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, ie, 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.