We propose a comprehensive Isogeometric Kirchhoff–Love shell framework that is capable of undergoing large elasto-plastic deformations. Central to this development, we reformulate the governing thin-shell equations in terms of the mid-surface velocity degrees of freedom, accommodating the material response in the time-rate form while ensuring objectivity. To handle complex multipatch geometries, we propose a consistent penalty coupling technique for enforcing the continuity conditions at patch interfaces. Penalty is also employed to weakly enforce symmetry boundary conditions. A recently proposed non-local penalty contact is adopted as part of the formulation in order to handle complex dynamic crushing simulations. Numerical examples, ranging from static elasto-plastic shell benchmarks to highly dynamic crushing scenarios, validate the accuracy, efficiency and robustness of the proposed framework.

Cite This Article Wang, Y., Wang, Z., Deng, X., Benson, D. J., Pasini, D. et al. (2020). Introduction to the Special Issue on Recent Developments of Isogeometric Analysis and Its Applications in Structural Optimization. CMES-Computer Modeling in Engineering & Sciences, 124(3), 783–785.

The paper presents results of experimental and numerical research on the mechanism of macrocavity collapse in highly heterogeneous, porous mixtures of Al and W particles with large differences in strength, ductility, and density of components. Mixtures with different grain sizes of W particles and porosity were investigated in plane-strain, high-strain-rate conditions using the explosively driven thick-walled cylinder method. It was demonstrated that macroscopic axial symmetry was preserved, and a pattern of localized shear bands was not formed, which was typical for many previously investigated brittle and ductile materials. The grain size has an influence on the size of the inner cavity microscale instabilities that are formed by the flow of plastically deformed softer Al particles between W particles. Initial porosity did not significantly influence the macrocavity collapse in the investigated materials.

In 2005, the term “Isogeometric Analysis” (IGA) was introduced by Hughes et al. [1]. Since then, reams of scientific research work has been devoted to this new finite element technology, whose main idea is to use the same geometrical description during the finite element analysis (FEA) that was previously used during the design process in the computer-aided design (CAD) environment. The most widely used and best understood mathematical description in CAD is based on non-uniform rational B-splines (NURBS). Hence NURBS-based shell and solid finite elements have been developed and implemented into LS-DYNA over the last few years. Although NURBS-based solids are available, the remainder of the paper will exclusively focus on isogeometric shell element formulations in LS-DYNA. In case of NURBS shells, thin-shell elements based on the Kirchhoff-Love shell theory as well as shear deformable shell elements based on the Reissner-Mindlin shell theory are available. LS-DYNA allows to perform finite element analysis on surface geometry descriptions based on trimmed NURBS and supports many other features that are commonly used, like contact boundary conditions, a huge library of material models, implicit and explicit time integration, mass scaling, eigenvalue analysis and others. Within the CAD environment, the geometry of a part is typically defined by a so-called boundary representation (B-Rep). This means, that a standard NURBS patch definition is expanded by a definition of various trimming curves that define visible and invisible regions of a surface. Thus, the outer surface is defined through an underlying NURBS patch description together with a set of outer trimming curves (boundary loop) living on the patch. Furthermore specific topology information is embedded in the CAD database to specify whether two or more trimmed patches represent a connected part or not. While in the CAD world it is sufficient to simply know the topological connection between individual trimmed NURBS patches, a finite element solver needs to make sure, that certain mechanical properties, like stresses, strains and bending moments, are consistently transferred from one patch to the other across the common interface. Breitenberger et al. [2] introduced the Isogeometric B-Rep Analysis (IBRA), which allows finite element analysis directly on B-Rep CAD models. For this, special interface elements are developed based on a classical penalty approach. As the method was initially developed for implicit static analysis based on thin Kirchhoff-Love type isogeometric shell elements, Leidinger et al. [3] extended the IBRA concept to nonlinear explicit dynamics, using shear deformable isogeometric shells available within LS-DYNA. The capabilities were demonstrated using the user-defined element interface in LS-DYNA. Inspired by the promising results, the proposed mechanical coupling method has been recently implemented into LS-DYNA and extended to rotation free thin shell isogeometric shell formulations.

