Geometrical and topological issues in octree based automatic meshing

Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is discussed. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary representation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractor. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed

A hierarchical structure for automatic meshing and adaptive FEM analysis

A new algorithm for generating automatically, from solid models of mechanical parts, finite element meshes that are organized as spatially addressable quaternary trees (for 2-D work) or octal trees (for 3-D work) is discussed. Because such meshes are inherently hierarchical as well as spatially addressable, they permit efficient substructuring techniques to be used for both global analysis and incremental remeshing and reanalysis. The global and incremental techniques are summarized and some results from an experimental closed loop 2-D system in which meshing, analysis, error evaluation, and remeshing and reanalysis are done automatically and adaptively are presented. The implementation of 3-D work is briefly discussed

Nonlinear finite element evaluation of the structural response to lateral accelerations of the adobe church of Andahuaylillas, Peru

The Saint Peter Apostle church of Andahuaylillas was built at the early 17th Century and is a representative example of colonial adobe churches in the Andes. Although it has been subjected to constant aesthetic restoration in the recent years, a complete study of its seismic behavior is needed due to the brittle condition of its structural system (composed by a unfired-clay-bricks and earthen mortar known as adobe masonry) and its location in a region with high seismic hazard. This work is part of the integral seismic assessment of the building and focuses on the seismic evaluation of the triumphal arch by means of a static nonlinear analysis. For this purpose, nonlinear finite element (FE) models of the arch were implemented in Abaqus/CAE Explicit and TNO Diana considering a damage-plasticity formulation and a total-strain crack constitutive relationship, respectively, for representing the adobe quasi-brittle behavior. Following an analysis approach simulating up to complete structural collapse, the FE models were used to identify the critical accelerations leading to collapse and the damage patterns. A sensitivity analysis was also carried out considering different material properties for determining the influence of these parameters in the lateral capacity of the studied sub-structure. In addition, different geometrical conditions were considered to increase the capacity of the triumphal arch. Removing the window openings from sidewalls provided more capacity and different crack patterns. Heightening the sidewalls also had a significant influence on capacity

(02) A Concrete Damage Plasticity Model For Ancient Roman Pozzolanic Concrete Vaulted (slides)

The invention of pozzolanic concrete (opus caementicium) provided ancient Roman engineers with an extraordinarily versatile and durable building material, which made possible the construction of some of the largest and most complex vaulted structures built in antiquity. In 2010, in collaboration with Ingraffea, we conducted an experimental study on Mode-I fracture properties of reproduced Imperial Roman pozzolanic mortar using an ad-hoc arc shaped bending test. In the present study we use these data in conjunction with post-critical compressive response data available from the literature to construct a non-linear damage plasticity formulation for opus caementicium suitable for 3D implementation in Abaqus Explicit. We use this FE formulation to evaluate how the structural design of the vault supporting system of Diocletian’s Frigidarium (298-306 AD), consisting of flanking shear walls and monolithic granite columns, affects the development and propagation of fractures and ultimately the static and seismic stability of the vault

How I Teach: Renato Perucchio

Renato Perucchio is a member of the Department of Mechanical Engineerin

The Mechanics of imperial Roman concrete and the structural design of vaulted monuments.

