PSI - Issue 77

Fang Liu et al. / Procedia Structural Integrity 77 (2026) 215–220 F. Liu/ Structural Integrity Procedia 00 (2026) 000–000

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2. Methodology 2.1. Geometry

In this study, the constitutive model was composed of four components: the transfemoral prosthetic socket, the residual limb, the residual femur and the base located at the bottom of the inner socket. The structure and dimensions of the above-knee prosthetic socket used in the model calculations were identical to those employed in Theodoros Marinopoulos's previous research (Marinopoulos et al., 2022). The residual limb and base were created from the internal surface of the socket using cut/merge Boolean operations in Abaqus . The length of the residual femur and the exact assembly position were confirmed based on clinical recommendations due to the lack of morphological information regarding the subject's lower limbs (Baum et al., 2008; Feldesman, 1992; Livingston, 1998). 2.2. Materials All model components were assumed homogeneous and isotropic, except for the femur. The socket and base were assigned a nonlinear elastic-plastic constitutive law, whereas the residual-limb soft tissues were represented using a first-order Ogden hyper-elastic formulation. Mesh discretization employed C3D4H elements (four-node linear tetrahedra with a hybrid constant-pressure degree of freedom). The final mesh comprised 55,354 elements, with global element sizes of 5 mm for the soft tissues and base and 8 mm for the socket. Interface mechanics were analysed using a two-factor parametric design. Three representative socket materials— PE, PETG, and HCFRPs—were selected to span a broad stiffness spectrum. In the ν study , the μ was fixed at 0.3 (Steer et al., 2021), with reference values of ν=0.46 for PE (Sundararaj & Subramaniyan, 2021), 0.389 for PETG (Kumar & Chhabra, 2023) and 0.35 for HCFRPs (Dolgikh et al., 2023); ν was then varied over 0.10, 0.20, 0.30, 0.40, 0.49. In the μ study, ν was held at its reference value and μ was varied in increments of 0.1 between 0.3 and 1. Variable inputs are summarised in Table 1, and constants in Table 2. Table 1 Parametric ranges of socket material ν and limb – socket interface μ used in simulations Parameter Values ν 0.1 0.2 0.3 0.4 0.49 / / / μ 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Table 2 Material properties and constitutive parameters assigned in the FE model Prosthetic socket and Base

Residual limb

Residual femur

PE

PETG

HCFRPs

Young ’ s modulus E (GPa)

0.86

2.9

260

Yield stress σ y (MPa)

14.51

31.74

570.50

Initial shear modulus μ 1 (MPa) Nonlinearity parameter α 1

0.15

Rigid body

5

Compressibility parameter D1 (MPa -1 )

4.3

Note: μ 1 governs the initial shear stiffness, α 1 controls the nonlinearity of the stress–strain response, and D 1 defines compressibility.

2.3. Boundary conditions All contact interfaces were defined using the general contact algorithm. An a xial load was applied at the foot reference plane, while rotational kinematics boundary conditions were prescribed at the knee joint center. Driving inputs were obtained from previously published data (Tang et al., 2015). The hip joint center was fully constrained (ENCASTRE condition). Coupling constraints were introduced to (i) connect the femur to the residual-limb soft tissues, (ii) couple the socket bottom to the knee joint center, and (iii) link the knee joint center to the foot reference plane. In addition, a tie constraint was applied between the base and the inner bottom surface of the socket, eliminating relative motion across this interface.