The nature of short and long duration high amplitude pulses is explored in a periodic composite made of an Al matrix with W cylindrical inclusions using numerical calculations. Their wave nature is compared to the observed solitary like waves created by high amplitude short duration impact, or steady shock waves created by long duration high amplitude incoming pulses in Al-W laminates. Both composites have the same volume content of components to explore the role of mesostructure on the wave nature. The observed stress wave, in the case of short duration impact doesn't propagate as a localized solitary like wave, as was the case in the laminate. For a long duration, high amplitude loading, a shock wave is observed similar to the one propagating in the laminate.

In the last few years, numerous research work has been devoted to Isogeometric Analysis (IGA). IGA is a finite element technology in which computer-aided design (CAD) geometric description is invoked to perform numerical analysis. The most widely used mathematical description in CAD is non-uniform rational B-splines (NURBS) and therefore NURBS-based shell and solid finite elements have been implemented into LS-DYNA. This paper describes the recent advances of the NURBS-based shell implementation in LS-DYNA to enable the IGA technology for the use in sheet metal forming applications. Necessary features like stress, strain, thickness, and history variable mapping from one stage to the other, the trimming of the formed part and other typical features used by the forming analysts have been enabled for the use with NURBS-shells. The new keywords will be explained and the multistage forming process will be analyzed by means of an example. A comparison with current state-of-the art methods is provided and further developments are outlined.

Initiation, self-organization of shear bands, and post-critical behavior of 4340 steel with initial low (2789 MPa) and high (5420 MPa) microhardnesses, but similar thermophysical properties, are studied using the explosively-driven Thick Wall Cylinder method and numerical simulations. In experiments, low hardness 4340 steel demonstrated the initiation of a pattern of shear bands at a global effective strain of about 0.53, which did not significantly change with an increase of global strain up to 0.8. High microhardness 4340 steel demonstrated extremely different post-critical behavior. At global strain 0.56, a few well-developed shear bands propagated through the sample with their transformation into a crack pattern at larger global strain 0.83. The propagation mechanism of shear bands in hardened 4340 steel is explained by the interfacial microcracking between inclusions and matrix. The Johnson-Cook material model with damage in numerical simulations correctly predicted the dramatic change of pattern of shear bands with the change in the initial steel properties at similar global strains. The pattern of shear bands was dependent on the number of initial material defects introduced by scaling of the yield strength of mesh elements.

