In this paper, we introduce the Moving Least Squares Material Point Method (MLS-MPM). MLS-MPM naturally leads to the formulation of Affine Particle-In-Cell (APIC) [Jiang et al. 2015] and Polynomial Particle-In-Cell [Fu et al. 2017] in a way that is consistent with a Galerkin-style weak form discretization of the governing equations. Additionally, it enables a new stress divergence discretization that effortlessly allows all MPM simulations to run two times faster than before. We also develop a Compatible Particle-In-Cell (CPIC) algorithm on top of MLS-MPM. Utilizing a colored distance field representation and a novel compatibility condition for particles and grid nodes, our framework enables the simulation of various new phenomena that are not previously supported by MPM, including material cutting, dynamic open boundaries, and two-way coupling with rigid bodies. MLS-MPM with CPIC is easy to implement and friendly to performance optimization.

A moving least squares material point method with displacement discontinuity and two-way rigid body coupling

This paper focuses on the recent development of soft pneumatic actuators for soft robotics over the past few years, concentrating on the following four categories: control systems, material and construction, modeling, and sensors. This review work seeks to provide an accelerated entrance to new researchers in the field to encourage research and innovation. Advances in methods to accurately model soft robotic actuators have been researched, optimizing and making numerous soft robotic designs applicable to medical, manufacturing, and electronics applications. Multi-material 3D printed and fiber optic soft pneumatic actuators have been developed, which will allow for more accurate positioning and tactile feedback for soft robotic systems. Also, a variety of research teams have made improvements to soft robot control systems to utilize soft pneumatic actuators to allow for operations to move more effectively. This review work provides an accessible repository of recent information and comparisons between similar works. Future issues facing soft robotic actuators include portable and flexible power supplies, circuit boards, and drive components.

Soft Robotics: A Review of Recent Developments of Pneumatic Soft Actuators

Inside-outside determination is a basic building block for higher-level geometry processing operations. Generalized winding numbers provide a robust answer for triangle meshes, regardless of defects such as self-intersections, holes or degeneracies. In this paper, we further generalize the winding number to point clouds. Previous methods for evaluating the winding number are slow for completely disconnected surfaces, such as triangle soups or-in the extreme case- point clouds. We propose a tree-based algorithm to reduce the asymptotic complexity of generalized winding number computation, while closely approximating the exact value. Armed with a fast evaluation, we demonstrate the winding number in a variety of new applications: voxelization, signing distances, generating 3D printer paths, defect-tolerant mesh booleans and point set surfaces.

Fast winding numbers for soups and clouds

The computation of smooth fields of orthogonal directions within a volume is a critical step in hexahedral mesh generation, used to guide placement of edges and singularities While this problem shares high-level structure with surface-based frame field problems, critical aspects are lost when extending to volumes, while new structure from the flat Euclidean metric emerges Taking these considerations into account, this article presents an algorithm for computing such “octahedral” fields Unlike existing approaches, our formulation achieves infinite resolution in the interior of the volume via the boundary element method (BEM), continuously assigning frames to points in the interior from only a triangle mesh discretization of the boundary The end result is an orthogonal direction field that can be sampled anywhere inside the mesh, with smooth variation and singular structure in the interior, even with a coarse boundary We illustrate our computed frames on a number of challenging test geometries Since the octahedral frame field problem is relatively new, we also contribute a thorough discussion of theoretical and practical challenges unique to this problem

Boundary Element Octahedral Fields in Volumes

Topological defects in condensed matter are attracting e significant attention due to their important role in phase transition and their fascinating characteristics. Among the various types of matter, ferroics which possess a switchable physical characteristic and form domain structure are ideal systems to form topological defects. In particular, a special class of topological defects-vortices-have been found to commonly exist in ferroics. They often manifest themselves as singular regions where domains merge in large systems, or stabilize as novel order states instead of forming domain structures in small enough systems. Understanding the characteristics and controllability of vortices in ferroics can provide us with deeper insight into the phase transition of condensed matter and also exciting opportunities in designing novel functional devices such as nano-memories, sensors, and transducers based on topological defects. In this review, we summarize the recent experimental and theoretical progress in ferroic vortices, with emphasis on those spin/dipole vortices formed in nanoscale ferromagnetics and ferroelectrics, and those structural domain vortices formed in multiferroic hexagonal manganites. We begin with an overview of this field. The fundamental concepts of ferroic vortices, followed by the theoretical simulation and experimental methods to explore ferroic vortices, are then introduced. The various characteristics of vortices (e.g. formation mechanisms, static/dynamic features, and electronic properties) and their controllability (e.g. by size, geometry, external thermal, electrical, magnetic, or mechanical fields) in ferromagnetics, ferroelectrics, and multiferroics are discussed in detail in individual sections. Finally, we conclude this review with an outlook on this rapidly developing field.

Characteristics and controllability of vortices in ferromagnetics, ferroelectrics, and multiferroics

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.

ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact.

ADD: analytically differentiable dynamics for multi-body systems with frictional contact

We propose a novel surface-only technique for simulating incompressible, inviscid and uniform-density liquids with surface tension in three dimensions. The liquid surface is captured by a triangle mesh on which a Lagrangian velocity field is stored. Because advection of the velocity field may violate the incompressibility condition, we devise an orthogonal projection technique to remove the divergence while requiring the evaluation of only two boundary integrals. The forces of surface tension, gravity, and solid contact are all treated by a boundary element solve, allowing us to perform detailed simulations of a wide range of liquid phenomena, including waterbells, droplet and jet collisions, fluid chains, and crown splashes.

Surface-only liquids

This paper presents a method for optimizing visco-elastic material parameters of a finite element simulation to best approximate the dynamic motion of real-world soft objects. We compute the gradient with respect to the material parameters of a least-squares error objective function using either direct sensitivity analysis or an adjoint state method. We then optimize the material parameters such that the simulated motion matches real-world observations as closely as possible. In this way, we can directly build a useful simulation model that captures the visco-elastic behaviour of the specimen of interest. We demonstrate the effectiveness of our method on various examples such as numerical coarsening, custom-designed objective functions, and of course real-world flexible elastic objects made of foam or 3D printed lattice structures, including a demo application in soft robotics.

Real2Sim: visco-elastic parameter estimation from dynamic motion

We present a method for simulating brittle fracture under the assumptions of quasi-static linear elastic fracture mechanics (LEFM). Using the boundary element method (BEM) and Lagrangian crack-fronts, we produce highly detailed fracture surfaces. The computational cost of the BEM is alleviated by using a low-resolution mesh and interpolating the resulting stress intensity factors when propagating the high-resolution crack-front. Our system produces physics-based fracture surfaces with high spatial and temporal resolution, taking spatial variation of material toughness and/or strength into account. It also allows for crack initiation to be handled separately from crack propagation, which is not only more reasonable from a physics perspective, but can also be used to control the simulation. Separating the resolution of the crack-front from the resolution of the computational mesh increases the efficiency and therefore the amount of visual detail on the resulting fracture surfaces. The BEM also allows us to re-use previously computed blocks of the system matrix.

/pdf/high-resolution-brittle-fracture-simulation-with-boundary-422cbg9zqm.pdf

David Hahn

Papers

ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact.

ADD: analytically differentiable dynamics for multi-body systems with frictional contact

Surface-only liquids

Real2Sim: visco-elastic parameter estimation from dynamic motion

High-resolution brittle fracture simulation with boundary elements