {Master Thesis}, author = {Almasi, Ashkan}, title = {Stochastic Analysis of Interfacial Effects on the Polymeric Nanocomposites}, doi = {10.25643/bauhaus-universitaet.2433}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20150709-24339}, school = {Bauhaus-Universit{\"a}t Weimar}, abstract = {The polymeric clay nanocomposites are a new class of materials of which recently have become the centre of attention due to their superior mechanical and physical properties. Several studies have been performed on the mechanical characterisation of these nanocomposites; however most of those studies have neglected the effect of the interfacial region between the clays and the matrix despite of its significant influence on the mechanical performance of the nanocomposites. There are different analytical methods to calculate the overall elastic material properties of the composites. In this study we use the Mori-Tanaka method to determine the overall stiffness of the composites for simple inclusion geometries of cylinder and sphere. Furthermore, the effect of interphase layer on the overall properties of composites is calculated. Here, we intend to get ounds for the effective mechanical properties to compare with the analytical results. Hence, we use linear displacement boundary conditions (LD) and uniform traction boundary conditions (UT) accordingly. Finally, the analytical results are compared with numerical results and they are in a good agreement. The next focus of this dissertation is a computational approach with a hierarchical multiscale method on the mesoscopic level. In other words, in this study we use the stochastic analysis and computational homogenization method to analyse the effect of thickness and stiffness of the interfacial region on the overall elastic properties of the clay/epoxy nanocomposites. The results show that the increase in interphase thickness, reduces the stiffness of the clay/epoxy naocomposites and this decrease becomes significant in higher clay contents. The results of the sensitivity analysis prove that the stiffness of the interphase layer has more significant effect on the final stiffness of nanocomposites. We also validate the results with the available experimental results from the literature which show good agreement.}, language = {en} } @inproceedings{TanLahmerSiddappa, author = {Tan, Fengjie and Lahmer, Tom and Siddappa, Manju Gyaraganahalll}, title = {SECTION OPTIMIZATION AND RELIABILITY ANALYSIS OF ARCH-TYPE DAMS INCLUDING COUPLED MECHANICAL-THERMAL AND HYDRAULIC FIELDS}, series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom}, organization = {Bauhaus-Universit{\"a}t Weimar}, issn = {1611-4086}, doi = {10.25643/bauhaus-universitaet.2821}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28212}, pages = {8}, abstract = {From the design experiences of arch dams in the past, it has significant practical value to carry out the shape optimization of arch dams, which can fully make use of material characteristics and reduce the cost of constructions. Suitable variables need to be chosen to formulate the objective function, e.g. to minimize the total volume of the arch dam. Additionally a series of constraints are derived and a reasonable and convenient penalty function has been formed, which can easily enforce the characteristics of constraints and optimal design. For the optimization method, a Genetic Algorithm is adopted to perform a global search. Simultaneously, ANSYS is used to do the mechanical analysis under the coupling of thermal and hydraulic loads. One of the constraints of the newly designed dam is to fulfill requirements on the structural safety. Therefore, a reliability analysis is applied to offer a good decision supporting for matters concerning predictions of both safety and service life of the arch dam. By this, the key factors which would influence the stability and safety of arch dam significantly can be acquired, and supply a good way to take preventive measures to prolong ate the service life of an arch dam and enhances the safety of structure.}, subject = {Angewandte Informatik}, language = {en} } @article{HamdiaLahmerNguyenThoietal., author = {Hamdia, Khader and Lahmer, Tom and Nguyen-Thoi, T. and Rabczuk, Timon}, title = {Predicting The Fracture Toughness of PNCs: A Stochastic Approach Based on ANN and ANFIS}, series = {Computational Materials Science}, journal = {Computational Materials Science}, pages = {304 -- 313}, abstract = {Predicting The Fracture Toughness of PNCs: A Stochastic Approach Based on ANN and ANFIS}, subject = {Angewandte Mathematik}, language = {en} }