Isogeometric analysis (IGA) uses the spline functions from CAD (computer-aided design) for analysis with the objectives of 1) reducing the effort of moving from design to analysis, 2) using the actual geometry of the parts from CAD instead of approximating them with polynomials, and 3) obtaining higher order accuracy through the higher order basis functions of CAD. LS-DYNA is the first commercial code to support IGA through the implementation of generalized elements, and then through key word descriptions of patches of B-spline and NURBS elements. Three shell formulations and a solid element formulation are currently available. Additional recently added capabilities, including improved contact, anisotropic material modeling, spotweld models and support for unstructured spline capabilities through the specification of their Bezier extractions. These and other recent additions are described and demonstrated. In addition, some of the difficulties industry has encountered in moving to this new technology are discussed. Introduction to Isogeometric Analysis NURBS are the most commonly used functions in computer aided design (CAD) for representing the geometry of the boundaries of parts. They are popular because they can represent basic geometric shapes exactly with only a small amount of data, while also being able to define very general shapes that are not amendable to being described by simple analytical functions, e.g., car bodies. NURBS are defined on rectangular patches. To represent more general shapes, trimmed NURBS are defined by deleting parts of the patches specified by trimming curves. Isogeometric analysis [1] was introduced in 2005 by Thomas J. R. Hughes and his students, Austin Cottrell and Yuri Bazilevs. Its objective was succinctly summarized in the abstract: “Basis functions generated from NURBS (Non-Uniform Rational B-Splines) are employed to construct an exact geometric model. For purposes of analysis, the basis is refined and/or its order elevated without changing the geometry or its parameterization.” Isogeometric analysis was originally tested in LS-DYNA through the generalized element formulation introduced and implemented in the code by D. Benson while on sabbatical at the University of Texas, Austin with Tom Hughes in 2007. During the next few years, they were added as part of the standard element library by the current development team of D. Benson, S. Hartmann, A. Nagy, and L. Li. This paper summarizes some of the recent additions made to the IGA capability in LS-DYNA that we believe will be of the greatest interest to the user community. The details of these additions are provided in separate papers. 15th International LS-DYNA® Users Conference Isogeometric Analysis June 10-12, 2018 2 The Importance of Geometry The primary motivation behind isogeometric analysis is the use of the exact geometry for the analysis. The two attributes of NURBS in CAD that provide the geometric flexibility are 1) using them to define the boundary representation and 2) trimming them to arbitrary shapes. Unfortunately, they introduce obstacles to the use of NURBS in analysis. The difficulty of using boundary representations (B-rep) for analysis is the absence of any basis functions on the interior of a solid object for representing the displacement field. This difficulty can be overcome by using boundary element methods (BEM), but that limits the solutions to linear problems. Trimmed NURBS surfaces have their own problems. Their arbitrary shape means that special integration rules need to be formulated for each trimmed element. Stability can also be a problem. By far, the biggest difficulty with them is joining the edges of trimmed boundaries together since their basis functions don’t line up like for untrimmed NURBS patches and standard finite element formulations. The CAD software packages introduce their own set of challenges. At the time that these packages were being developed, no thought was given to the possibility of using the NURBS patches in the future for analysis. Ideally, each part would be represented by a minimal number of patches to maximize the smoothness of the geometric description and the convergence rate of the analysis. However, CAD models are revised over and over again during their lifetime, with the result that patches proliferate and minute gaps in the geometry are filled in with patches that are little more than slivers. These issues not only have a negative effect on analysis, but also on other uses of CAD geometry such as 3-D printing and importing CAD models from one CAD program to another. As a result, there is an entire industry devoted to “healing” CAD models with products such as Elysium’s CADdoctor. The process of generating a mesh from a CAD model is referred to as “mesh generation” and in IGA, it is referred to as “creating an analysis suitable geometry” (ASG). Many of the basis functions used in the ASG are not commonly used in CAD. Since CAD defines solids in terms of two-dimensional boundary representations, even the simplest three-dimensional NURBS function is not found in CAD models. Some of these basis functions allow local refinement of the computational mesh and relatively unstructured meshes in comparison to NURBS. This is a very active area of research in the mathematics and engineering communities.

Isogeometric analysis (IGA), which uses the same geometry from CAD (computer-aided design) for numerical analysis, has been studied more and more in the past few years. The continuous development of IGA with shell and solid element has been added to LS-DYNA. Many of the standard analysis capabilities in LS-DYNA are now available for IGA such as explicit and implicit analysis. In this paper, we will provide updates on IGA: dynamics analysis using IGA solid, the implementation of user defined material including anisotropic material modeling and support for unstructured Spline capabilities through their Bézier extractions.

A physically based, finite deformation, rate and temperature dependent theory and model have been developed to simulate the deformation and failure of FRP composite materials and structures. Failure modes include: inter alia, fiber crushing and kinking as occurs during extreme compressive loading; fiber fracture as occurs in for example fragmentation; interlaminar shear as occurs at elevated temperatures and that leads to kinking; debonding and delamination including the coupling with laminate kinking; and debonding as occurs in cored FRP panels. The theory/model is capable of describing quasi-static (including creep) as occurs at elevated temperatures, and dynamic deformation and failure as occurs during shock, blast or impact. The model is implemented within LS DYNA and specific example simulations are described that illustrate the theory/model capabilities. In Part I, fragmentation is not covered in detail. Fiber fracture and fragmentation are to be covered to detail with specific examples in Part II.

