Evolutionary numerical methods applied to minimum weight structural design and cardiac mechanics

This paper deals with the identification of material parameters in constitutive models of cyclic plasticity for sheet metals using the bending moment vs. curvature diagrams obtained by cyclic bending tests. After a brief discussion on the identification for some simple plasticity models, a new identification method based on the iterative multipoint approximation concept is presented for complicated elastic-plastic consititutive models incorporating many numbers of material parameters. As an example, eight material parameters in Chaboche-Rosselier's model were identified by this method. This approach has been verified by comparing the simulated stress-strain curve using the constitutive model incorporating the identified material parameters with the experimental curve determined by uniaxial tension.

Dynamic plastic response of a circular plate based on unified strength theory

This paper proposes a topology optimization method for a dielectric optical cloak that provides results that are perfectly free from intermediate materials, based on a level set boundary expression and the Finite Element Method. The finite element mesh is re-generated to fit the iso-surface of the level set function at every iterative step, to remove intermediate materials, so that the obtained optimal structure consists of only two materials, the dielectric material and air. First, the level set-based topology optimization is formulated and a topology optimization algorithm is proposed for the exact level set approach. Next, design requirements for the dielectric optimal cloak device are clarified and an objective functional for the design is formulated. The proposed method is then applied to a simple numerical problem to illustrate its effectiveness.

3D printed patient-specific fixation plates for the treatment of slipped capital femoral epiphysis: Topology optimization vs. conventional design

The production of complex functional structures becomes possible using Additive Manufacturing (AM) technology. Topology optimization allows to obtain lightweight and high-performance parts. In this study, the combining of topology optimization with additive manufacturing is proposed. This combination is mainly motivated by two principal reasons. Firstly, topology optimization generates complex structures that cannot be achieved by conventional processes. Secondly, a great flexibility in part design is provided by additive manufacturing. Indeed, an automated algorithm for the topology optimization of structures obtained by additive manufacturing is presented. The proposed methodology is based on the generation of the geometry and the mesh of the studied structure using ANSYS software that uses finite element analysis (FEA). Then, the topology optimization algorithm is implemented in MATLAB. The developed algorithm is illustrated by a numerical example involving the minimization of the compliance of 3D beam structure.

ABSTRACT: The objective of this paper is to develop a two-dimensional Cohesive Element Model (CZM) coupled with a Continuum Damage Mechanics (CDM) model. The novel cohesive element model allows expressing the separation criterion in terms of the damage tensor used in the CDM model implemented in the neighboring volume elements. Above a critical damage value, debonding triggers. The residual tensile and shearing strength of the CZM follow a linear softening law. The proposed model was calibrated against published triaxial compression tests conducted on shale. Single-cohesive zone tests highlight that the proposed approach allows simulation of hardening during damage propagation followed by softening and failure. The model predicts different strengths in tension and compression and different stiffnesses and strengths for different confinements. A boundary-value problem was solved by using a mesh with embedded cohesive zones at all interfaces. It is shown that the 2D model can predict realistic stress/strain curves, stress and strain fields, and fracture patterns for biaxial compression tests. The advantage of the proposed approach is that it can be used to simulate diffuse damage followed by localized fracture with a smooth transfer of field variables between the finite and cohesive elements. 1 INTRODUCTION Simulating fracture propagation from the inception of microscopic cracks to the localization of macroscopic fractures remains a challenge. To date, finite element modeling approaches based on Continuum Damage Mechanics (CDM) and Cohesive Zone Models (CZM) emerge as the most widely used approaches. The goal of this study is to couple both, in order to take advantage of the benefits that each technique can bring. In CDM, sets micro-cracks are represented by a damage tensor, which is modeled as an internal variable within the framework of thermodynamic irreversible processes. Stiffness and strength decrease as damage accumulates. CDM models can be formulated based on phenomenological principles (Xu and Arson, 2014) or micromechanics principles (Jin and Arson, 2017). Exhaustive reviews of damage rock mechanics are available in (Arson and Gatmiri, 2008; Arson, 2020).

The estimation of material parameters in constitutive models for soft biological materials such as myocardium is a challenging problem due to the complex behavior of the material. Here we present a systematic scheme to solve the inverse problem of estimating material parameters from experimentally observed deformation. This scheme couples a genetic algorithm with nonlinear finite element analysis. The approach is very general and can be applied to a wide range of inverse boundary value problems. Effectiveness of this scheme is demonstrated through examples involving two-dimensional and three-dimensional hyperelastic material models. Finally, a problem involving variation of material parameter through the ventricular wall is investigated.

An integrated method of topological optimization and path design for 3D concrete printing

