62 research outputs found
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
Neural Metamaterial Networks for Nonlinear Material Design
Nonlinear metamaterials with tailored mechanical properties have applications
in engineering, medicine, robotics, and beyond. While modeling their
macromechanical behavior is challenging in itself, finding structure parameters
that lead to ideal approximation of high-level performance goals is a
challenging task. In this work, we propose Neural Metamaterial Networks (NMN)
-- smooth neural representations that encode the nonlinear mechanics of entire
metamaterial families. Given structure parameters as input, NMN return
continuously differentiable strain energy density functions, thus guaranteeing
conservative forces by construction. Though trained on simulation data, NMN do
not inherit the discontinuities resulting from topological changes in finite
element meshes. They instead provide a smooth map from parameter to performance
space that is fully differentiable and thus well-suited for gradient-based
optimization. On this basis, we formulate inverse material design as a
nonlinear programming problem that leverages neural networks for both objective
functions and constraints. We use this approach to automatically design
materials with desired strain-stress curves, prescribed directional stiffness
and Poisson ratio profiles. We furthermore conduct ablation studies on network
nonlinearities and show the advantages of our approach compared to native-scale
optimization
A Finite Element Method for Interactive Physically Based Shape Modelling with Quadratic Tetrahedra
We present an alternative approach to standard geometric shape editing using physically-based simulation. With our technique, the user can deform complex objects in real-time. The enabling technology of this approach is a fast and accurate finite element implementation of an elasto-plastic material model, specifically designed for interactive shape manipulation. Using quadratic shape functions, we avoid the inherent drawback of volume locking exhibited by methods based on linear finite elements.
The physical simulation uses a tetrahedral mesh, which is constructed from a coarser approximation of the detailed surface. Having computed a deformed state of the tetrahedral mesh, the deformation is transferred back to the high detail surface. This can be accomplished in an accurate and efficient way using the quadratic shape functions.
In order to guarantee stability and real-time frame rates during the simulation, we cast the elasto-plastic problem into a linear formulation. For this purpose, we present a corotational formulation for quadratic finite elements. We demonstrate the versatility of our approach in interactive manipulation sessions and show that our animation system can be coupled with further physics-based animations like, e.g. fluids and cloth, in a bi-directional way
Differentiable Stripe Patterns for Inverse Design of Structured Surfaces
Stripe patterns are ubiquitous in nature and everyday life. While the
synthesis of these patterns has been thoroughly studied in the literature,
their potential to control the mechanics of structured materials remains
largely unexplored. In this work, we introduce Differentiable Stripe Patterns
-- a computational approach for automated design of physical surfaces
structured with stripe-shaped bi-material distributions. Our method builds on
the work by Knoppel and colleagues for generating globally-continuous and
equally-spaced stripe patterns. To unlock the full potential of this design
space, we propose a gradient-based optimization tool to automatically compute
stripe patterns that best approximate macromechanical performance goals.
Specifically, we propose a computational model that combines solid shell finite
elements with XFEM for accurate and fully-differentiable modeling of elastic
bi-material surfaces. To resolve non-uniqueness problems in the original
method, we furthermore propose a robust formulation that yields unique and
differentiable stripe patterns. %Finally, we introduce design space
regularizers to avoid numerical singularities and improve stripe neatness We
combine these components with equilibrium state derivatives into an end-to-end
differentiable pipeline that enables inverse design of mechanical stripe
patterns. We demonstrate our method on a diverse set of examples that
illustrate the potential of stripe patterns as a design space for structured
materials. Our simulation results are experimentally validated on physical
prototypes.Comment: 14 page
Extrusion-Based Ceramics Printing with Strictly-Continuous Deposition
International audienceWe propose a method for integrated tool path planning and support structuregeneration tailored to the specific constraints of extrusion-based ceramicsprinting. Existing path generation methods for thermoplastic materials relyon transfer moves to navigate between different print paths in a given layer.However, when printing with clay, these transfer moves can lead to severeartifacts and failure. Our method eliminates transfer moves altogether bygenerating deposition paths that are continuous within and across layers.Our algorithm is implemented as a sequential top-down pass through thelayer stack. In each layer, we detect points that require support, connectsupport points and model paths, and optimize the shape of the resultingcontinuous path with respect to length, smoothness, and distance to themodel. For each of these subproblems, we propose dedicated solutions thattake into account the fabrication constraints imposed by printable clay.We evaluate our method on a set of examples with multiple disconnectedcomponents and challenging support requirements. Comparisons to existingpath generation methods designed for thermoplastic materials show that ourmethod substantially improves print quality and often makes the differencebetween success and failure
ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact
We present a differentiable dynamics solver that is able to handle frictional
contact for rigid and deformable objects within a unified framework. Through a
principled mollification of normal and tangential contact forces, our method
circumvents the main difficulties inherent to the non-smooth nature of
frictional contact. We combine this new contact model with fully-implicit time
integration to obtain a robust and efficient dynamics solver that is
analytically differentiable. In conjunction with adjoint sensitivity analysis,
our formulation enables gradient-based optimization with adaptive trade-offs
between simulation accuracy and smoothness of objective function landscapes. We
thoroughly analyse our approach on a set of simulation examples involving rigid
bodies, visco-elastic materials, and coupled multi-body systems. We furthermore
showcase applications of our differentiable simulator to parameter estimation
for deformable objects, motion planning for robotic manipulation, trajectory
optimization for compliant walking robots, as well as efficient self-supervised
learning of control policies.Comment: Moritz Geilinger and David Hahn contributed equally to this wor
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