# Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition

@article{Zhou2006MultimaterialST, title={Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition}, author={Shiwei Zhou and Michael Yu Wang}, journal={Structural and Multidisciplinary Optimization}, year={2006}, volume={33}, pages={89-111} }

This paper describes a phase field method for the optimization of multimaterial structural topology with a generalized Cahn–Hilliard model. Similar to the well-known simple isotropic material with penalization method, the mass concentration of each material phase is considered as design variable. However, a variational approach is taken with the Cahn–Hilliard theory to define a thermodynamic model, taking into account of the bulk energy and interface energy of the phases and the elastic strain…

## 203 Citations

### Isogeometric Analysis for Topology Optimization with a Phase Field Model

- Mathematics
- 2012

We consider a phase field model for the formulation and solution of topology optimization problems in the minimum compliance case. In this model, the optimal topology is obtained as the steady state…

### Multi-phase field topology optimization of polycrystalline microstructure for maximizing heat conductivity

- Physics
- 2018

The present study proposes multi-scale topology optimization for polycrystalline microstructures applying a multi-phase field method. The objective function is to maximize the heat compliance of…

### A multi-resolution approach for multi-material topology optimization based on isogeometric analysis

- Computer Science
- 2017

### Topological design for mechanical metamaterials using a multiphase level set method

- Materials Science, Engineering
- 2016

A topological shape optimization method for design of mechanical metamaterials of thermoelastic micro-structured composites is developed, which integrates numerical homogenization method with a multi-phase level set method (MPLSM).

### A phase field model for stress‐based evolution of load‐bearing structures

- GeologyInternational Journal for Numerical Methods in Engineering
- 2018

We present a continuum‐type optimality algorithm for the evolution of load‐bearing solid structures with linear elastic material. The objective of our model is to generate structures with help of a…

### Multiscale concurrent topology optimization of structures and microscopic multi-phase materials for thermal conductivity

- Materials ScienceEngineering Computations
- 2019

PurposeThe optimal material microstructures in pure material design are no longer efficient or optimal when accounting macroscopic structure performance with specific boundary conditions. Therefore,…

### MULTI-PHASE STRUCTURAL OPTIMIZATION VIA A LEVEL SET METHOD ∗, ∗∗

- Computer Science
- 2014

It turns out that the optimization of a diffuse interface has its own interest in material science, for example to optimize functionally graded materials and various approaches based on Hadamard method of boundary variations are discussed.

### Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method

- Engineering
- 2014

### Design of buckling constrained multiphase material structures using continuum topology optimization

- EngineeringMeccanica
- 2019

A Jacobi active-phase algorithm is used to generate multiphase topology optimization and a modified material interpolation scheme solving spurious buckling modes problem which occurs in the multi-material topology optimized process is given and discussed.

## References

SHOWING 1-10 OF 42 REFERENCES

### The Cahn-Hilliard equation with elasticity-finite element approximation and qualitative studies

- Physics
- 2001

We consider the Cahn–Hilliard equation — a fourth–order, nonlinear parabolic diffusion equation describing phase separation of a binary alloy which is quenched below a critical temperature. The…

### Phase Field: A Variational Method for Structural Topology Optimization

- Computer Science
- 2004

A variational method to address the topology optimization problem – the phase transition method is presented and it is suggested that such a variational approach may represent a promising alternative to the widely-used material distribution model for the future development in topological optimization.

### Shape optimization by the homogenization method

- Mathematics
- 1997

Summary.In the context of shape optimization, we seek minimizers of the sum of the elastic compliance and of the weight of a solid structure under specified loading. This problem is known not to be…

### A diffuse interface model for microstructural evolution in elastically stressed solids

- Materials Science
- 1998

### A MultiPhase Field Concept: Numerical Simulations of Moving Phase Boundaries and Multiple Junctions

- MathematicsSIAM J. Appl. Math.
- 1999

We present numerical simulations which support the formal asymptotic analysis relating a multiorder parameter Allen--Cahn system to a multiphase interface problem with curvature-dependent evolution…

### Color level sets: a multi-phase method for structural topology optimization with multiple materials

- Mathematics
- 2004

### Nonlinear diffusions in topology optimization

- Materials Science
- 2004

Filtering has been a major technique used in homogenization-based methods for topology optimization of structures. It plays a key role in regularizing the basic problem into a well-behaved setting,…

### Material interpolation schemes in topology optimization

- Materials Science
- 1999

Summary In topology optimization of structures, materials and mechanisms, parametrization of geometry is often performed by a grey-scale density-like interpolation function. In this paper we analyze…