This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself. Concerning the first topic, we investigate different means to improve the robustness of density-based numerical models including geometrical nonlinearities. The conventional approach (scaling the local material properties) can result in convergence problems due to excessive deformation in low-stiffness finite elements. To avoid excessive deformation, we combine the element connectivity parameterization method (adapting the connectivity between finite elements) with level-set-based topology optimization. Furthermore, we achieve greater robustness of analysis method using a second and improved approach called element deformation scaling. This approach eliminates the need for solving internal equilibrium equations (needed for the element connectivity parameterization method) via an explicit relation between the local internal and global external displacement field. The second focus of this thesis is on the optimization process of level-set-based topology optimization, and in particular its numerical consistency. We observe that signed-distance reinitialization of the level-set function affects the shape of a design in the optimization process. To minimize this effect, we propose a discrete level-set method that is based on an approximate Heaviside function and focusing on the implementation. Furthermore, we also propose a level-set-based topology optimization method using an exact Heaviside function and mathematical programming that effectively eliminates the need for reinitialization. We demonstrate that our density-based level-set method is closely related to conventional density-based topology optimization methods, while offering the advantage of more control over the geometrical complexity. On the other hand, we confirm that the dependence of the final result on the initial design which remains one of the big challenges for level-set-based topology optimization. The potential of the proposed level-set method is shown by applying it on problems with stress constraints and geometrical nonlinearities and performing manufacturing tolerant topology optimization. Finally, this thesis offers a review of level-set methods for structural topology optimization to identify and discuss the different approaches that are available in literature. We can distinguish between level-set methods by examination of their design parameterization, sensitivities, update procedures and regularization techniques. A level-set-based design parameterization offers the advantage of a crisp distinction between subdomains. For this reason, X-FEM approaches and conforming discretizations are an interesting option to retain the crisp nature of the level-set-based description of the design. Many level-set methods are combined with density-based numerical models and are, therefore, closely related to conventional density-based topology optimization methods. In particular, recently proposed projection methods have much in common with a level-set-based design description. The results of level-set-based TO methods often rely heavily on regularization techniques that introduce inconsistencies in the optimization process. Numerical consistency does not necessarily lead to the best search direction, but is essential to find a Karush-Kuhn-Tucker point of the discretized optimization problem.

Topology optimization is the procedure of determining the connectivity, shape and location of voids inside a given design domain. This chapter proposes a quantum-inspired evolutionary algorithm (QEA) for structural topology optimization. It reviews the formulation of the continuum structural topology optimization model and the characteristics of quantum computing. The chapter also proposes the detailed implementation of a QEA-based topology optimization. It discusses two issues: the density-based continuum structural topology optimization formulation and the characteristics of quantum computing, which may be conducive to reducing the computational expense of topology optimization. The entire theoretical procedure of quantum-inspired topology optimization, which mainly combines FEM analysis, design sensitivity solution and quantum-inspired search, is accomplished for continuum structures. As the experimental implementation of quantum computation needs initialization, coherent manipulation, control and read of the fragile quantum system, practically building quantum computers has proved extremely difficult.

This paper deals with topology optimization seen from an industrial and a manufacturing point of view. What the industrial users see as key issues when implementing topology optimization are frequently not the topics that the academic environments consider when implementing topology optimization. One of the key issues is that topology optimization should be integrated into an existing CAD and CAE environment (example of FE-solvers: ABAQUS, ANSYS, CATOPO, NX Nastran, MSc Nastran, MSc Marc and Permas). Here, it is of importance to note that the models analyzed in the industrial CAE environments often consist of many finite elements (can be more than 2 million elements) and different types of elements (continuum, beam, membrane, shell, bar and rigid elements) which all can be employed in the same model. Furthermore, symmetry and manufacturing constraints are important for ensuring that the results of the topology optimized are manufacturable. Several examples will be given of how structural topology optimization can be used as an add-on module in existing CAE environments However, from an academic point of view an add-on module including topology optimization for commercial FE-solvers is also of interest because the latest finite element and solver technology can be applied in the modeling for the topology optimization. Furthermore, the aim is also to show where the industry is today and which demands exist for the future. The results reported here are based upon the work done by FE-Design and their industrial partners using the topology optimization module (TOSCA.topo) and smooth module (TOSCA.smooth) of the program TOSCA.

In the laser powder bed fusion process (PBF-LB), components are built up incrementally by locally melting metal powder with a laser beam. This process leads to inhomogeneous material properties of the manufactured components. By integrating these specific material properties into a topology optimization algorithm, product developers can be supported in the early phases of the product development process, such as design finding. For this purpose, a topology optimization method was developed, which takes the inhomogeneous material properties of components fabricated in the PBF-LB process into account. The complex pore architecture in PBF-LB components was studied with micro-computed tomography (µCT). Thereby, three characteristic regions of different porosity were identified and analyzed. The effective stiffness in each of these regions was determined by means of resonant ultrasonic spectroscopy (RUS) as well as finite element analysis. Afterward, the effective stiffness is iteratively considered in the developed topology optimization method. The resulting design proposals of two optimization cases were analyzed and compared to design proposals derived from a standard topology optimization. To evaluate the developed topology optimization method, the derived design proposals were additionally manufactured in the PBF-LB process, and the characteristic pore architecture was analyzed by means of µCT.

This paper presents a topology optimization method of compliant grippers considering stress constraints. The proportional topology optimization (PTO) algorithm is applied to the design of compliant grippers, and it is improved by introducing weight factors into the objective function and adding stress conditions on the basis of constraints. In the current gradient modeling of topology optimization, the global maximum stress is measured by P-norm function, and its sensitivity analysis of stress constraints is derived by adjoint equations. It is worth noting that more rigorous gradient calculations are employed in stress problems and their computation brings an additional computational burden. By contrast, the non-gradient method using PTO algorithm allocates design variables to the element proportionally according to the values of stress. It can eliminate difficulties in the analytical derivation and calculation of gradient, and improve the calculation efficiency. Subsequently, performances of compliant grippers generated by these two methods are compared through finite element analysis. Finally, the optimized compliant gripper prototype is manufactured by three-dimensional (3D) printing using flexible thermoplastic urethane. Experimental results indicate that the non-gradient method is effective, and the optimized compliant gripper has excellent characteristics of low stress and high output performance.

A robust topological derivative-based multi-material optimization approach: Optimality condition and computational algorithm

Adaptive volume constraint algorithm for stress limit-based topology optimization