4,360 research outputs found
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
A stable FSI algorithm for light rigid bodies in compressible flow
In this article we describe a stable partitioned algorithm that overcomes the
added mass instability arising in fluid-structure interactions of light rigid
bodies and inviscid compressible flow. The new algorithm is stable even for
bodies with zero mass and zero moments of inertia. The approach is based on a
local characteristic projection of the force on the rigid body and is a natural
extension of the recently developed algorithm for coupling compressible flow
and deformable bodies. Normal mode analysis is used to prove the stability of
the approximation for a one-dimensional model problem and numerical
computations confirm these results. In multiple space dimensions the approach
naturally reveals the form of the added mass tensors in the equations governing
the motion of the rigid body. These tensors, which depend on certain surface
integrals of the fluid impedance, couple the translational and angular
velocities of the body. Numerical results in two space dimensions, based on the
use of moving overlapping grids and adaptive mesh refinement, demonstrate the
behavior and efficacy of the new scheme. These results include the simulation
of the difficult problem of a shock impacting an ellipse of zero mass.Comment: 32 pages, 20 figure
A modeling framework for contact, adhesion and mechano-transduction between excitable deformable cells
Cardiac myocytes are the fundamental cells composing the heart muscle. The
propagation of electric signals and chemical quantities through them is
responsible for their nonlinear contraction and dilatation. In this study, a
theoretical model and a finite element formulation are proposed for the
simulation of adhesive contact interactions between myocytes across the
so-called gap junctions. A multi-field interface constitutive law is proposed
for their description, integrating the adhesive and contact mechanical response
with their electrophysiological behavior. From the computational point of view,
the initial and boundary value problem is formulated as a structure-structure
interaction problem, which leads to a straightforward implementation amenable
for parallel computations. Numerical tests are conducted on different couples
of myocytes, characterized by different shapes related to their stages of
growth, capturing the experimental response. The proposed framework is expected
to have impact on the understanding how imperfect mechano-transduction could
lead to emergent pathological responses.Comment: 31 pages, 17 figure
The non-smooth contact dynamics method
International audienceThe main features of the Non-Smooth Contact Dynamics method are presented in this paper, the use of the dynamical equation, the non-smooth modelling of unilateral contact and Coulomb's law, fully implicit algorithms to solve the dynamical frictional contact problem for systems with numerous contacting points, in particular large collections of rigid or deformable bodies. Emphasis is put on contact between deformable bodies. Illustrating numerical simulation examples are given for granular materials, deep drawing and buildings made of stone blocks
Implicit solutions with consistent additive and multiplicative components
Use of multiple-point-constraint
Robust interactive simulation of deformable solids with detailed geometry using corotational FEM
This thesis focuses on the interactive simulation of highly detailed deformable solids modelled with the Corotational Finite Element Method.
Starting from continuum mechanics we derive the discrete equations of motion and present a simulation scheme with support for user-in-the-loop interaction, geometric constraints and contact treatment. The interplay between accuracy and computational cost is discussed in depth, and practical approximations are analyzed with an emphasis on robustness and efficiency, as required by interactive simulation.
The first part of the thesis focuses on deformable material discretization using the Finite Element Method with simplex elements and a corotational linear constitutive model, and presents our contributions to the solution of widely reported robustness problems in case of large stretch deformations and finite element degeneration. First,we introduce a stress differential approximation for quasi-implicit corotational linear FEM that improves its results for large deformations and closely matches the fullyimplicit solution with minor computational overhead. Next, we address the problem ofrobustness and realism in simulations involving element degeneration, and show that existing methods have previously unreported flaws that seriously threaten robustness and physical plausibility in interactive applications. We propose a new continuous-time approach, degeneration-aware polar decomposition, that avoids such flaws and yields robust degeneration recovery.
In the second part we focus on geometry representation and contact determination for deformable solids with highly detailed surfaces. Given a high resolution closed surface mesh we automatically build a coarse embedding tetrahedralization and a partitioned representation of the collision geometry in a preprocess. During simulation, our proposed contact determination algorithm finds all intersecting pairs of deformed triangles using a memory-efficient barycentric bounding volume hierarchy, connects them into potentially disjoint intersection curves and performs a topological flood process on the exact intersection surfaces to discover a minimal set of contact points. A novel contact normal definition is used to find contact point correspondences suitable for contact treatment.Aquesta tesi tracta sobre la simulació interactiva de sòlids deformables amb superfícies detallades, modelats amb el Mètode dels Elements Finits (FEM) Corotacionals. A partir de la mecànica del continuu derivem les equacions del moviment discretes i presentem un esquema de simulació amb suport per a interacció d'usuari, restriccions geomètriques i tractament de contactes. Aprofundim en la interrelació entre precisió i cost de computació, i analitzem aproximacions pràctiques fent èmfasi en la robustesa i l'eficiència necessàries per a la simulació interactiva. La primera part de la tesi es centra en la discretització del material deformable mitjançant el Mètode dels Elements Finits amb elements de tipus s'implex i un model constituent basat en elasticitat linial corotacional, i presenta les nostres contribucions a la solució de problemes de robustesa àmpliament coneguts que apareixen en cas de sobreelongament i degeneració dels elements finits. Primer introduïm una aproximació dels diferencials d'estress per a FEM linial corotacional amb integració quasi-implícita que en millora els resultats per a deformacions grans i s'apropa a la solució implícita amb un baix cost computacional. A continuació tractem el problema de la robustesa i el realisme en simulacions que inclouen degeneració d'elements finits, i mostrem que els mètodes existents presenten inconvenients que posen en perill la robustesa plausibilitat de la simulació en aplicacions interactives. Proposem un enfocament nou basat en temps continuu, la descomposició polar amb coneixement de degeneració, que evita els inconvenients esmentats i permet corregir la degeneració de forma robusta. A la segona part de la tesi ens centrem en la representació de geometria i la determinació de contactes per a sòlids deformables amb superfícies detallades. A partir d'una malla de superfície tancada construím una tetraedralització englobant de forma automàtica en un preprocés, i particionem la geometria de colisió. Proposem un algorisme de detecció de contactes que troba tots els parells de triangles deformats que intersecten mitjançant una jerarquia de volums englobants en coordenades baricèntriques, els connecta en corbes d'intersecció potencialment disjuntes i realitza un procés d'inundació topològica sobre les superfícies d'intersecció exactes per tal de descobrir un conjunt mínim de punts de contacte. Usem una definició nova de la normal de contacte per tal de calcular correspondències entre punts de contacte útils per al seu tractament.Postprint (published version
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