Material Reconstruction Using Data Driven Approach

Deformation is a common phenomenon in the real world and we refer to those objects which can exhibit elastic resistent against undergoing deformation as elastos.As the developement of computer science and technology constantly shapes our life,the technology of physical-based simulation is widely used in many aspects of our world like the visually plausible deformable objects in movie industry,virtual surgery,soft robotics simulation and structural analysis in construction etc.The constitutive model defines the relationship between stress and strain of deformable body,and with a specific constitutive model,the elastic parameters define the stiffness,resistence against stretching,compression and shearing on different parts of deformable body.The damping model,at the same time,defines viscosity of the system.The modeling of a deformable object,both geometrically and mechanically,is the premises of simulation.Compared with the geometrical modeling,the mechanical modeling is a far more complicated and tedious work.The mechanical modeling of objects consists of two aspects,choosing a specific constitutive model first and then an appropriate distribution of mechanical parameters.When modeling the real world object,the accuracy of the modeling largely depends on whether the chosen constitutive model suits the real mechanical system and the distribution of mechanical parameters matches with the real on.The conventional constitutive models can cover only a small fraction of real world phenomenon.In order to expand the covering domain,we need a more general setting of constitutive model to enclose as many phenomenon as possible.Traditionally,with a given standard constitutive model,people can get an appropriate model setting through parameter tuning.As the elastic objects get more complicated,in order to achieve the desired accuracy or visual results,people suffer from constant and tedious tuning process,consuming quite a lot labour work and time.All these sufferings give rise to some auto-modeling technologies which become quite popular recently.With data driven approach,computer can automatically reconstruct the distribution of mechanical parameters and even choosing an appropriate constitutive model at the same time through captured data.The main target of this thesis is to make use of differentiable simulation to develope a fully automitic material reconstruction framework which can reconstruct both constitutive model and distribution of mechanical parameters.We focus on two selling points,on the one hand we propose a generalize constitutive model which can cover most of the constitutive model,on the other hand,we propose a new reconstruction framework which can achieves a much better convergence,with better reconstruction accuracy and guarantees the stability of simulation during the process.Specifically speaking,the main contributions of this thesis are as following:1.In order to expand the border of standard constitutive model,we propose a new constitutive model based on B-spline with which,even the deformable body undergoes an extreme deformation,we can still guarantees the stability of simulation and reconstruction.2.We propose a new reconstruction frame work based on the trajectory fitting of periodic forced vibration.Compared with the standard reconstruction framework,the new framework exhibits much better convergent property,required far less iterations and less computational expense within one iteration.3.We borrow part of the idea from traditional harmonic balance method to overcome the burden of transient state's simulation and greatly speed up the simulation of the steady state of periodic forced vibration.At the mean time,we improve the traditional harmonic balance method to encapsolate the information of temporal descritization to expand the application scope of our reconstruction framework with different integrators.