In the present communication, we introduce a class of material models primarily aimed at simulating the elastic and viscous behavior of biological soft tissues in LS-DYNA®. The constitutive law is modular and each module may comprise of different models. Consequently, the analyst may easily change models in a module and also include additional modules to account for more complex material behaviors within the same keyword. In its most general form, the material is considered nearly incompressible, anisotropic, and hyperelastic with the passive behavior defined using a decoupled strain energy function. The contractile and viscoelastic behavior of the tissue may be considered by invoking extra modules. The models are verified using a wide range of recently published results and show excellent agreement.

We explore the role of the microstructure of AISI 4340 steel with different values of microhardness (as-received and hardened) on shear band nucleation and post-critical behavior with a well-developed pattern of shear bands. Critical and post-critical behavior was investigated with the help of the explosively-driven Thick-Walled Cylinder technique, which allowed comparative study of the material deformation at similar strain rates and final strains. It was observed that the collapsed as-received AISI 4340 samples were resilient to shear localization and propagation and mainly preserved its cylindrical geometry at the investigated small and larger global strains. The hardened specimens at the similar final global strains exhibited a dramatically different behavior. At small strains, some well-developed shear bands were observed. Larger global strains were accommodated mostly by growth of the initially generated shear bands, resulting in the complete loss of cylindrical symmetry. Numerical simulations reproduced the main features observed in the experiments and the dramatic difference in behavior of as-received and hardened AISI 4340 steel. It is shown that the initial number of defects introduced in calculations as well as the material constants used for the material model have a direct effect on the pattern of shear bands.

Explosively driven fragmentation mechanisms of Al-W particulate composite rings were investigated. The effect of mesostructures (particulate Al and W, particulate Al and W fibers) and bonding between Al particles (processing via cold isostatic and cold isostatic + hot isostatic pressing) were determined. The kinematics of the expansion process was monitored using Photon Doppler Velocimetry measurements of the velocity of the outer surface of the rings. Numerical simulations of the expansion velocity of rings were in agreement with experimental data. Agglomerated fragments larger than sizes of initial Al particles were observed in experiments. The characteristic size of these agglomerates is most likely determined by the spacing between W inclusions. The simulations show that the dynamically expanded rings had clusters of particulates between shear bands (developing into macrocracks), which expand without significant plastic deformation, generating agglomerated fragments with sizes larger than initial Al particles, as observed in experiments. It was also demonstrated that debris has a measurable fraction of particles with sizes below the original particle sizes. The mesostructure of the fragments demonstrated that Al particles were heavily deformed within the regions having locally high strain plastic flow, which may result in fragments sizes below initial Al particle diameter. Simulations agree with experiments in that Al particles between neighboring W particles/fibers are heavily plastically deformed in comparison with Al particles away from W inclusions. Simulations also demonstrated that increasing initial porosity increases the plastic straining of Al particles between W particles/fibers. Thus, initial porosity may cause an increase in temperature of the Al fragments and cracking their surface oxide layers, therefore increasing the chance of subsequent rapid oxidation in air.

In this two-part paper we begin the development of a new class of methods for modeling fluid–structure interaction (FSI) phenomena for air blast. We aim to develop accurate, robust, and practical computational methodology, which is capable of modeling the dynamics of air blast coupled with the structure response, where the latter involves large, inelastic deformations and disintegration into fragments. An immersed approach is adopted, which leads to an a-priori monolithic FSI formulation with intrinsic contact detection between solid objects, and without formal restrictions on the solid motions. In Part I of this paper, the core air-blast FSI methodology suitable for a variety of discretizations is presented and tested using standard finite elements. Part II of this paper focuses on a particular instantiation of the proposed framework, which couples isogeometric analysis (IGA) based on non-uniform rational B-splines and a reproducing-kernel particle method (RKPM), which is a Meshfree technique. The combination of IGA and RKPM is felt to be particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of both discretizations, and relative simplicity of RKPM in handling fragmentation scenarios. A collection of mostly 2D numerical examples is presented in each of the parts to illustrate the good performance of the proposed air-blast FSI framework.

