We describe a modeling methodology intended as a preliminary step in the identification of appropriate constitutive frameworks for the time-dependent response of biological tissues. The modeling approach comprises a customizable rheological network of viscous and elastic elements governed by user-defined 1D constitutive relationships. The model parameters are identified by iterative nonlinear optimization, minimizing the error between experimental and model-predicted structural (load-displacement) tissue response under a specific mode of deformation. We demonstrate the use of this methodology by determining the minimal rheological arrangement, constitutive relationships, and model parameters for the structural response of various soft tissues, including ex vivo perfused porcine liver in indentation, ex vivo porcine brain cortical tissue in indentation, and ex vivo human cervical tissue in unconfined compression. Our results indicate that the identified rheological configurations provide good agreement with experimental data, including multiple constant strain rate load/unload tests and stress relaxation tests. Our experience suggests that the described modeling framework is an efficient tool for exploring a wide array of constitutive relationships and rheological arrangements, which can subsequently serve as a basis for 3D constitutive model development and finite-element implementations. The proposed approach can also be employed as a self-contained tool to obtain simplified 1D phenomenological models of the structural response of biological tissue to single-axis manipulations for applications in haptic technologies.

The cervix plays a crucial role in maintaining a healthy pregnancy, acting as a mechanical barrier to hold the fetus in utero during gestation. Altered mechanical properties of the cervical tissue are suspected to play a critical role in spontaneous preterm birth. Both MRI and X-ray data in the literature indicate that cervical stroma contains regions of preferentially aligned collagen fibers along anatomical directions (circumferential/longitudinal/radial). In this study, a mechanical testing protocol is developed to investigate the large-strain response of cervical tissue in uniaxial tension and compression along its three orthogonal anatomical directions. The stress response of the tissue along the different orthogonal directions is captured using a minimal set of model parameters generated by fitting a one-dimensional time-dependent rheological model to the experimental data. Using model parameters, mechanical responses can be compared between samples from patients with different obstetric backgrounds, between samples from different anatomical sites, and between the different loading directions for a single specimen. The results presented in this study suggest that cervical tissue is mechanically anisotropic with a uniaxial response dependent on the direction of loading, the anatomical site of the specimen, and the obstetric history of the patient. We hypothesize that the directionality of the tissue mechanical response is primarily due to collagen orientation in the cervical stroma, and provides an interpretation of our mechanical findings consistent with the literature data on preferential collagen alignment.

Tooling cost is a major contributor to the total cost of small-lot production of sheet metal components. Within the framework of an academic/industrial/government partnership devoted to the development of a reconfigurable tool for stretch forming, we have implemented a Finite Element-based procedure to determine optimal die shape. In the reconfigurable forming tool (Hardt, D. E. et al., 1993, “A CAD Driven Flexible Forming System for Three-Dimensional Sheet Metal Parts,” Sheet Metal and Stamping Symp., Int. Congress and Exp., Detroit, MI, SAE Technical Paper Series 930282, pp. 69–76.), the die surface is created by the ends of an array of square pins, which can be individually repositioned by computer driven servo-mechanisms. An interpolating polymer layer is interposed between the part and the die surface to attain a smooth pressure distribution. The objective of the die design algorithm is to determine optimal positions for the pin array, which will result in the desired part shape. The proposed “spring-forward” method was originally developed for matched-die forming (Karafillis, A. P., and Boyce, M. C., 1992, “Tooling Design in Sheet Metal Forming using Springback Calculations,” Int. J. Mech. Sci., Vol. 34, pp. 113–131.; Karafillis, A. P., and Boyce, M. C., 1996, “Tooling And Binder Design for Sheet Metal Forming Processes Compensating Springback Error,” Int. J. Tools Manufac., Vol. 36, pp. 503–526.) and it is here extended and adapted to the reconfigurable tool geometry and stretch forming loading conditions. An essential prerequisite to the implementation of the die design procedure is the availability of an accurate FE model of the entire forming operation. The particular nature of the discrete die and issues related to the behavior of the interpolating layer introduce additional challenges. We have first simulated the process using a model that reproduces, as closely as possible, the actual geometry of the discrete tool. In order to optimize the delicate balance between model accuracy and computational requirements, we have then used the information gathered from the detailed analyses to develop an equivalent die model. An automated algorithm to construct the equivalent die model based on the discrete tool geometry (pin-positions) is integrated with the spring-forward method, to generate an iterative die design procedure that can be easily interfaced with the reconfiguring tool. The success of the proposed procedure in selecting an optimal die configuration is confirmed by comparison with experimental results.