Related papers: A Note on Optimal Design of Multiphase Elastic Str…
The paper establishes exact lower bound on the effective elastic energy of two-dimensional, three-material composite subjected to the homogeneous, anisotropic stress. It is assumed that the materials are mixed with given volume fractions…
The level-set method of topology optimization is used to design isotropic two-phase periodic multifunctional composites in three dimensions. One phase is stiff and insulating whereas the other is conductive and mechanically compliant. The…
Plasticity is inherent to many engineering materials such as metals. While it can degrade the load-carrying capacity of structures via material yielding, it can also protect structures through plastic energy dissipation. To fully harness…
We present a multi-phase design parameterization to obtain optimized heterogeneous lattice structures. The 3D domain is discretized into a cubical grid wherein each cube has eight distinct unit cell types or phases. When all phases are…
Long range order and symmetry in heterogeneous materials architected on crystal lattices lead to elastic and inelastic anisotropies and thus limit mechanical functionalities in particular crystallographic directions. Here, we present a…
The concept of concurrent material and structure optimization aims at alleviating the computational discovery of optimum microstructure configurations in multiphase hierarchical systems, whose macroscale behavior is governed by their…
A design problem of finding an optimally stiff membrane structure by selecting one-dimensional fiber reinforcements is formulated and solved. The membrane model is derived in a novel manner from a particular three-dimensional linear elastic…
Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer.…
Our goal is to unravel the mechanisms that lead to failure of a ductile two-phase material - that consists of a ductile soft phase and a relatively brittle hard phase. An idealized microstructural model is used to study damage propagation…
A general model is formulated for elasto-plastic materials undergoing linear kinematic hardening to describe microstructure evolution associated with phase transformations. Using infinitesimal strain theory, the model is based on…
The paper concerns the problem of minimization of the compliance of linear elastic structures made of an isotropic material. The bulk and shear moduli are the design variables, both viewed as non-negative fields on the design domain. The…
A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, is optimized. This allows us to handle topology changes and multiple materials. We prove continuity and…
Most of the commercially important alloys are multicomponent, producing multiphase microstructures as a result of processing. When the coexisting phases are elastically coherent, the elastic interactions between these phases play a major…
Composites are ideally suited to achieve desirable multifunctional effective properties since the best properties of different materials can be judiciously combined with designed microstructures. Here we establish cross-property relations…
We discuss a topology optimization problem for an elastoplastic medium. The distribution of material in a region is optimized with respect to a given target functional taking into account compliance. The incremental elastoplastic problem…
Inspired by recent experiments, we present a phase-field model of microphase separation in an elastomer swollen with a solvent. The imbalance between the molecular scale of demixing and the mesoscopic scale beyond which elasticity operates…
Emerging multi-material 3D printing techniques have paved the way for the rational design of metamaterials with not only complex geometries but also arbitrary distributions of multiple materials within those geometries. Varying the spatial…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…
Multi-phase material are frequently applied in a wide variety of products, as they posses a unique set of properties by combining two or more distinct phases at the level of the microstructure. Although the macroscopic stiffness and…