Research On The Fast Computing Algorithms For 3D Interaction Of Soft Material

In recent years,with the fast development of physics-based simulating techniques,3D interactions of soft materials have been widely used in virtual areas like movies,animation,and games.The 3D interacting procedures may contain multiple complex physical phenomena,such as non-smooth interface contact,uncertain boundary constrains,non-linear constitutive model,isotropic/anisotropic deformation,etc.In order to accurately model each possible effect,it is required to make lots of meticulous treatment on the numerical methods.Consequently,it is very hard to handle massive computation with limited CPU time and storage memory.Besides,the simulation complexity and the computation cost are generally contradictory.How to make a trade-off between them has become a long-standing difficulty for researchers.This dissertation gives a deep research on the key issues of soft body interactions,and establishes a complete research system consisting of theoretical deduction,numerical implementation,and software development.The aim of this paper is to solve the three bottleneck problems occurring in the 3D interacting procedures: contact detection,contact solution,and deformation computation.Several corresponding methods have been proposed,which can obtain high-quality simulating results as well as very fast computing speed.The main contents of this work are summarized as follows:1.We present a three-stage scheme for the contact inspections between soft bodies.In the top global search phase,an incremental-volume-based method has been proposed to quickly exclude the impossible contacting bodies as well as obtain balanced binary tree structure.In the middle phase for local mesh intersection,a hybrid method by using separated node primitive and finite element primitive has been carried out.This strategy can directly result in vertex-face pairs for subsequent contact solution,and efficiently reduce duplicate elementary tests during the binary tree traversal.Finally,in the low phase,a perturbation-based algorithm combined with isoparametric surface projection has been applied.This algorithm is to determine whether the elementary pairs can satisfy the contact mapping relationship,and also to obtain accurate contact penetration information.Besides,to address the possible self-contact situations when soft body deforms largely,a hierarchy tree by means of normal cone formulations has also been presented.The numerical experiments show that,our proposed algorithms can efficiently handle the contact detection problems for soft material system,and possess much better computational performance compared with other traditional methods.2.Within augmented Lagrangian framework,we propose a fast computing algorithm to deal with the static interacting cases.Since considering multiple non-linearities together can case huge computational burden,a reduction pretreatment for the inverse of initial stiffness matrix is firstly performed.Then,we approximate the expensive Delassus operator at each time step by using the co-rotating matrices of contact nodes.This process can greatly accelerate the local contact solution without losing much accuracy.To address the variational inequalities,a unique mathematical factor is introduced within the framework of augmented Lagrange.This factor can make certain mathematic reduction,because it does not add additional unknowns compared to general Lagrangian multiplier.Numerical tests show that our algorithm can accurately describe the mechanical behavior of large deformation and large rotation,and can achieve very fast computational speed at the cost of taking into account strong nonlinear characteristics like multiple-contact coupling and frictional contact.To address the slow iterative speed of bi-potential-based Uzawa method,an improved method by using the changeable incremental step from dual optimized algorithms has been proposed.Numerical experiments show that,this method can achieve the same precision as the original one,but with fewer iterations and faster computing speed.3.We present a new velocity-based semi-explicit method to handle the dynamic contact cases.Under dynamic conditions,the mass matrix and damping matrix should be considered.However,it may case inaccuracy by continue using the co-rotational approximated strategy proposed in point 2,in particular for large deformation situations.In terms of this issue,a special implicit coupling relation between contact reactions and local relative velocity are established.The coupled relation permits the unknowns to be separately solved via a semiexplicit scheme: firstly,reaction forces can be obtained through the implicit iterations within augmented Lagrangian method,and then can be explicitly incorporated into global govern equations for the velocity solution.This strategy allows the whole solution to be processed without solution of large-scaled system of equations,nonlinear Newton-Raphson iterations,factorization of global stiffness matrix,and inverse computation of large sparse matrix,thus leading to very fast computing speed.The algorithm also considers multiple-contact coupling effects,as well as the velocity-based Signorini-Coulomb contact model,so that the simulating accuracy can be well guaranteed.Additionally,the stiffness effects including anisotropy hyper-elasticity and visco-elasticity can be reflected by the HEML-based calculation of internal forces,and the description of soft material is not limited to a particular constitutive model.Numerical tests show that,our proposed method can achieve similar precision,but much better computing performance over the popular pure implicit methods.4.We develop an interactive software named LiToTac,which aims at solving and analyzing multi-body contacting system characterized by soft materials.By using Object-Oriented Programming method and Open GL + Qt techniques,several crucial components are incorporated into the software,these include interactive graphical user interface,standard mechanical elements and material libraries,static/dynamic solver engines,module data manager,and file transportation connector.By using the proposed contact detection methods,LiToTac is able to perform automatic contact detection,which can avoid the tedious operations of pre-defining master-slave contact sets in commercial CAE software.The fast finite element methods implemented in LiToTac allow users to handle numerous 3D interacting situations,and to analyze the mechanical behavior with multiple nonlinearities.In addition,professional material models can be inserted flexibly into LiToTac,and the internal structure can be observed by perspective functions.By comparing with commercial CAE software like ANSYS and ABAQUS,the accuracy and robustness of LiToTac is well demonstrated.