(Ph. D.)--University of Rochester. Dept. of Mechanical Engineering, 2011.This dissertation explores the mechanical behavior of ancient Roman concrete and the structural behavior of the cross-vaulted form as they collaborate in Roman vaulted concrete monuments. The scale alone of these buildings, with spans in excess of 25m, makes their creation with unreinforced concrete a remarkable engineering success. This achievement is compounded by their extraordinary survival over the centuries, amidst seismic ground motions and differential settling on weakly consolidated bedrock--often with minimal maintenance--all the more remarkable. And yet many fundamental insights into their functionality as structures remain elusive. This dissertation is intended to fill in some of the current gaps in knowledge, as well as create a formal engineering approach that will facilitate other works to do so. First, the state of the art of several central topics are critically reviewed and synthesized into guidelines for structural analysis. The modern concrete design code and plastic design theory recommend conflicting approaches in the analytical assessment of structural function. The various assumptions that are made to describe the mechanical behavior of the constituent materials are at the root of these differences; this motivates an examination of the results of previous experimental tests on ancient Roman concrete and its component materials. This review indicates that it is accurate to assume that ancient Roman concrete possesses an appreciable tensile strength. An examination of past analytical treatments of three ancient Roman vaulted concrete monuments--the so-called "Temple of Minerva Medica" by Giovannoni, the Heliocaminus by Tosi, and the Basilica of Maxentius by Samuelli Ferretti--reveals both inspirational ideas and analytical shortcomings. These analytical considerations, together with the findings from the experimental data, guide the following structural analyses. The structural analyses examine the Great Hall of Trajan's Markets and the Frigidarium of Diocletian's Baths. Specifically, the analyses represent the monuments' immediate static responses, i.e., the instant of disarming from the temporary constructional formwork used to realize the curved vault forms. The immediate static response allows for an assessment of the functionality of the structures (or, structural designs) as a whole, and of the various components therein, when the structural geometry, applied loads, and boundary conditions can be characterized without excessive speculation. A force-based methodology is devised to visualize and assess the equilibrium states in terms of free-body diagrams, in addition to tensile stress distributions. For the latter, a simplified measure is defined that approximately quantifies the safety of the overall equilibrium state according to an aggregated volumetric measure of the Maximum Principal stress state. Two novel results, in particular, emerge from the analyses: in the Great Hall, the lateral arches, often interpreted as flying buttresses, are instead found not to support the main vault, while in the Frigidarium the granite columns are revealed to significantly increase tensile stresses in the main vault. The results point to the importance of including the mechanical degradation behavior of Roman concrete in the analytical models. The Fictitious Crack Model is thus adopted to apply nonlinear fracture mechanics to describe the Mode-I tensile fracture of Roman concrete, subject to assumed fracture properties. A damaged-plasticity model is verified to effectively implement the assumed constitutive behavior in a three-dimensional analysis, with an acceptable amount of mesh sensitivity. An energetic failure criterion that relates the total stored energy with the total dissipated energy is introduced and found to effectively identify a failure state in Roman vaulted concrete structures. The damaged-plasticity model is employed to explore the effect of variations in the tensile fracture properties, in particular the tensile strength, on the structural-scale failure behavior. The structural performance of spanning structures is found to strongly depend on the tensile strength and, for pure Mode-I loading and appreciable tensile strengths, also depend on the tensile Fracture Energy. Assumed fracture properties are then used to expand the evaluation of the immediate static responses of the Great Hall and Frigidarium and define a margin of safety that effectively incorporates the mechanical degradation behavior. An experimental investigation aims to measure the fracture properties of a laboratory-fabricated Roman mortar, as part of a broader study to ascertain the structural-scale fracture properties of the ancient composite concrete. A new experimental fracture testing system is created to test arc-shaped mortar specimens in three-point bending. Three ages of the re-fabricated mortar are tested after curing durations of 28, 90, and 180 days. Inverse analysis extrapolates the Young's Modulus, Modulus of Rupture, and traction-separation description from experimental data. Mechanical and fracture properties increase with curing duration

Numerical evaluation of the dynamic response of masonry heritage structures

Thesis (Ph. D.)--University of Rochester. Dept. of Mechanical Engineering, 2015.A concrete damage plasticity model for non-linear FE analysis is calibrated in order to simulate the static and dynamic response of monumental structures built with pozzolanic concrete (opus caementicium) in Imperial Rome and adobe masonry in Peru. In the case of the opus caementicium, the inelastic portion of this quasi-brittle material is represented in tension by a bilinear softening law. The tensile strength σt, the fracture energy Gf, and the tensile damage factor dt numerically determined from a series of experimental arc-shaped three-point bending tests on recreated Roman pozzolanic mortar samples are used. The inelastic compressive behavior is characterized by a hardening/softening response curve derived from experimental tests on actual opus caementicium available in the literature. These damage plasticity parameters are used in Abaqus to analyze the structural response of the Frigidarium of the Baths of Diocletian under gravitational loads, lateral accelerations and dynamic base motion ground acceleration loading conditions. The results give insights on the structural role of monolithic columns and flanking shear walls in supporting the concrete vault. For the adobe masonry, the inelastic portion of this quasi-brittle material is represented in tension by an exponential softening curve while in compression a parabolic representation is assumed. This research uses in-situ operational modal analysis (OMA) tests to calibrate numerical finite element models developed in Abaqus CAE by comparing the numerical and experimental frequencies and mode shapes of the bell tower of the church St. Peter the Apostle in Andahuaylillas, Peru. The study of this structure evaluates the overall response of the church due to lateral accelerations and dynamic base motion ground acceleration loading conditions. The results give insights into the behavior and vulnerability of certain structural aspects of the church. This body of work demonstrates the applicability of a concrete damage plasticity model for the non-linear finite element evaluation of quasi-brittle masonry materials in Abaqus CAE. The in-situ tests confirmed that the modeling techniques implemented in this study can be used to accurately represent monumenta

