@Article{icces.2023.09893,
AUTHOR = {Pai Liu, Weida Wu, Yangjun Luo, Yifan Zhang},
TITLE = {Topological	Design	of	Negative	Poisson’s	Ratio	Material	Microstructure	 Under	Large	Deformation	with	a Gradient-Free	Method},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {25},
YEAR = {2023},
NUMBER = {2},
PAGES = {1--1},
URL = {http://www.techscience.com/icces/v25n2/53823},
ISSN = {1933-2815},
ABSTRACT = {Lightweight	 metamaterials	 with	 negative	 Poisson’s	 ratios	 (NPRs)	 have	 great	 potential	 for	 controlling	
deformation,	absorbing	energy,	etc.	The	topology	optimization	[1]	technique	is	an	effective	way	to	design	
metamaterials.	 However,	 as	 studied	 in	 [2],	 the	 NPR	 metamaterial	 configuration	 obtained	 under	 small	
deformation	assumption	may	not	maintain	the	desired	Poisson’s	ratio	under	relatively	large	deformation	
conditions.	This	paper	focuses	on	the	large-deformation	NPR	metamaterial	design	based	on	a	gradient-free	
topology	 optimization	 method,	 i.e.	 the	 material-field	 series	 expansion	 (MFSE)	 method	 [3].	 The	
metamaterial’s	performance	is	evaluated	using	the	finite	element	method,	taking	into	account	the	geometry	
nonlinearity.	 By	 considering	 the	 spatial	 correlation	 of	 the	 microstructural	 topology,	 the	 MFSE	 method	
significantly	reduces	the	number	of	design	variables.	An	optimization	formulation	is	adopted	to	minimize	
the	error	between	the	desired	and	the	current	metamaterial	performances,	taking	advantage	of	the	MFSE	
topological	parameterization.	A	two-step	gradient-free	optimization	solution	strategy	based	on	the	Kriging	
surrogate	 model	 is	 suggested.	 Several	 target	 NPRs	 design	 problems	 are	 considered	 in	 the	 numerical	
examples	 and	 the	 optimized	 metamaterial	 performances	 are	 checked	 with	 conformal	 mesh	 in	 the	
commercial	software.	The	numerical	calculation	results	show	that	this	method	can	generate	metamaterials	
that	can	maintain	the	required	NPR	well	under	large	deformation	conditions.	This	method	does	not	require	
the	 non-trivial	 sensitivity	 derivation	in	 the	 current	 design	 scenario,	 and	 provides	 an	 alternative	 way	 to	
design	metamaterials	with	nonlinearities	for	engineers.},
DOI = {10.32604/icces.2023.09893}
}