125 research outputs found
Asynchronous Variational Contact Mechanics
An asynchronous, variational method for simulating elastica in complex
contact and impact scenarios is developed. Asynchronous Variational Integrators
(AVIs) are extended to handle contact forces by associating different time
steps to forces instead of to spatial elements. By discretizing a barrier
potential by an infinite sum of nested quadratic potentials, these extended
AVIs are used to resolve contact while obeying momentum- and
energy-conservation laws. A series of two- and three-dimensional examples
illustrate the robustness and good energy behavior of the method
Model reduction for the material point method via an implicit neural representation of the deformation map
This work proposes a model-reduction approach for the material point method
on nonlinear manifolds. Our technique approximates the by
approximating the deformation map using an implicit neural representation that
restricts deformation trajectories to reside on a low-dimensional manifold. By
explicitly approximating the deformation map, its spatiotemporal gradients --
in particular the deformation gradient and the velocity -- can be computed via
analytical differentiation. In contrast to typical model-reduction techniques
that construct a linear or nonlinear manifold to approximate the (finite number
of) degrees of freedom characterizing a given spatial discretization, the use
of an implicit neural representation enables the proposed method to approximate
the deformation map. This allows the kinematic
approximation to remain agnostic to the discretization. Consequently, the
technique supports dynamic discretizations -- including resolution changes --
during the course of the online reduced-order-model simulation.
To generate for the generalized coordinates, we propose a
family of projection techniques. At each time step, these techniques: (1)
Calculate full-space kinematics at quadrature points, (2) Calculate the
full-space dynamics for a subset of `sample' material points, and (3) Calculate
the reduced-space dynamics by projecting the updated full-space position and
velocity onto the low-dimensional manifold and tangent space, respectively. We
achieve significant computational speedup via hyper-reduction that ensures all
three steps execute on only a small subset of the problem's spatial domain.
Large-scale numerical examples with millions of material points illustrate the
method's ability to gain an order of magnitude computational-cost saving --
indeed -- with negligible errors
Wire mesh design
We present a computational approach for designing wire meshes, i.e., freeform surfaces composed of woven wires arranged in a regular grid. To facilitate shape exploration, we map material properties of wire meshes to the geometric model of Chebyshev nets. This abstraction is exploited to build an efficient optimization scheme. While the theory of Chebyshev nets suggests a highly constrained design space, we show that allowing controlled deviations from the underlying surface provides a rich shape space for design exploration. Our algorithm balances globally coupled material constraints with aesthetic and geometric design objectives that can be specified by the user in an interactive design session. In addition to sculptural art, wire meshes represent an innovative medium for industrial applications including composite materials and architectural façades. We demonstrate the effectiveness of our approach using a variety of digital and physical prototypes with a level of shape complexity unobtainable using previous methods
- …