Multiphase composites with extremal bulk modulus

By L. Gibiansky, Ole Sigmund. 2000

358 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/9ca5957666721305a41bb1b98ecd2b00015ded1d

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Multi-material topology optimization with multiple volume constraints: a general approach applied to ground structures with material nonlinearity (2017, methodology): “2b); or assign an individual volume constraint to each material (e.g., Sigmund and Torquato (1997), Gibiansky and Sigmund (2000), Wallin et al. (2015), Zhou and Wang (2007), Tavakoli and Mohseni (2014), Wang and Wang (2004), and Wang et al. (2005)), which may impose higher demands on computational…”
Material interpolation schemes for unified topology and multi-material optimization (2011, background): “Sigmund and Torquato (1997) and Gibiansky and Sigmund (2000). We propose to parametrize the topology question as follows.”
Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method (2014, methodology): “Using the homogenization method, the design of three-phase composites with extremal thermal expansion, piezoelectricity and bulk modulus have been considered in [16, 17], [18] and [19] respectively (cf.”
Current and future trends in topology optimization for additive manufacturing (2018, methodology): “Sigmund and his colleagues (Sigmund 1997; Gibiansky and Sigmund 2000) applied multi-material topology optimization to design extreme material properties, and Bendsoe and Sigmund (Bendsøe and Sigmund 1999) summarized the rules of multi-material interpolation under the density-based framework.”
Design of manufacturable 3D extremal elastic microstructure (2014, methodology): “Gibiansky and Sigmund (2000) demonstrate the method on the design of three-phase elastic materials, and Sigmund and Torquato (1999) extend this to obtain designs with prescribed thermal and electrothermal properties.”
Topological design of structures and composite materials with multiobjectives (2007, methodology): “The topology optimization technique is applied to distribute single- (Sigmund, 1994b) or multi-phase (Gibiansky and Sigmund, 2000; Sigmund, 2000) candidate materials such that the desirable physical properties can be achieved.”
Analytical sensitivity in topology optimization for elastoplastic composites (2015, background): “…of fiber in a fiber-reinforced composite (Hammer 1999) (Stegmann and Lund 2005) and of determining the optimal layout of constituent materials (Gibiansky and Sigmund 2000) (Sigmund and Torquato 1997), but they mostly focus on a linear elastic regime, as do the studies focusing on a single…”
Discrete material optimization of general composite shell structures (2005, methodology): “This was also realized by Sigmund and co-workers who used the following formulation for two distinct materials (three phases) [17, 18]: C = (xe 0)p ([1 − (xe 1)p]C1 + (xe 1)p C2) , 0 xi 1 (8)”