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Guo, Y. (author), Sharma, S. (author), Kumar, Siddhant (author)Smooth and curved microstructural topologies found in nature—from soap films to trabecular bone—have inspired several mimetic design spaces for architected metamaterials and bio-scaffolds. However, the design approaches so far are ad hoc, raising the challenge: how to systematically and efficiently inverse design such artificial...journal article 2024
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van 't Sant, S. (author), Thakolkaran, P. (author), Martínez, Jonàs (author), Kumar, Siddhant (author)Advancements in machine learning have sparked significant interest in designing mechanical metamaterials, i.e., materials that derive their properties from their inherent microstructure rather than just their constituent material. We propose a data-driven exploration of the design space of growth-based cellular metamaterials based on star-shaped...journal article 2023
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Glaesener, R. N. (author), Kumar, Siddhant (author), Lestringant, C. (author), Butruille, T. (author), Portela, C. M. (author), Kochmann, D. M. (author)Although architected materials based on truss networks have been shown to possess advantageous or extreme mechanical properties, those can be highly affected by tolerances and uncertainties in the manufacturing process, which are usually neglected during the design phase. Deterministic computational tools typically design structures with the...journal article 2023
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Tang, Jian (author), Kumar, Siddhant (author), De Lorenzis, Laura (author), Hosseini, Ehsan (author)We propose Neural Cellular Automata (NCA) to simulate the microstructure development during the solidification process in metals. Based on convolutional neural networks, NCA can learn essential solidification features, such as preferred growth direction and competitive grain growth, and are up to six orders of magnitude faster than the...journal article 2023
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Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLIDFlaschel, Moritz (author), Yu, Huitian (author), Reiter, Nina (author), Hinrichsen, Jan (author), Budday, Silvia (author), Steinmann, Paul (author), Kumar, Siddhant (author), De Lorenzis, Laura (author)We propose an automated computational algorithm for simultaneous model selection and parameter identification for the hyperelastic mechanical characterization of biological tissue and validate it on experimental data stemming from human brain tissue specimens. Following the motive of the recently proposed computational framework EUCLID ...journal article 2023
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Hille, Helge C. (author), Kumar, Siddhant (author), De Lorenzis, Laura (author)The numerical simulation of additive manufacturing techniques promises the acceleration of costly experimental procedures to identify suitable process parameters. We recently proposed Floating Isogeometric Analysis (FLIGA), a new computational solid mechanics approach, which is mesh distortion-free in one characteristic spatial direction....journal article 2023
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Boddapati, Jagannadh (author), Flaschel, Moritz (author), Kumar, Siddhant (author), De Lorenzis, Laura (author), Daraio, Chiara (author)When the elastic properties of structured materials become direction-dependent, the number of their descriptors increases. For example, in two-dimensions, the anisotropic behavior of materials is described by up to 6 independent elastic stiffness parameters, as opposed to only 2 needed for isotropic materials. Such high number of parameters...journal article 2023
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Flaschel, Moritz (author), Kumar, Siddhant (author), De Lorenzis, Laura (author)We extend the scope of our recently developed approach for unsupervised automated discovery of material laws (denoted as EUCLID) to the general case of a material belonging to an unknown class of constitutive behavior. To this end, we leverage the theory of generalized standard materials, which encompasses a plethora of important constitutive...journal article 2023
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Zheng, Li (author), Karapiperis, Konstantinos (author), Kumar, Siddhant (author), Kochmann, Dennis M. (author)The rise of machine learning has fueled the discovery of new materials and, especially, metamaterials—truss lattices being their most prominent class. While their tailorable properties have been explored extensively, the design of truss-based metamaterials has remained highly limited and often heuristic, due to the vast, discrete design space...journal article 2023
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Marino, Enzo (author), Flaschel, Moritz (author), Kumar, Siddhant (author), De Lorenzis, Laura (author)We extend EUCLID, a computational strategy for automated material model discovery and identification, to linear viscoelasticity. For this case, we perform a priori model selection by adopting a generalized Maxwell model expressed by a Prony series, and deploy EUCLID for identification. The methodology is based on four ingredients: i. full...journal article 2023
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Bastek, Jan Hendrik (author), Kumar, Siddhant (author), Telgen, Bastian (author), Glaesener, Raphaël N. (author), Kochmann, Dennis M. (author)Inspired by crystallography, the periodic assembly of trusses into architected materials has enjoyed popularity for more than a decade and produced countless cellular structures with beneficial mechanical properties. Despite the successful and steady enrichment of the truss design space, the inverse design has remained a challenge: While...journal article 2022
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Thakolkaran, P. (author), Joshi, A. (author), Zheng, Y. (author), Flaschel, Moritz (author), De Lorenzis, Laura (author), Kumar, Siddhant (author)We propose a new approach for unsupervised learning of hyperelastic constitutive laws with physics-consistent deep neural networks. In contrast to supervised learning, which assumes the availability of stress–strain pairs, the approach only uses realistically measurable full-field displacement and global reaction force data, thus it lies...journal article 2022
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Joshi, A. (author), Thakolkaran, P. (author), Zheng, Y. (author), Escande, Maxime (author), Flaschel, Moritz (author), De Lorenzis, Laura (author), Kumar, Siddhant (author)Within the scope of our recent approach for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID), we propose an unsupervised Bayesian learning framework for discovery of parsimonious and interpretable constitutive laws with quantifiable uncertainties. As in deterministic EUCLID, we do not resort to stress data, but...journal article 2022
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Hille, Helge C. (author), Kumar, Siddhant (author), De Lorenzis, Laura (author)We propose Floating Isogeometric Analysis (FLIGA), which extends IGA to extreme deformation analysis. The method is based on a novel tensor-product construction of B-Splines for the update of the basis functions in one direction of the parametric space. With basis functions “floating” deformation-dependently in this direction, mesh distortion...journal article 2022
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Flaschel, Moritz (author), Kumar, Siddhant (author), De Lorenzis, Laura (author)We propose an approach for data-driven automated discovery of material laws, which we call EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery), and we apply it here to the discovery of plasticity models, including arbitrarily shaped yield surfaces and isotropic and/or kinematic hardening laws. The approach is...journal article 2022
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Voss, Jendrik (author), Martin, R.P. (author), Sander, Oliver (author), Kumar, Siddhant (author), Kochmann, Dennis M. (author), Neff, Patrizio (author)Deciding whether a given function is quasiconvex is generally a difficult task. Here, we discuss a number of numerical approaches that can be used in the search for a counterexample to the quasiconvexity of a given function W. We will demonstrate these methods using the planar isotropic rank-one convex function Wmagic+(F)=λmaxλmin-logλmaxλmin...journal article 2022
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Flaschel, Moritz (author), Kumar, Siddhant (author), De Lorenzis, Laura (author)We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically available through mechanical testing and digital image correlation techniques; it delivers interpretable...journal article 2021
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Zheng, Li (author), Kumar, Siddhant (author), Kochmann, Dennis M. (author)We present a two-scale topology optimization framework for the design of macroscopic bodies with an optimized elastic response, which is achieved by means of a spatially-variant cellular architecture on the microscale. The chosen spinodoid topology for the cellular network on the microscale (which is inspired by natural microstructures...journal article 2021
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Kumar, Siddhant (author), Tan, S. (author), Zheng, Li (author), Kochmann, Dennis M. (author)After a decade of periodic truss-, plate-, and shell-based architectures having dominated the design of metamaterials, we introduce the non-periodic class of spinodoid topologies. Inspired by natural self-assembly processes, spinodoid metamaterials are a close approximation of microstructures observed during spinodal phase separation. Their...journal article 2020