The elastoplastic field induced by a self-similar dynamic expansion of a pressurized spherical cavity is investigated for the compressible Mises solid. The governing system consists of two ordinary differential equations for two stress components where radial velocity and density are known functions of these stresses. Numerical illustrations of radial profiles of field variables are presented for several metals. We introduce a new solution based on expansion in powers of the nondimensionalized cavity expansion velocity, for both elastic/perfectly plastic response and strain-hardening behavior. A Bernoulli-type solution for the dynamic cavitation pressure is obtained from the second-order expansion along with a more accurate third-order solution. These solutions are mathematically closed and do not need any best fit procedure to numerical data, like previous solutions widely used in the literature. The simple solution for elastic/perfectly plastic materials reveals the effects of elastic-compressibility and yield stress on dynamic response. Also, an elegant procedure is suggested to include strain-hardening in the simple elastic/perfectly plastic solution. Numerical examples are presented to demonstrate the validity of the approximate solutions. Applying the present cavitation model to penetration problems reveals good agreement between analytical predictions and penetration depth tests.

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Accurate modeling of arterial response to physiological or pathological loads may shed light on the processes leading to initiation and progression of a number of vascular diseases, and may serve as a tool for prediction and diagnosis. In this study, a micro-structure based hyperelastic constitutive model is developed for passive media of porcine coronary arteries. The most general model contains twelve independent parameters representing the three-dimensional (3D) inner fibrous structure of the media, and includes the effects of residual stresses and osmotic swelling. Parameter estimation and model validation were based on mechanical data of porcine left anterior descending (LAD) media under radial inflation, axial extension, and twist tests. The results show that a reduced four parameter model is sufficient to reliably predict the passive mechanical properties. These parameters represent the stiffness and the helical orientation of each lamellae fibers, and the stiffness of the inter-lamellar struts interconnecting these lamellae. Other structural features, such as orientational distribution of helical fibers and anisotropy of the inter-lamellar network, as well as possible transmural distribution of structural features, were found to have little effect on the global media mechanical response. It is shown that the model provides good predictions of the LAD media twist response based on parameters estimated from only biaxial tests of inflation and extension. In addition, good predictive capabilities are demonstrated for the model behavior at high axial stretch ratio based on data of law stretches.

Dynamic steady-state spherical cavitation fields are examined with emphasis on material porosity at large strain. Cavity expansion is driven by constant internal pressure in presence of remote tension or compression. The plastic branch of constitutive relations is described by the Gurson model, with arbitrary strain hardening. The mathematical model is reduced to a system of four ordinary nonlinear coupled differential equations. Numerical examples show that a plastic shock wave builds up as expansion velocity approaches a critical value and jump conditions across the shock are accounted for. At critical levels of remote tension, quasi-static cavitation of all internal voids is induced before dynamic cavity expansion occurs.

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