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In this paper, we propose a numerical framework for optimizing the fracture resistance of quasi-brittle composites through a modification of the topology of the inclusion phase. The phase field method to fracturing is adopted within a regularized description of discontinuities, allowing to take into account cracking in regular meshes, which is highly advantageous for topology optimization purpose. Extended bi-directional evolutionary structural optimization (BESO) method is employed and formulated to find the optimal distribution of inclusion phase, given a target volume fraction of inclusion and seeking a maximal fracture resistance. A computationally efficient adjoint sensitivity formulation is derived to account for the whole fracturing process, involving crack initiation, propagation and complete failure of the specimen. The effectiveness of developed framework is illustrated through a series of 2D and 3D benchmark tests. [ABSTRACT FROM AUTHOR]

A topology optimization framework for improving the dynamic fracture resistance of structures is proposed. The phase field method for fracture is combined with Solid Isotropic Material with Penalization (SIMP) topology optimization. The topology optimization problem is defined as minimizing the fracture energy during the whole dynamic loading process, from initiation of cracks to full failure of the structure, under volume and compliance constraints. Semi analytical expressions of sensitivities in a dynamic context are provided to solve the topology optimization problem efficiently. Numerical examples involving structures subjected to impact loading are investigated. It is shown that the present framework allows a significant reduction of the fracture energy as compared to designs obtained by static optimization. [ABSTRACT FROM AUTHOR]

A phase field model for anisotropic, elastoplastic fracture model in layered structures obtained by 3D printing processes is proposed. An extension of anisotropic phase field to elastoplasticity model is developed. The model is able to describe a transition from quasi-brittle to elastoplastic fracture behaviors depending on the angle of layers in the microstructure with respect to the external loading. Such feature is of special interest to describe the anisotropic fracture behavior in layered 3D printed materials. The present model introduces two phase field variables, one bulk fracture damage and one micro interfacial damage variables, describing two different micro damage mechanisms. Finally, we have proposed an original methodology to identify the macroscopic strain density as a function of the micro interfacial damage variable using numerical homogenization on Representative Volume Elements. Numerical investigations show that the present model is convergent with respect to mesh refinement, and allows to describe complex crack initiation and propagation in layered elastoplastic structures. An experimental comparison is provided to validate the use of such model for 3D printed polymer materials. [ABSTRACT FROM AUTHOR]

We propose a novel nonlinear topology optimization framework tailored for flexoelectric soft dielectrics undergoing large deformation. A numerical method based on Isogeometric analysis (IGA) is introduced to nonlinear soft dielectrics at finite strain, ensuring the C 1 -continuity for flexoelectric problems. We outline the process of consistent linearizations and IGA discretizations. Additionally, we introduce an innovative and efficient Strain Density Function (SDF) interpolation scheme for optimizing electromechanical coupling factors (ECFs). In this scheme, the interpolation of electromechanical and hyper-elastic energy terms is grounded in the SIMP model, while a linear material interpolation model is employed for the dielectric energy. Our numerical analysis highlights the remarkable performance of the proposed SDF interpolation scheme in nonlinear electromechanical optimization scenarios. An energy remedy scheme is applied to void regions to eliminate the instability of nonlinear optimization, effectively preventing distortion deformations in low-stiffness elements. Furthermore, we investigate the influence of size effect and larger deformation on the optimization of flexoelectric soft materials. The proposed topology optimization framework adeptly leverages the interplay between size effect and larger deformation, resulting in a notable improvement in ECFs within the optimized structures. Finally, the electromechanical coupling factors (ECFs) of the optimized structures in all the examined cases exhibit enhancements up to 9 times as compared to the reference guess designs. [ABSTRACT FROM AUTHOR]

A Coarse Mesh Condensation Multiscale Method (CMCM) is proposed to solve large heterogeneous linear structures without scale separation assumption. The technique aims to approximate the full field solution in heterogeneous structures by performing parallel calculations on subdomains. In the linear case, treated in this paper, direct linear relationships can be established between a reduced number of parameters describing Dirichlet boundary conditions on the subdomains boundaries and the degrees of freedom of a coarse mesh. The problem associated with the coarse mesh can be solved in one iteration and allows reconstructing the fine mesh solution in all subdomains. The accuracy of the method is analyzed through benchmarks involving subdomains crossed by the interfaces. Applications to large industrial finite element applications are presented, including one involving around 1.3 billion degrees of freedom. [ABSTRACT FROM AUTHOR]