Inverted distribution of ductile deformation in the relatively “dry” middle crust across the Woodroffe Thrust, central Australia

Thrust fault systems typically distribute shear strain preferentially into the hanging wall rather than the footwall. The Woodroffe Thrust in the Musgrave Block of central Australia is a regional-scale example that does not fit this model. It developed due to intracontinental shortening during the Petermann Orogeny (ca. 560–520 Ma) and is interpreted to be at least 600 km long in its E–W strike direction, with an approximate top-to-north minimum displacement of 60–100 km. The associated mylonite zone is most broadly developed in the footwall. The immediate hanging wall was only marginally involved in the mylonitization process, as can be demonstrated from the contrasting thorium signatures of mylonites derived from the upper amphibolite facies footwall and the granulite facies hanging wall protoliths. Thermal weakening cannot account for such an inverse deformation gradient, as syn-deformational P–T estimates for the Petermann Orogeny in the hanging wall and footwall from the same locality are very similar. The distribution of pseudotachylytes, which acted as preferred nucleation sites for shear deformation, also cannot provide an explanation, since these fault rocks are especially prevalent in the immediate hanging wall. The most likely reason for the inverted deformation gradient across the Woodroffe Thrust is water-assisted weakening due to the increased, but still limited, presence of aqueous fluids in the footwall. We also establish a qualitative increase in the abundance of fluids in the footwall along an approx. 60 km long section in the direction of thrusting, together with a slight decrease in the temperature of mylonitization (ca. 100 °C). These changes in ambient conditions are accompanied by a 6-fold decrease in thickness (from ca. 600 to 100 m) of the Woodroffe Thrust mylonitic zone.

Inverted distribution of ductile deformation in the relatively “dry” middle crust across the Woodroffe Thrust, central Australia

Thrust fault systems typically distribute shear strain preferentially into the hanging wall rather than the footwall. In this paper, we present a regional-scale example that does not fit this model. The Woodroffe Thrust developed due to intracontinental shortening during the Petermann Orogeny (ca. 560–520 Ma) in central Australia. It is interpreted to be at least 600 km long in its general E-W strike direction, with an approximate top-to-north minimum relative displacement of 60–100 km. The associated mylonite zone is most broadly developed in the footwall. The immediate hanging wall was only marginally involved in mylonitization, as can be demonstrated from the contrasting thorium signatures of the upper amphibolite facies footwall and the granulite facies hanging wall protoliths. Thermal weakening cannot account for such an inverse deformation gradient, as syn-deformational P-T estimates for the Petermann Orogeny in the hanging wall and footwall from the same locality are very similar. The distribution of pseudotachylytes, which act as preferred nucleation sites for shear deformation, also cannot provide an explanation, since these are prevalent in the immediate hanging wall. The most likely reason for the inverted deformation gradient across the Woodroffe Thrust is water-assisted weakening due to the increased, but still limited, presence of aqueous fluids in the footwall. On the contrary, the presence or absence of aqueous fluids does not appear to be linked to the regional variation in mylonite thickness, which generally increases with increasing metamorphic grade.

A Cartesian Scheme for Compressible Multimaterial Hyperelastic Models with Plasticity

We describe a numerical model to simulate the non-linear elasto-plastic dynamics of compressible materials. The model is fully Eulerian and it is discretized on a fixed Cartesian mesh. The hyperelastic constitutive law considered is neohookean and the plasticity model is based on a multiplicative decomposition of the inverse deformation tensor. The model is thermodynamically consistent and it is shown to be stable in the sense that the norm of the deviatoric stress tensor beyond yield is non increasing. The multimaterial integration scheme is based on a simple numerical flux function that keeps the interfaces sharp. Numerical illustrations in one to three space dimensions of high-speed multimaterial impacts in air are presented.

The inverse deformation problem

Given a commutative complete local noetherian ring $A$ with finite residue field $\boldsymbol{k}$, we show that there is a topologically finitely generated profinite group $\unicode[STIX]{x1D6E4}$ and an absolutely irreducible continuous representation $\overline{\unicode[STIX]{x1D70C}}:\unicode[STIX]{x1D6E4}\rightarrow \text{GL}_{n}(\boldsymbol{k})$ such that $A$ is a universal deformation ring for $\unicode[STIX]{x1D6E4},\overline{\unicode[STIX]{x1D70C}}$.

Inverse-Motion-Based Modeling for Electromechanics With Application to Electrostrictive Polyurethane

In this work the inverse motion problem for electroelasticity is considered. For given loads and boundary conditions, and a given deformed shape of the electro elastic body, the initially unknown undeformed configuration is sought. The boundary-value problem for the inverse motion is obtained by reparameterization of the forward motion equations in terms of the inverse deformation map. In order to account for incompressibility, a mixed formulation is adopted. The finite element method is used to calculate the undeformed configuration for an electro-active gripper application.

Towards Inverse Form Finding Methods for a Deep Drawing Steel DC04

A challenge in the design of functional parts in metal forming processes is the determination of the initial, undeformed shape such that under a given load a part will obtain the desired deformed shape. An inverse mechanical or a shape optimization formulation might be used to solve this problem, which is inverse to the standard kinematic analysis in which the undeformed shape is known and the deformed shape unknown. The objective of the inverse mechanical formulation aims in the inverse deformation map that determines the (undeformed) material configuration, where the spatial (deformed) configuration and the mechanical loads are given. The shape optimization formulation predicts the initial shape in the sense of an inverse problem via successive iterations of the direct problem. In this paper, both methods are presented using a formulation in the logarithmic strain space. An update of the reference configuration of the sheet of metal during the optimization process is proposed in order to avoid mesh distortions. A first example showed the results obtained with both methods in isotropic hyperelasticity. A second example illustrated a simplified deep drawing computed with the shape optimization formulation in isotropic elastoplasticity. From the undeformed shapes obtained with both methods the deformed shapes are acquired with the direct mechanical formulation. Compared to the target deformed shape a minor difference in node coordinates is found. The computation time is lower with the inverse mechanical formulation in hyperelasticity. The update of the reference configuration in the shape optimization formulation allowed to avoid mesh distortions but increased the computational costs.