We investigated numerically the nature of high amplitude stress waves generated by plate impact on Al/W viscoplastic laminates with different cell sizes. Weakly attenuating localized travelling waves, closely resembling solitary waves, quickly form near the impacted surface at relatively short duration of incoming pulse. They have properties similar to solitary solutions of the Korteweg-de Vries equation with the dispersive and nonlinear parameters connected to laminate properties. The peak temperature in the localized stress wave is dramatically different than the temperature corresponding to the shock wave at the same pressure, reflecting different paths of loading. Increase of the duration of the incoming pulse results in a train of solitary pulses or in oscillatory stationary shock like stress waves. The leading front of the shock like stress wave is closely described by the rising part of solitary stress wave.

The shock waves generated by a plate impact are numerically investigated in Al-W laminates with different mesostructures. The main characteristic time scales (and the corresponding spatial scales) related to the formation of the stationary shock are identified: the duration (width) of the leading front, the time (distance) from the impact required to establish a stationary profile, and the shock front width, identified as a time span (distance) from the initial state to the final quasiequilibrium state. It is demonstrated that the width of the leading front and the maximum strain rates are determined by the dispersive and the nonlinear parameters of the laminate and not by the dissipation, as is the case for uniform solids. The characteristic spatial scale of the leading front is related to the spatial scale observed on solitarylike waves, which are satisfactorily described by the Korteweg-de Vries (KdV) approximation, as well as the speed of the wave and the ratio of maximum to final strain. The dissipation affects the width of the transition distance (shock front width) where multiple loading-unloading cycles bring the laminate into the final quasiequilibrium state. This spatial scale is of the same order of magnitude as the distance to form stationary shock wave. The period of fast decaying oscillations is well described by the KdV approach and scales linearly with the cell size. The rate of the decay of the oscillations in the numerical calculations does not scale with the square of the cell size as expected from the dissipative KdV approach that assumes a constant viscosity. This is due to the different mechanisms of dissipation in high-amplitude compression pulses.

In the last decade numerous research has been done in the area of Isogeometric Analysis (IGA). The intention of this rather new technology is the wish to have a stronger integration of Computer Aided Design (CAD) and Finite Element Analysis (FEA). Its basic idea is to use the same mathematical description for the geometry as well in the design process (CAD) as in the later analysis (FEA). One of the wide spread geometry description methodology in CAD-systems is the usage of Non-Uniform Rational B-Splines (NURBS) as basis functions. NURBS-based finite elements have been proven to be very well suited for computational analysis leading to qualitatively more accurate results in comparison with standard finite elements based on Lagrange polynomials. Therefore continuous development of Isogeometric Analysis has been added to LS-DYNA in the last years. The present contribution will give an overview about the current possibilities in LS-DYNA to use NURBS-based CAD-geometry description for numerical simulation and outline future plans for their enhancements.

In this paper, we present an accurate and efficient isogeometric topology optimization method that integrates the non-uniform rational B-splines based isogeometric analysis and the parameterized level set method for minimal compliance problems. The same NURBS basis functions are used to parameterize the level set function and evaluate the objective function, and therefore the design variables are associated with the control points. The coefficient matrix that parameterizes the level set function is set up by a collocation method that uses the Greville abscissae. The zero-level set boundary is obtained from the interpolation points corresponding to the vertices of the knot spans. Numerical examples demonstrate the validity and efficiency of the proposed method.

Effective perforating gun firing constitutes a key process toward achieving safe and productive wells in hydrocarbon reservoir exploitation. Within this field, the present work pursues a novel modeling approach with two main aims: investigating the physical phenomena involved in the firing of a perforating gun in air at atmospheric pressure, by identifying all key factors stressing the gun carrier; assessing perforating gun performance dependence and optimization on the scallop geometry, in terms of the piercing capability of the carrier outcoming jets and of the gun carrier resistance. This is investigated through challenging 3D Eulerian FEM simulations, displaying coherence with key experimental evidences. The obtained results provide crucial information toward the understanding of the physical phenomena involved in gun firing and of the scallop geometry implications on gun performance. The present simulations set as an advanced tool for perforating gun design and optimization, in comparison with other methodologies like Lagrangian simulations or analytical modeling.