Dynamic Multivariate Simplex Splines For Volume Representation And Modeling

Volume representation and modeling of heterogeneous objects acquired from real world are very challenging research tasks and playing fundamental roles in many potential applications, e.g., volume reconstruction, volume simulation and volume registration. In order to accurately and efficiently represent and model the real-world objects, this dissertation proposes an integrated computational framework based on dynamic multivariate simplex splines (DMSS) that can greatly improve the accuracy and efficacy of modeling and simulation of heterogenous objects. The framework can not only reconstruct with high accuracy geometric, material, and other quantities associated with heterogeneous real-world models, but also simulate the complicated dynamics precisely by tightly coupling these physical properties into simulation. The integration of geometric modeling and material modeling is the key to the success of representation and modeling of real-world objects. The proposed framework has been successfully applied to multiple research areas, such as volume reconstruction and visualization, nonrigid volume registration, and physically based modeling and simulation

Design and fabrication of materials with desired deformation behavior

Figure 1: Two examples of real and replicated objects. Thanks to our data-driven process, we are able to measure, simulate, and obtain material combinations of non-linear base materials that match a desired deformation behavior. We can then print those objects with multi-material 3D printers using two materials (blue and black) with varying internal microstructure. This paper introduces a data-driven process for designing and fab-ricating materials with desired deformation behavior. Our process starts with measuring deformation properties of base materials. For each base material we acquire a set of example deformations, and we represent the material as a non-linear stress-strain relationship in a finite-element model. We have validated our material measure-ment process by comparing simulations of arbitrary stacks of base materials with measured deformations of fabricated material stacks. After material measurement, our process continues with designing stacked layers of base materials. We introduce an optimization pro-cess that finds the best combination of stacked layers that meets a user’s criteria specified by example deformations. Our algorithm employs a number of strategies to prune poor solutions from the combinatorial search space. We demonstrate the complete process by designing and fabricating objects with complex heterogeneous materials using modern multi-material 3D printers

Data-driven finite elements for geometry and material design

Crafting the behavior of a deformable object is difficult---whether it is a biomechanically accurate character model or a new multimaterial 3D printable design. Getting it right requires constant iteration, performed either manually or driven by an automated system. Unfortunately, Previous algorithms for accelerating three-dimensional finite element analysis of elastic objects suffer from expensive precomputation stages that rely on a priori knowledge of the object's geometry and material composition. In this paper we introduce Data-Driven Finite Elements as a solution to this problem. Given a material palette, our method constructs a metamaterial library which is reusable for subsequent simulations, regardless of object geometry and/or material composition. At runtime, we perform fast coarsening of a simulation mesh using a simple table lookup to select the appropriate metamaterial model for the coarsened elements. When the object's material distribution or geometry changes, we do not need to update the metamaterial library---we simply need to update the metamaterial assignments to the coarsened elements. An important advantage of our approach is that it is applicable to non-linear material models. This is important for designing objects that undergo finite deformation (such as those produced by multimaterial 3D printing). Our method yields speed gains of up to two orders of magnitude while maintaining good accuracy. We demonstrate the effectiveness of the method on both virtual and 3D printed examples in order to show its utility as a tool for deformable object design.National Science Foundation (U.S.) (Grant CCF-1138967)United States. Defense Advanced Research Projects Agency (N66001-12-1-4242

Multifarious Hierarchies of Mechanical Models for Artist Assigned Levels-of-Detail

International audienceWe present a new framework for artist driven level of detail in solid simulations. Simulated objects are simultaneously embedded in several, separately designed deformation models with their own independent degrees of freedom. The models are ordered to apply their deformations hierarchically, and we enforce the uniqueness of the dynamics solutions using a novel kinetic filtering operator designed to ensure that each child only adds detail motion to its parent without introducing redundancies. This new approach allows artists to easily add fine-scale details without introducing unnecessary degrees-of-freedom to the simulation or resorting to complex geometric operations like anisotropic volume meshing. We illustrate the utility of our approach with several detail enriched simulation examples

High-strain deformation of conglomerates: Numerical modelling, strain analysis, and an example from the Wutai Mountains, North China Craton

Conglomerates have been widely used to investigate deformation history and rheology, strain, vorticity and viscosity. Previous studies reveal that several factors, such as pebble shapes and concentrations, as well as material properties, affect conglomerate deformation. However, how pebble concentration and interaction between pebbles affect deformation is not understood very well. We use the 2D numerical modelling platform ELLE coupled to the full field crystal visco-plasticity code (VPFFT) to simulate the deformation of conglomerates with various viscosity contrasts between pebbles and matrix and different pebble concentrations, with both linear (stress exponent n = 1) and power-law (n = 3) viscous rheologies, under simple shear conditions up to a shear strain of ten. Pebbles can behave as effectively passive, deformable or effectively rigid. An increase in pebble concentrations/viscosity contrasts enhances pebble deformation, but reduces their rotation. A mean aspect ratio (Rf) - orientation (ϕ) plot is proposed to gain an estimate of pebble deformation behaviour and the amount of bulk strain. Closely spaced rigid or deformable pebbles can form clusters that mechanically act as single inclusions. Rigid clusters rotate and survive for only short strain increments, whereas the more stable deformable ones keep on elongating with minor rotation. We provide a natural example of deformed conglomerates from the Wutai Mountains, North China Craton. These consist of banded-iron-formation (BIF) pebbles embedded in a schistose matrix. Using the mean Rf-ϕ plot, a finite strain of ∼6 under simple shear could be determined. The viscosity of the pebbles is estimated at about 5-8 times that of the matrix for a linear rheology (n = 1), or 2 to 5 times if a power-law rheology with n = 3 is assumed