Techniques for extended modeling of cardiac morphogenesis in the embryonic chick

Thesis (Ph. D.)--University of Rochester. Dept. of Mechanical Engineering, 2010.Computational models that simulate the biophysical mechanisms of early cardiac morphogenesis in the embryonic chick heart have been used to demonstrate the influence of biomechanics in cardiac development. However, algorithms for the automatic coding of material subroutines that govern the constitutive relations of biological tissues, generating realistic geometries, transferring solution results correctly during analysis continuation procedures, and for including advanced biomechanical components of the developing cardiac environment limit current models from demonstrating the role biomechanics has on normal cardiac development. The purpose of our work is to develop and demonstrate novel techniques to resolve each of the aforementioned limitations and use new techniques to model the hypothetical role of biomechanics in cardiac development. First, we use the symbolic mathematics software Mathematica and nonlinear continuum mechanics to automatically generate FORTRAN based user material subroutines. The Mathematica notebook only requires the definition of a pseudoelastic strain energy function to generate the current Cauchy stress and Tensor of Elasticity for all integration points in the model. We demonstrate the accuracy of the automatically generated code using uniaxial, equibiaxial, and simple shear tests of materials defined by a Fung-Orthotropic pseudoelastic strain energy function. The code is also capable of modeling continuum growth, and we therefore test it by curling and twisting a bilayered bar. The Mathematica user material subroutine generator automatically generated user material subroutines that performed well for standard tests in hyperelasticity and complex problems in biomechanics. Therefore, we made the code freely available as supplemental material to an article we published in the Journal of Biomechanical Engineering. We then describe the generation of realistic geometries by demonstrating the benets and drawbacks to voxel based reconstructions. To resolve the limitations of the pure voxel based mesh, we present both results smoothing and mesh smoothing algorithms. We adapt the theory of membranes to design an algorithm, which recalculates the results on the boundaries of a pure voxel based mesh. Additionally, we implement Laplacian band-pass smoothing to modify the pure voxel based mesh, and thus generate a new smoothed geometric mesh. We conclude that results recalculation is only valid if the radius of curvatures represented in the model are large compared to voxel size. However, the mesh smoothing technique used here provides a realistic valid mesh, which can be used in nonlinear analyses. Next we outline the standard technique for solution transfer and demonstrate its limitation when transferring field discontinuities. We develop a novel solution transfer scheme that reduces the diffusion of solution fields during analysis transfer. We demonstrate the benets of our novel solution transfer technique in a simple growth based example that relates to cardiac morphogenesis. Finally, we include the presence of the splanchnopleure, implement cohesive contact to simulate fusion of the omphalomesenteric veins, include element deletion to simulate the rupture of the dorsal mesocardium, and recast the developmental biomechanics of early cardiac morphogenesis using a nonlinear explicit dynamics solver. The new computational model extends previously studied mechanisms of cardiac morphogenesis to study c-looping in a single simulation. We maintain the growth stretches used to simulate normal development, while we independently eliminate the major structural components of the heart model to provide secondary validation of the hypothesized growth mechanisms of normal development. The predicted deformation, stress, and strain of the extended model are qualitatively and quantitatively agreeable compared to in vivo observations of cardiac development in the embryonic chick. The algorithms we describe and implement in this work extend the capabilities of current computational models in describing the biomechanics of cardiac morphogenesis. We use a variety of numerical tools to overcome the limitations of current models, and though our focus is on cardiac development, these tools are beneficial for studying related problems in growth and remodeling