A novel contact interaction formulation for voxel-based micro-finite-element models of bone

Voxel-based micro-finite-element (μFE) models are used extensively in bone mechanics research. A major disadvantage of voxel-based μFE models is that voxel surface jaggedness causes distortion of contact-induced stresses. Past efforts in resolving this problem have only been partially successful; i.e., mesh smoothing failed to preserve uniformity of the stiffness matrix, resulting in (excessively) larger solution times, whereas reducing contact to a bonded interface introduced spurious tensile stresses at the contact surface. This paper introduces a novel ‘smooth’ contact formulation that defines gap distances based on an artificial smooth surface representation while using the conventional penalty contact framework. Detailed analyses of a sphere under compression demonstrated that the smooth formulation predicts contact-induced stresses more accurately than the bonded contact formulation. When applied to a realistic bone contact problem, errors in the smooth contact result were under 2%, whereas errors in the bonded contact result were up to 42.2%. We conclude that the novel smooth contact formulation presents a memory-efficient method for contact problems in voxel-based μFE models. It presents the first method that allows modeling finite slip in large-scale voxel meshes common to high-resolution image-based models of bone while keeping the benefits of a fast and efficient voxel-based solution scheme.