Density Gradient IWP Lattice Structural Force-energy Synergistic Response

doi:10.3969/j.issn.1004-132X.2026.01.020

Abstract

Abstract:

TPMS lattice structures were a type of lightweight structure based on mathematical surfaces， which widely used in additive manufacturing. Among them， the I-wrapped package（IWP） demonstrated suitability for aerospace lightweighting due to the combination of low mass and high strength， while the tunable mechanics properties confered potential for medical applications. Therefore， a series of IWP lattice structures were designed with the same relative density， where the density gradients included linear， sine， and cosine function gradients. To reveal the optimization potential of gradient design， comparative analyses were conducted between uniform lattice structures and gradient structures. DLP technology was employed to produce lattice structures， and compression tests were performed to study mechanics response， energy absorption response， and stress distribution of each structure， ultimately selecting the best force-energy synergistic response structure and validating the reliability of the compression tests through finite element simulation. The results indicate that for the projection relationship curves of each gradient structure， the peak variation patterns are highly consistent with the monotonicity of the constructed gradient functions. The sine lattice（SIN） structure demonstrates excellent force-energy synergistic response， bearing high stress while stable energy absorption， with the energy absorbed per unit volume of the SIN structure increasing by 17.65% compared to uniform structures when reaching densification strain.

Key words: triply periodic minimal surface（TPMS）, density gradient, lattice structure, force-energy synergistic response, digital light processing（DLP） technology

摘要：

三周期极小曲面点阵结构是一种基于数学曲面的轻量化结构，广泛应用于增材制造领域，其中IWP（I-wrapped package）因轻质高强度适用于航天轻量化设计，且因力学性能可调控具有医用潜力。设计了一系列相对密度相同的IWP点阵结构，其中密度梯度包含线性、正弦函数和余弦函数梯度。为揭示梯度设计的优化潜力，对均匀点阵结构和梯度结构进行对比分析，利用数字光处理技术制备点阵结构，通过压缩试验对各结构的力学响应、吸能响应以及应力分布展开研究，优选出最佳的力-能协同响应结构，并通过有限元仿真验证压缩试验的可靠性。结果表明，对于各梯度结构的投影关系曲线，其峰值变化规律与构造的梯度函数的单调性高度一致；正弦点阵（SIN）结构具有优异的力-能协同响应特性，承载高应力的同时可协同进行稳定吸能，当达到致密化应变时，SIN结构每单位体积吸收的能量相较于均匀结构提高了17.65%。

关键词: 三周期极小曲面, 密度梯度, 点阵结构, 力-能协同响应, 数字光处理技术

CLC Number:

TB34

WANG Guangyang, JI Xiaogang, NIU Guofa, MEI Jianchi. Density Gradient IWP Lattice Structural Force-energy Synergistic Response[J]. China Mechanical Engineering, 2026, 37(1): 192-200.

王广阳, 纪小刚, 牛国法, 梅剑驰. 密度梯度的IWP点阵结构力-能协同响应[J]. 中国机械工程, 2026, 37(1): 192-200.

Figures/Tables 15

Fig.1 The relationship between parameter t and relative density ρ

Tab.1 Parameter settings

梯度类型

t₀

线性点阵

（LINEAR）

0.24

-

0.24z

-

余弦点阵

（COSINE）

-

0.64

1.1

-

4.023

-

0.64cos（1.1z）

-

4.023

正弦点阵

（SIN）

-

0.44

1.1

-

4.008

-

0.44sin（1.1z）

-

4.008

Tab.1 Parameter settings

梯度类型

t₀

线性点阵

（LINEAR）

0.24

-

0.24z

-

余弦点阵

（COSINE）

-

0.64

1.1

-

4.023

-

0.64cos（1.1z）

-

4.023

正弦点阵

（SIN）

-

0.44

1.1

-

4.008

-

0.44sin（1.1z）

-

4.008

Fig.2 Lattice structure design drawings and forming effects

Fig.3 Modeling process

Tab.2 Material parameters

密度/

（g·cm $- 3$ ）

弹性模量/

MPa

Tab.2 Material parameters

密度/

（g·cm $- 3$ ）

弹性模量/

MPa

泊松比

拉伸强度/ MPa

1.13

1.01

0.45

1.79

Fig.4 The stress contour of lattice structure and the relationship curve of stress value and projection position

Fig.5 Compression test method for lattice structure

Fig.6 Experimental stress-strain curves of different lattice structures

Ta.3 Mechanics response value of each structure

力学响应	UNIFORM	LINEAR	COSINE	SIN
弹性模量E/MPa	0.222	0.239	0.245	0.259
致密化应变ε_D	0.519	0.525	0.523	0.550
平台应力σ_pl/MPa	0.036	0.033	0.034	0.039
平均应力σ_avg /MPa	0.034	0.031	0.032	0.036
ULC值C_ULC	0.408	0.469	0.505	0.559

Ta.4 Gibson-Ashby coefficients for each structure

梯度类型	C₁（0.1~4.0）	α（1.4~2.0）
UNIFORM	4.341	2.137
LINEAR	4.674	2.111
COSINE	4.792	2.120
SIN	5.065	2.000

Fig.7 Energy absorption curve during compression

Fig.8 Energy absorption efficiency curve

Fig.9 Normalized energy absorption of lattice structures

Fig.10 Stress-strain curves from experiments and simulations of 4 types of lattice structures

Fig.11 Comparison of elastic modulus of simulations and experiments

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