Challenges and Status on Design and Computation for Emerging Additive Manufacturing Technologies

The revolution of additive manufacturing (AM) has led to many opportunities in fabricating complex and novel products. The increase of printable materials and the emergence of novel fabrication processes continuously expand the possibility of engineering systems in which product components are no longer limited to be single material, single scale, or single function. In fact, a paradigm shift is taking place in industry from geometry-centered usage to supporting functional demands. Consequently, engineers are expected to resolve a wide range of complex and difficult problems related to functional design. Although a higher degree of design freedom beyond geometry has been enabled by AM, there are only very few computational design approaches in this new AM-enabled domain to design objects with tailored properties and functions. The objectives of this review paper are to provide an overview of recent additive manufacturing developments and current computer-aided design methodologies that can be applied to multimaterial, multiscale, multiform, and multifunctional AM technologies. The difficulties encountered in the computational design approaches are summarized and the future development needs are emphasized. In the paper, some present applications and future trends related to additive manufacturing technologies are also discussed

Applicability of the Eshelby Formalism to Viscous Power-Law Materials: A Numerical Validation

Fabric is important for the interpretation of tectonic evolutions. In the process of extrapolating small-scale fabric to tectonics, modeling frameworks are needed. Neither the early kinematic models nor the contemporary computational geodynamics are able to capture the complexities of the fabric development in natural deformation systems. Eshelby proposed a formalism in micro-mechanics, and it is now well understood that this formalism works well for the linear viscous deformations. However, given that most of the natural rocks are power-law materials, the Eshelby Formalism cannot be directly applied to geological problems. This problem was largely solved when Lebensohn and Tom (1993, Acta Metallurgica et Materialia, vol 41, 2611-2624) incorporated a linearization scheme with Eshelby Formalism, known as the Tangent Linearization. The purpose of this project is to validate the applicability of the Eshelby Formalism with Tangent Linearization (EFTL) or with Secant Linearization (EFSL) to power-law material deformations. Two types of simulations are proceeded, one is based on EFTL / EFSL, while the other one based on 2D finite difference geodynamic method. Comparisons of the two simulations show that even in the most general situation of power-law material deformations, EFSL has major differences with the simulated power-law behavior while EFTL has only an approximately 10% deviation. Through this project, EFTL is validated to be a new, sufficient framework for fabric modeling, which marks a new era of fabric interpretation both in theoretical simulations and in field work practice

A Heterogeneous and Multi-Range Soft-Tissue Deformation Model for Applications in Adaptive Radiotherapy

During fractionated radiotherapy, anatomical changes result in uncertainties in the applied dose distribution. With increasing steepness of applied dose gradients, the relevance of patient deformations increases. Especially in proton therapy, small anatomical changes in the order of millimeters can result in large range uncertainties and therefore in substantial deviations from the planned dose. To quantify the anatomical changes, deformation models are required. With upcoming MR-guidance, the soft-tissue deformations gain visibility, but so far only few soft-tissue models meeting the requirements of high-precision radiotherapy exist. Most state-of-the-art models either lack anatomical detail or exhibit long computation times. In this work, a fast soft-tissue deformation model is developed which is capable of considering tissue properties of heterogeneous tissue. The model is based on the chainmail (CM)-concept, which is improved by three basic features. For the first time, rotational degrees of freedom are introduced into the CM-concept to improve the characteristic deformation behavior. A novel concept for handling multiple deformation initiators is developed to cope with global deformation input. And finally, a concept for handling various shapes of deformation input is proposed to provide a high flexibility concerning the design of deformation input. To demonstrate the model flexibility, it was coupled to a kinematic skeleton model for the head and neck region, which provides anatomically correct deformation input for the bones. For exemplary patient CTs, the combined model was shown to be capable of generating artificially deformed CT images with realistic appearance. This was achieved for small-range deformations in the order of interfractional deformations, as well as for large-range deformations like an arms-up to arms-down deformation, as can occur between images of different modalities. The deformation results showed a strong improvement in biofidelity, compared to the original chainmail-concept, as well as compared to clinically used image-based deformation methods. The computation times for the model are in the order of 30 min for single-threaded calculations, by simple code parallelization times in the order of 1 min can be achieved. Applications that require realistic forward deformations of CT images will benefit from the improved biofidelity of the developed model. Envisioned applications are the generation of plan libraries and virtual phantoms, as well as data augmentation for deep learning approaches. Due to the low computation times, the model is also well suited for image registration applications. In this context, it will contribute to an improved calculation of accumulated dose, as is required in high-precision adaptive radiotherapy

SOFA: A Multi-Model Framework for Interactive Physical Simulation

International audienceSOFA (Simulation Open Framework Architecture) is an open-source C++ library primarily targeted at interactive computational medical simulation. SOFA facilitates collaborations between specialists from various domains, by decomposing complex simulators into components designed independently and organized in a scenegraph data structure. Each component encapsulates one of the aspects of a simulation, such as the degrees of freedom, the forces and constraints, the differential equations, the main loop algorithms, the linear solvers, the collision detection algorithms or the interaction devices. The simulated objects can be represented using several models, each of them optimized for a different task such as the computation of internal forces, collision detection, haptics or visual display. These models are synchronized during the simulation using a mapping mechanism. CPU and GPU implementations can be transparently combined to exploit the computational power of modern hardware architectures. Thanks to this flexible yet efficient architecture, \sofa{} can be used as a test-bed to compare models and algorithms, or as a basis for the development of complex, high-performance simulators