Subdivision Shell Elements with Anisotropic Growth

A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow for arbitrary in-plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a few standard loading benchmarks. With this powerful tool at hand, we demonstrate the broad range of possible applications by numerical solution of several growth scenarios, ranging from the uniform growth of a sphere, to boundary instabilities induced by large anisotropic growth. Finally, it is shown that the problem of a slowly and uniformly growing sheet confined in a fixed hollow sphere is equivalent to the inverse process where a sheet of fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless, quasi-static, elastic limit.Comment: 20 pages, 12 figures, 1 tabl

A consistent bending model for cloth simulation with corotational subdivision finite elements

Modelling bending energy in a consistent way is decisive for the realistic simulation of cloth. With existing approaches characteristic behaviour like folding and buckling cannot be reproduced in a physically convincing way. We present a new method based on a corotational formulation of subdivision finite elements. Due to the non-local nature of the employed subdivision basis functions a C1-continuous displacement field can be defined. It is thus possible to use the governing equations of thin shell analysis leading to a physically accurate bending behaviour. Using a corotated strain tensor allows the large displacement analysis of cloth while retaining a linear system of equations. Hence, known convergence properties and computational efficiency are preserved

NeuralClothSim: Neural Deformation Fields Meet the Kirchhoff-Love Thin Shell Theory

Cloth simulation is an extensively studied problem, with a plethora of solutions available in computer graphics literature. Existing cloth simulators produce realistic cloth deformations that obey different types of boundary conditions. Nevertheless, their operational principle remains limited in several ways: They operate on explicit surface representations with a fixed spatial resolution, perform a series of discretised updates (which bounds their temporal resolution), and require comparably large amounts of storage. Moreover, back-propagating gradients through the existing solvers is often not straightforward, which poses additional challenges when integrating them into modern neural architectures. In response to the limitations mentioned above, this paper takes a fundamentally different perspective on physically-plausible cloth simulation and re-thinks this long-standing problem: We propose NeuralClothSim, i.e., a new cloth simulation approach using thin shells, in which surface evolution is encoded in neural network weights. Our memory-efficient and differentiable solver operates on a new continuous coordinate-based representation of dynamic surfaces, i.e., neural deformation fields (NDFs); it supervises NDF evolution with the rules of the non-linear Kirchhoff-Love shell theory. NDFs are adaptive in the sense that they 1) allocate their capacity to the deformation details as the latter arise during the cloth evolution and 2) allow surface state queries at arbitrary spatial and temporal resolutions without retraining. We show how to train our NeuralClothSim solver while imposing hard boundary conditions and demonstrate multiple applications, such as material interpolation and simulation editing. The experimental results highlight the effectiveness of our formulation and its potential impact.Comment: 27 pages, 22 figures and 3 tables; project page: https://4dqv.mpi-inf.mpg.de/NeuralClothSim

Phase field modeling of brittle fracture in large-deformation solid shells with the efficient quasi-Newton solution and global–local approach

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).To efficiently predict the crack propagation in thin-walled structures, a global–local approach for phase field modeling using large-deformation solid shell finite elements considering the enhanced assumed strain (EAS) and the assumed natural strain (ANS) methods for the alleviation of locking effects is developed in this work. Aiming at tackling the poor convergence performance of standard Newton schemes, a quasi-Newton (QN) scheme is proposed for the solution of coupled governing equations stemming from the enhanced assumed strain shell formulation in a monolithic manner. The excellent convergence performance of this QN monolithic scheme for the multi-field shell formulation is demonstrated through several paradigmatic boundary value problems, including single edge notched tension and shear, fracture of cylindrical structure under mixed loading and fatigue induced crack growth. Compared with the popular alternating minimization (AM) or staggered solution scheme, it is also found that the QN monolithic solution scheme for the phase field modeling using enhanced strain shell formulation is very efficient without the loss of robustness, and significant computational gains are observed in all the numerical examples. In addition, to further reduce the computational cost in fracture modeling of large-scale thin-walled structures, a specific global–local phase field approach for solid shell elements in the 3D setting is proposed, in which the full displacement-phase field problem is considered at the local level, while addressing only the elastic problem at the global level. Its capability is demonstrated by the modeling of a cylindrical structure subjected to both static and fatigue cyclic loading conditions, which can be appealing to industrial applications

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells